Problem representation and mathematical problem solving of students of varying math ability.

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Krawec, Jennifer L

2014-01-01

The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD, n = 25), low-achieving students (LA, n = 30), and average-achieving students (AA, n = 29). The primary interest was to analyze the processes students use to translate and integrate problem information while solving problems. Paraphrasing, visual representation, and problem-solving accuracy were measured in eighth grade students using a researcher-modified version of the Mathematical Processing Instrument. Results indicated that both students with LD and LA students struggled with processing but that students with LD were significantly weaker than their LA peers in paraphrasing relevant information. Paraphrasing and visual representation accuracy each accounted for a statistically significant amount of variance in problem-solving accuracy. Finally, the effect of visual representation of relevant information on problem-solving accuracy was dependent on ability; specifically, for students with LD, generating accurate visual representations was more strongly related to problem-solving accuracy than for AA students. Implications for instruction for students with and without LD are discussed.

Improving mathematical problem solving skills through visual media

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Widodo, S. A.; Darhim; Ikhwanudin, T.

2018-01-01

The purpose of this article was to find out the enhancement of students’ mathematical problem solving by using visual learning media. The ability to solve mathematical problems is the ability possessed by students to solve problems encountered, one of the problem-solving model of Polya. This preliminary study was not to make a model, but it only took a conceptual approach by comparing the various literature of problem-solving skills by linking visual learning media. The results of the study indicated that the use of learning media had not been appropriated so that the ability to solve mathematical problems was not optimal. The inappropriateness of media use was due to the instructional media that was not adapted to the characteristics of the learners. Suggestions that can be given is the need to develop visual media to increase the ability to solve problems.

Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers

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Evans, Brian R.

2012-01-01

It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…

Mathematical problem solving ability of sport students in the statistical study

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Sari, E. F. P.; Zulkardi; Putri, R. I. I.

2017-12-01

This study aims to determine the problem-solving ability of sport students of PGRI Palembang semester V in the statistics course. Subjects in this study were sport students of PGRI Palembang semester V which amounted to 31 people. The research method used is quasi experiment type one case shoot study. Data collection techniques in this study use the test and data analysis used is quantitative descriptive statistics. The conclusion of this study shown that the mathematical problem solving ability of PGRI Palembang sport students of V semester in the statistical course is categorized well with the average of the final test score of 80.3.

Errors of Students Learning With React Strategy in Solving the Problems of Mathematical Representation Ability

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Delsika Pramata Sari

2017-06-01

Full Text Available The purpose of this study was to investigate the errors experienced by students learning with REACT strategy and traditional learning in solving problems of mathematical representation ability. This study used quasi experimental pattern with static-group comparison design. The subjects of this study were 47 eighth grade students of junior high school in Bandung consisting of two samples. The instrument used was a test to measure students' mathematical representation ability. The reliability coefficient about the mathematical representation ability was 0.56. The most prominent errors of mathematical representation ability of students learning with REACT strategy and traditional learning, was on indicator that solving problem involving arithmetic symbols (symbolic representation. In addition, errors were also experienced by many students with traditional learning on the indicator of making the image of a real world situation to clarify the problem and facilitate its completion (visual representation.

Does chess instruction improve mathematical problem-solving ability? Two experimental studies with an active control group.

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Sala, Giovanni; Gobet, Fernand

2017-12-01

It has been proposed that playing chess enables children to improve their ability in mathematics. These claims have been recently evaluated in a meta-analysis (Sala & Gobet, 2016, Educational Research Review, 18, 46-57), which indicated a significant effect in favor of the groups playing chess. However, the meta-analysis also showed that most of the reviewed studies used a poor experimental design (in particular, they lacked an active control group). We ran two experiments that used a three-group design including both an active and a passive control group, with a focus on mathematical ability. In the first experiment (N = 233), a group of third and fourth graders was taught chess for 25 hours and tested on mathematical problem-solving tasks. Participants also filled in a questionnaire assessing their meta-cognitive ability for mathematics problems. The group playing chess was compared to an active control group (playing checkers) and a passive control group. The three groups showed no statistically significant difference in mathematical problem-solving or metacognitive abilities in the posttest. The second experiment (N = 52) broadly used the same design, but the Oriental game of Go replaced checkers in the active control group. While the chess-treated group and the passive control group slightly outperformed the active control group with mathematical problem solving, the differences were not statistically significant. No differences were found with respect to metacognitive ability. These results suggest that the effects (if any) of chess instruction, when rigorously tested, are modest and that such interventions should not replace the traditional curriculum in mathematics.

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

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Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

Investigating a Proposed Problem Solving Theory in the Context of Mathematical Problem Solving: A Multi-Case Study

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Mills, Nadia Monrose

2015-01-01

The ability to succeed in Science, Technology, Engineering, and Mathematics (STEM) careers is contingent on a student's ability to engage in mathematical problem solving. As a result, there has been increased focus on students' ability to think critically by providing them more with problem solving experiences in the classroom. Much research has…

Pattern of mathematic representation ability in magnetic electricity problem

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Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.

2018-03-01

The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.

Exploring Primary Student’s Problem-Solving Ability by Doing Tasks Like PISA's Question

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Rita Novita

2012-07-01

Full Text Available Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term “problem solving” refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. In addition, the contextual problem that requires students to connect their mathematical knowledge in solving mathematical situational problem is believed to be an impact on the development students’ problem-solving ability. The tasks that have been developed by PISA meet both of these criteria. As stated by the NCTM, that problem-solving skill and ability should be developed to students when they were in primary school (K5-8, therefore, it is important to do an effort to guide students in developing problem-solving ability from primary school such as accustom students to do some mathematical solving-problem tasks. Thus, in this research we tried to investigate how to develop mathematical problem-solving tasks like PISA’s question that have potential effect toward students’ mathematical problem-solving abilities?. We used a  formative evaluation type of development research as an mean  to achieve this research goal. This type of research is conducted in two steps, namely preliminary stage and formative evaluation stage covering self evaluation, prototyping (expert reviews, one-to-one, and small group, and  field test. This research involve four primary schools in Palembang, there are SD Muhammadiyah 6 Palembang, MIN 1 & MIN 2 Palembang, and SDN 179 Palembang. The result of this research showed that the mathematical problem-solving tasks  that have been developed have potential effect in exploring mathematical problem-solving ability of the primary school students. It  is shown from their work in solving problem where all of the indicators of problem solving competency have emerged quite well category. In addition, based on interview

GeoGebra Assist Discovery Learning Model for Problem Solving Ability and Attitude toward Mathematics

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Murni, V.; Sariyasa, S.; Ardana, I. M.

2017-09-01

This study aims to describe the effet of GeoGebra utilization in the discovery learning model on mathematical problem solving ability and students’ attitude toward mathematics. This research was quasi experimental and post-test only control group design was used in this study. The population in this study was 181 of students. The sampling technique used was cluster random sampling, so the sample in this study was 120 students divided into 4 classes, 2 classes for the experimental class and 2 classes for the control class. Data were analyzed by using one way MANOVA. The results of data analysis showed that the utilization of GeoGebra in discovery learning can lead to solving problems and attitudes towards mathematics are better. This is because the presentation of problems using geogebra can assist students in identifying and solving problems and attracting students’ interest because geogebra provides an immediate response process to students. The results of the research are the utilization of geogebra in the discovery learning can be applied in learning and teaching wider subject matter, beside subject matter in this study.

Writing and mathematical problem solving in Grade 3

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Belinda Petersen

2017-06-01

Full Text Available This article looks at writing tasks as a methodology to support learners’ mathematical problemsolving strategies in the South African Foundation Phase context. It is a qualitative case study and explores the relation between the use of writing in mathematics and development of learners’ problem-solving strategies and conceptual understanding. The research was conducted in a suburban Foundation Phase school in Cape Town with a class of Grade 3 learners involved in a writing and mathematics intervention. Writing tasks were modelled to learners and implemented by them while they were engaged in mathematical problem solving. Data were gathered from a sample of eight learners of different abilities and included written work, interviews, field notes and audio recordings of ability group discussions. The results revealed an improvement in the strategies and explanations learners used when solving mathematical problems compared to before the writing tasks were implemented. Learners were able to reflect critically on their thinking through their written strategies and explanations. The writing tasks appeared to support learners in providing opportunities to construct and apply mathematical knowledge and skills in their development of problem-solving strategies.

Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem

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Ahmad, Herlina; Febryanti, Fatimah; Febryanti, Fatimah; Muthmainnah

2018-01-01

This research was conducted qualitative which was aim to describe metacognitive ability to understand and solve the problems of mathematics. The subject of the research was the first year students at computer and networking department of SMK Mega Link Majene. The sample was taken by purposive sampling technique. The data obtained used the research instrument based on the form of students achievements were collected by using test of student’s achievement and interview guidance. The technique of collecting data researcher had observation to ascertain the model that used by teacher was teaching model of developing metacognitive. The technique of data analysis in this research was reduction data, presentation and conclusion. Based on the whole findings in this study it was shown that student’s metacognitive ability generally not develops optimally. It was because of limited scope of the materials, and cognitive teaching strategy handled by verbal presentation and trained continuously in facing cognitive tasks, such as understanding and solving problem.

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

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Edwin Musdi

2016-01-01

This research aims to develop a mathematics instructional model based realistic mathematics education (RME) to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase.  At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characterist...

The effectiveness of problem-based learning on students’ problem solving ability in vector analysis course

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Mushlihuddin, R.; Nurafifah; Irvan

2018-01-01

The student’s low ability in mathematics problem solving proved to the less effective of a learning process in the classroom. Effective learning was a learning that affects student’s math skills, one of which is problem-solving abilities. Problem-solving capability consisted of several stages: understanding the problem, planning the settlement, solving the problem as planned, re-examining the procedure and the outcome. The purpose of this research was to know: (1) was there any influence of PBL model in improving ability Problem solving of student math in a subject of vector analysis?; (2) was the PBL model effective in improving students’ mathematical problem-solving skills in vector analysis courses? This research was a quasi-experiment research. The data analysis techniques performed from the test stages of data description, a prerequisite test is the normality test, and hypothesis test using the ANCOVA test and Gain test. The results showed that: (1) there was an influence of PBL model in improving students’ math problem-solving abilities in vector analysis courses; (2) the PBL model was effective in improving students’ problem-solving skills in vector analysis courses with a medium category.

Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

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Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel

2016-01-01

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

Errors of Students Learning with React Strategy in Solving the Problems of Mathematical Representation Ability

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Sari, Delsika Pramata; Darhim; Rosjanuardi, Rizky

2018-01-01

The purpose of this study was to investigate the errors experienced by students learning with REACT strategy and traditional learning in solving problems of mathematical representation ability. This study used quasi experimental pattern with static-group comparison design. The subjects of this study were 47 eighth grade students of junior high…

Solving applied mathematical problems with Matlab

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Xue, Dingyu

2008-01-01

Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.

Critical Thinking Skills of an Eighth Grade Male Student with High Mathematical Ability in Solving Problem

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Ismail

2018-01-01

This study aims to describe student’s critical thinking skill of grade VIII in solving mathematical problem. A qualitative research was conducted to a male student with high mathematical ability. Student’s critical thinking skill was obtained from a depth task-based interview. The result show that male student’s critical thinking skill of the student as follows. In understanding the problem, the student did categorization, significance decoding, and meaning clarification. In devising a plan he examined his ideas, detected his argument, analyzed his argument and evaluated his argument. During the implementation phase, the skill that appeared were analyzing of the argument and inference skill such as drawing conclusion, deliver alternative thinking, and problem solving skills. At last, in rechecking all the measures, they did self-correcting and self-examination.

Profile of Secondary School Students with High Mathematics Ability in Solving Shape and Space Problem

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Putra, Mulia; Novita, Rita

2015-01-01

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show…

Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

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Sahendra, A.; Budiarto, M. T.; Fuad, Y.

2018-01-01

This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

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Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim

2013-01-01

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

How to solve mathematical problems

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Wickelgren, Wayne A

1995-01-01

Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

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Edwin Musdi

2016-02-01

Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase.  At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.

Cognitive Backgrounds of Problem Solving: A Comparison of Open-Ended vs. Closed Mathematics Problems

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Bahar, Abdulkadir; Maker, C. June

2015-01-01

Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary…

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

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E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

2017-02-01

This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Affect and mathematical problem solving a new perspective

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Adams, Verna

1989-01-01

Research on cognitive aspects of mathematical problem solving has made great progress in recent years, but the relationship of affective factors to problem-solving performance has been a neglected research area. The purpose of Affect and Mathematical Problem Solving: A New Perspective is to show how the theories and methods of cognitive science can be extended to include the role of affect in mathematical problem solving. The book presents Mandler's theory of emotion and explores its implications for the learning and teaching of mathematical problem solving. Also, leading researchers from mathematics, education, and psychology report how they have integrated affect into their own cognitive research. The studies focus on metacognitive processes, aesthetic influences on expert problem solvers, teacher decision-making, technology and teaching problem solving, and beliefs about mathematics. The results suggest how emotional factors like anxiety, frustration, joy, and satisfaction can help or hinder performance in...

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

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María F. Ayllón

2016-04-01

Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

Processes involved in solving mathematical problems

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Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra

2018-04-01

This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.

Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications

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Zollman, Alan

2009-01-01

Improving students' problem-solving abilities is a major, if not the major, goal of middle grades mathematics. To address this goal, the author, who is a university mathematics educator, and nine inner-city middle school teachers developed a math/science action research project. This article describes their unique approach to mathematical problem…

Learning via problem solving in mathematics education

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Piet Human

2009-09-01

Full Text Available Three forms of mathematics education at school level are distinguished: direct expository teaching with an emphasis on procedures, with the expectation that learners will at some later stage make logical and functional sense of what they have learnt and practised (the prevalent form, mathematically rigorous teaching in terms of fundamental mathematical concepts, as in the so-called “modern mathematics” programmes of the sixties, teaching and learning in the context of engaging with meaningful problems and focused both on learning to become good problem solvers (teaching for problem solving andutilising problems as vehicles for the development of mathematical knowledge andproficiency by learners (problem-centred learning, in conjunction with substantialteacher-led social interaction and mathematical discourse in classrooms.Direct expository teaching of mathematical procedures dominated in school systems after World War II, and was augmented by the “modern mathematics” movement in the period 1960-1970. The latter was experienced as a major failure, and was soon abandoned. Persistent poor outcomes of direct expository procedural teaching of mathematics for the majority of learners, as are still being experienced in South Africa, triggered a world-wide movement promoting teaching mathematics for and via problem solving in the seventies and eighties of the previous century. This movement took the form of a variety of curriculum experiments in which problem solving was the dominant classroom activity, mainly in the USA, Netherlands, France and South Africa. While initially focusing on basic arithmetic (computation with whole numbers and elementary calculus, the problem-solving movement started to address other mathematical topics (for example, elementary statistics, algebra, differential equations around the turn of the century. The movement also spread rapidly to other countries, including Japan, Singapore and Australia. Parallel with the

Mathematical Abstraction in the Solving of Ill-Structured Problems by Elementary School Students in Korea

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Hong, Jee Yun; Kim, Min Kyeong

2016-01-01

Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…

How to make university students solve physics problems requiring mathematical skills: The "Adventurous Problem Solving" approach

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de Mul, F.F.M.; Martin Batlle, C.; Martin i Batlle, Cristina; de Bruijn, Imme; Rinzema, K.; Rinzema, Kees

2003-01-01

Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential

Flexibility in Mathematics Problem Solving Based on Adversity Quotient

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Dina, N. A.; Amin, S. M.; Masriyah

2018-01-01

Flexibility is an ability which is needed in problem solving. One of the ways in problem solving is influenced by Adversity Quotient (AQ). AQ is the power of facing difficulties. There are three categories of AQ namely climber, camper, and quitter. This research is a descriptive research using qualitative approach. The aim of this research is to describe flexibility in mathematics problem solving based on Adversity Quotient. The subjects of this research are climber student, camper student, and quitter student. This research was started by giving Adversity Response Profile (ARP) questioner continued by giving problem solving task and interviews. The validity of data measurement was using time triangulation. The results of this research shows that climber student uses two strategies in solving problem and doesn’t have difficulty. The camper student uses two strategies in solving problem but has difficulty to finish the second strategies. The quitter student uses one strategy in solving problem and has difficulty to finish it.

Clinical and Cognitive Characteristics Associated with Mathematics Problem Solving in Adolescents with Autism Spectrum Disorder.

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Oswald, Tasha M; Beck, Jonathan S; Iosif, Ana-Maria; McCauley, James B; Gilhooly, Leslie J; Matter, John C; Solomon, Marjorie

2016-04-01

Mathematics achievement in autism spectrum disorder (ASD) has been understudied. However, the ability to solve applied math problems is associated with academic achievement, everyday problem-solving abilities, and vocational outcomes. The paucity of research on math achievement in ASD may be partly explained by the widely-held belief that most individuals with ASD are mathematically gifted, despite emerging evidence to the contrary. The purpose of the study was twofold: to assess the relative proportions of youth with ASD who demonstrate giftedness versus disability on applied math problems, and to examine which cognitive (i.e., perceptual reasoning, verbal ability, working memory) and clinical (i.e., test anxiety) characteristics best predict achievement on applied math problems in ASD relative to typically developing peers. Twenty-seven high-functioning adolescents with ASD and 27 age- and Full Scale IQ-matched typically developing controls were assessed on standardized measures of math problem solving, perceptual reasoning, verbal ability, and test anxiety. Results indicated that 22% of the ASD sample evidenced a mathematics learning disability, while only 4% exhibited mathematical giftedness. The parsimonious linear regression model revealed that the strongest predictor of math problem solving was perceptual reasoning, followed by verbal ability and test anxiety, then diagnosis of ASD. These results inform our theories of math ability in ASD and highlight possible targets of intervention for students with ASD struggling with mathematics. © 2015 International Society for Autism Research, Wiley Periodicals, Inc.

Problem solving through recreational mathematics

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Averbach, Bonnie

1999-01-01

Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics - problems, puzzles and games - to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire ga

Graphic Organizer in Action: Solving Secondary Mathematics Word Problems

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Khoo Jia Sian

2016-09-01

Full Text Available Mathematics word problems are one of the most challenging topics to learn and teach in secondary schools. This is especially the case in countries where English is not the first language for the majority of the people, such as in Brunei Darussalam. Researchers proclaimed that limited language proficiency and limited Mathematics strategies are the possible causes to this problem. However, whatever the reason is behind difficulties students face in solving Mathematical word problems, it is perhaps the teaching and learning of the Mathematics that need to be modified. For example, the use of four-square-and-a-diamond graphic organizer that infuses model drawing skill; and Polya’s problem solving principles, to solve Mathematical word problems may be some of the strategies that can help in improving students’ word problem solving skills. This study, through quantitative analysis found that the use of graphic organizer improved students’ performance in terms of Mathematical knowledge, Mathematical strategy and Mathematical explanation in solving word problems. Further qualitative analysis revealed that the use of graphic organizer boosted students’ confidence level and positive attitudes towards solving word problems.Keywords: Word Problems, Graphic Organizer, Algebra, Action Research, Secondary School Mathematics DOI: http://dx.doi.org/10.22342/jme.7.2.3546.83-90

Growing geometric reasoning in solving problems of analytical geometry through the mathematical communication problems to state Islamic university students

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Mujiasih; Waluya, S. B.; Kartono; Mariani

2018-03-01

Skills in working on the geometry problems great needs of the competence of Geometric Reasoning. As a teacher candidate, State Islamic University (UIN) students need to have the competence of this Geometric Reasoning. When the geometric reasoning in solving of geometry problems has grown well, it is expected the students are able to write their ideas to be communicative for the reader. The ability of a student's mathematical communication is supposed to be used as a marker of the growth of their Geometric Reasoning. Thus, the search for the growth of geometric reasoning in solving of analytic geometry problems will be characterized by the growth of mathematical communication abilities whose work is complete, correct and sequential, especially in writing. Preceded with qualitative research, this article was the result of a study that explores the problem: Was the search for the growth of geometric reasoning in solving analytic geometry problems could be characterized by the growth of mathematical communication abilities? The main activities in this research were done through a series of activities: (1) Lecturer trains the students to work on analytic geometry problems that were not routine and algorithmic process but many problems that the process requires high reasoning and divergent/open ended. (2) Students were asked to do the problems independently, in detail, complete, order, and correct. (3) Student answers were then corrected each its stage. (4) Then taken 6 students as the subject of this research. (5) Research subjects were interviewed and researchers conducted triangulation. The results of this research, (1) Mathematics Education student of UIN Semarang, had adequate the mathematical communication ability, (2) the ability of this mathematical communication, could be a marker of the geometric reasoning in solving of problems, and (3) the geometric reasoning of UIN students had grown in a category that tends to be good.

The semantic system is involved in mathematical problem solving.

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Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

The Role of Expository Writing in Mathematical Problem Solving

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Craig, Tracy S.

2016-01-01

Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the…

Metacognition Process of Students with High Mathematics Anxiety in Mathematics Problem-Solving

OpenAIRE

Patrisius Afrisno Udil; Tri Atmojo Kusmayadi; Riyadi Riyadi

2017-01-01

This study aims to find out students’ metacognition process while solving the mathematics problem. It focuses on analyzing the metacognition process of students with high mathematics anxiety based on Polya’s problem solving phases. This study uses qualitative research with case study strategy. The subjects consist of 8 students of 7th grade selected through purposive sampling. Data in the form of Mathematics Anxiety Scale (MAS) result and recorded interview while solving mathematics problems ...

The relation between early constructive play and mathematical word problem solving is mediated by spatial ability. A path analysis in sixth grade students.

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Oostermeijer, M.; Boonen, A.J.H.; Jolles, J.

2014-01-01

The scientific literature shows that constructive play activities are positively related to children's spatial ability. Likewise, a close positive relation is found between spatial ability and mathematical word problem-solving performances. The relation between children's constructive play and their

Solving Mathematical Problems A Personal Perspective

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Tao, Terence

2006-01-01

Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.

Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style

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Indraswari, N. F.; Budayasa, I. K.; Ekawati, R.

2018-01-01

This study aimed to describe algebraic reasoning of secondary school’s pupils with different learning styles in solving mathematical problem. This study begins by giving the questionnaire to find out the learning styles and followed by mathematical ability test to get three subjects of 8th-grade whereas the learning styles of each pupil is visual, auditory, kinesthetic and had similar mathematical abilities. Then it continued with given algebraic problems and interviews. The data is validated using triangulation of time. The result showed that in the pattern of seeking indicator, subjects identified the things that were known and asked based on them observations. The visual and kinesthetic learners represented the known information in a chart, whereas the auditory learner in a table. In addition, they found the elements which makes the pattern and made a relationship between two quantities. In the pattern recognition indicator, they created conjectures on the relationship between two quantities and proved it. In the generalization indicator, they were determining the general rule of pattern found on each element of pattern using algebraic symbols and created a mathematical model. Visual and kinesthetic learners determined the general rule of equations which was used to solve problems using algebraic symbols, but auditory learner in a sentence.

Student’s scheme in solving mathematics problems

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Setyaningsih, Nining; Juniati, Dwi; Suwarsono

2018-03-01

The purpose of this study was to investigate students’ scheme in solving mathematics problems. Scheme are data structures for representing the concepts stored in memory. In this study, we used it in solving mathematics problems, especially ratio and proportion topics. Scheme is related to problem solving that assumes that a system is developed in the human mind by acquiring a structure in which problem solving procedures are integrated with some concepts. The data were collected by interview and students’ written works. The results of this study revealed are students’ scheme in solving the problem of ratio and proportion as follows: (1) the content scheme, where students can describe the selected components of the problem according to their prior knowledge, (2) the formal scheme, where students can explain in construct a mental model based on components that have been selected from the problem and can use existing schemes to build planning steps, create something that will be used to solve problems and (3) the language scheme, where students can identify terms, or symbols of the components of the problem.Therefore, by using the different strategies to solve the problems, the students’ scheme in solving the ratio and proportion problems will also differ.

Improving mathematical problem solving : A computerized approach

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Harskamp, EG; Suhre, CJM

Mathematics teachers often experience difficulties in teaching students to become skilled problem solvers. This paper evaluates the effectiveness of two interactive computer programs for high school mathematics problem solving. Both programs present students with problems accompanied by instruction

Self-Regulation and Problem Solving Ability in 7E-Learning Cycle Based Goal Orientation

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Mulyono; Noor, N. L.

2017-04-01

Goal orientation differences between mastery goals and performance goals can be a cause of high and low self-regulation and problem-solving abilities. To overcome these problems applied 7E-learning cycle in which students learn and develop ways to optimise the power of reason through the learning phase elicit, engage, explore, explain, elaborate, evaluate, and extend. This study aimed to test the effectiveness of learning by 7E-learning cycle and describe self-regulation and mathematics problem solving based on goal-orientation after the implementation 7E-learning cycle. This study used mix method design with research subject is graders XII sciences MA NU Nurul Ulum Jekulo Kudus which divided into goal orientation is mastery goal and performance goal. The independent variable of this research is learning model, while the dependent variable is problem solving and self-regulation. Then, collecting data using scale, interviews and tests. The data processed with the proportion of test, t-test, paired samples t-test, and Normality-gain. The results show problem-solving abilities of students through 7E-learning cycle the average of mathematical problem-solving capability class, self-regulation at 7E-learning cycle is better than the traditional model study. The problem-solving skills at 7E-learning cycle are better than the traditional model study, there is an increase in self-regulation through 7E-learning cycle of 0.4 (medium), and there is an increased problem-solving ability through 7E-learning cycle by 0.79 (high). Based on the qualitative analysis, self-regulation and problem-solving ability after the implementation of 7E-learning cycle students of a mastery goal group are better than the performance goal team. It is suggested to implement 7E-learning cycle to improve self-regulation and problem-solving ability as well as directing and fostering mastery goal on the student in the learning process.

Interference thinking in constructing students’ knowledge to solve mathematical problems

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Jayanti, W. E.; Usodo, B.; Subanti, S.

2018-04-01

This research aims to describe interference thinking in constructing students’ knowledge to solve mathematical problems. Interference thinking in solving problems occurs when students have two concepts that interfere with each other’s concept. Construction of problem-solving can be traced using Piaget’s assimilation and accommodation framework, helping to know the students’ thinking structures in solving the problems. The method of this research was a qualitative method with case research strategy. The data in this research involving problem-solving result and transcripts of interviews about students’ errors in solving the problem. The results of this research focus only on the student who experience proactive interference, where student in solving a problem using old information to interfere with the ability to recall new information. The student who experience interference thinking in constructing their knowledge occurs when the students’ thinking structures in the assimilation and accommodation process are incomplete. However, after being given reflection to the student, then the students’ thinking process has reached equilibrium condition even though the result obtained remains wrong.

The Enhancement of Junior High School Students' Abilities in Mathematical Problem Solving Using Soft Skill-based Metacognitive Learning

OpenAIRE

Murni, Atma; Sabandar, Jozua; S. Kusumah, Yaya; Kartasamita, Bana Goerbana

2013-01-01

The aim of this study is to know the differences of enhancement in mathematical problem solving ability (MPSA) between the students who received soft skill- based metacognitive learning (SSML) with the students who got conventional learning (CL). This research is a quasi experimental design with pretest-postest control group. The population in this study is the students of Junior High School in Pekanbaru city. The sample consist of 135 students, 68 of them are from the high-level...

On Teaching Problem Solving in School Mathematics

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Erkki Pehkonen

2013-12-01

Full Text Available The article begins with a brief overview of the situation throughout the world regarding problem solving. The activities of the ProMath group are then described, as the purpose of this international research group is to improve mathematics teaching in school. One mathematics teaching method that seems to be functioning in school is the use of open problems (i.e., problem fields. Next we discuss the objectives of the Finnish curriculum that are connected with problem solving. Some examples and research results are taken from a Finnish–Chilean research project that monitors the development of problem-solving skills in third grade pupils. Finally, some ideas on “teacher change” are put forward. It is not possible to change teachers, but only to provide hints for possible change routes: the teachers themselves should work out the ideas and their implementation.

Effectiveness of discovery learning model on mathematical problem solving

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Herdiana, Yunita; Wahyudin, Sispiyati, Ririn

2017-08-01

This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.

Improving Teaching Quality and Problem Solving Ability through Contextual Teaching and Learning in Differential Equations: A Lesson Study Approach

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Khotimah, Rita Pramujiyanti; Masduki

2016-01-01

Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

Pre-Service Mathematics Teachers’ Problem Solving Processes with Geometer’s Sketchpad: Mirror Problem

OpenAIRE

ÖÇAL, Mehmet Fatih; ŞİMŞEK, Mertkan

2016-01-01

Problem solving skill is the core of mathematics education and its importance cannot be denied. This study specifically examined 56 freshmen pre-service mathematics teachers’ problem solving processes on a specific problem with the help of Geometer’s Sketchpad (GSP). They were grouped into two-person teams to solve a problem called "the mirror problem". They were expected to solve it by means of GSP. According to their works on GSP and related reflections, there appeared two differe...

Gender Differences in Solving Mathematics Problems among Two-Year College Students in a Developmental Algebra Class and Related Factors.

Science.gov (United States)

Schonberger, Ann K.

A study was conducted at the University of Maine at Orono (UMO) to examine gender differences with respect to mathematical problem-solving ability, visual spatial ability, abstract reasoning ability, field independence/dependence, independent learning style, and developmental problem-solving ability (i.e., formal reasoning ability). Subjects…

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

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Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

2016-02-01

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

Problem Solving Reasoning and Problem Based Instruction in Geometry Learning

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Sulistyowati, F.; Budiyono, B.; Slamet, I.

2017-09-01

This research aims to analyze the comparison Problem Solving Reasoning (PSR) and Problem Based Instruction (PBI) on problem solving and mathematical communication abilities viewed from Self-Regulated Learning (SRL). Learning was given to grade 8th junior high school students. This research uses quasi experimental method, and then with descriptive analysis. Data were analyzed using two-ways multivariate analysis of variance (MANOVA) and one-way analysis of variance (ANOVA) with different cells. The result of data analysis were learning model gives different effect, level of SRL gives the same effect, and there is no interaction between the learning model with the SRL on the problem solving and mathematical communication abilities. The t-test statistic was used to find out more effective learning model. Based on the test, regardless of the level of SRL, PSR is more effective than PBI for problemsolving ability. The result of descriptive analysis was PSR had the advantage in creating learning that optimizing the ability of learners in reasoning to solve a mathematical problem. Consequently, the PSR is the right learning model to be applied in the classroom to improve problem solving ability of learners.

The Transitory Phase to the Attainment of Self-Regulatory Skill in Mathematical Problem Solving

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Lazakidou, G.; Paraskeva, F.; Retalis, S.

2007-01-01

Three phases of development of self-regulatory skill in the domain of mathematical problem solving were designed to examine students' behaviour and the effects on their problem solving ability. Forty-eight Grade 4 students (10 year olds) participated in this pilot study. The students were randomly assigned to one of three groups, each representing…

The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours, motivation, and metacognition

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Çiğdem Özcan, Zeynep

2016-04-01

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students' self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving skills. The aim of this study is to investigate the relationship between mathematical problem-solving skills and the three dimensions of self-regulated learning (motivation, metacognition, and behaviour), and whether this relationship is of a predictive nature. The sample of this study consists of 323 students from two public secondary schools in Istanbul. In this study, the mathematics homework behaviour scale was administered to measure students' homework behaviours. For metacognition measurements, the mathematics metacognition skills test for students was administered to measure offline mathematical metacognitive skills, and the metacognitive experience scale was used to measure the online mathematical metacognitive experience. The internal and external motivational scales used in the Programme for International Student Assessment (PISA) test were administered to measure motivation. A hierarchic regression analysis was conducted to determine the relationship between the dependent and independent variables in the study. Based on the findings, a model was formed in which 24% of the total variance in students' mathematical problem-solving skills is explained by the three sub-dimensions of the self-regulated learning model: internal motivation (13%), willingness to do homework (7%), and post-problem retrospective metacognitive experience (4%).

Scientific Approach to Improve Mathematical Problem Solving Skills Students of Grade V

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Roheni; Herman, T.; Jupri, A.

2017-09-01

This study investigates the skills of elementary school students’ in problem solving through the Scientific Approach. The purpose of this study is to determine mathematical problem solving skills of students by using Scientific Approach is better than mathematical problem solving skills of students by using Direct Instruction. This study is using quasi-experimental method. Subject of this study is students in grade V in one of state elementary school in Cirebon Regency. Instrument that used in this study is mathematical problem solving skills. The result of this study showed that mathematical problem solving skills of students who learn by using Scientific Approach is more significant than using Direct Instruction. Base on result and analysis, the conclusion is that Scientific Approach can improve students’ mathematical problem solving skills.

The role of problem solving method on the improvement of mathematical learning

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Saeed Mokhtari-Hassanabad

2012-10-01

Full Text Available In history of education, problem solving is one of the important educational goals and teachers or parents have intended that their students have capacity of problem solving. In present research, it is tried that study the problem solving method for mathematical learning. This research is implemented via quasi-experimental method on 49 boy students at high school. The results of Leven test and T-test indicated that problem solving method has more effective on the improvement of mathematical learning than traditional instruction method. Therefore it seems that teachers of mathematics must apply the problem solving method in educational systems till students became self-efficiency in mathematical problem solving.

Schema building profiles among elementary school students in solving problems related to operations of addition to fractions on the basis of mathematic abilities

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Gembong, S.; Suwarsono, S. T.; Prabowo

2018-03-01

Schema in the current study refers to a set of action, process, object and other schemas already possessed to build an individual’s ways of thinking to solve a given problem. The current study aims to investigate the schemas built among elementary school students in solving problems related to operations of addition to fractions. The analyses of the schema building were done qualitatively on the basis of the analytical framework of the APOS theory (Action, Process, Object, and Schema). Findings show that the schemas built on students of high and middle ability indicate the following. In the action stage, students were able to add two fractions by way of drawing a picture or procedural way. In the Stage of process, they could add two and three fractions. In the stage of object, they could explain the steps of adding two fractions and change a fraction into addition of fractions. In the last stage, schema, they could add fractions by relating them to another schema they have possessed i.e. the least common multiple. Those of high and middle mathematic abilities showed that their schema building in solving problems related to operations odd addition to fractions worked in line with the framework of the APOS theory. Those of low mathematic ability, however, showed that their schema on each stage did not work properly.

Exploring Primary Student's Problem-Solving Ability by Doing Tasks Like PISA's Question

OpenAIRE

Novita, Rita; Zulkardi, Zulkardi; Hartono, Yusuf

2012-01-01

Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term “problem solving” refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. In addition, the contextual problem that requires students to connect their mathematical knowledge in solving mathematical situational problem is believed to be an impact on the development student...

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

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Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

2016-01-01

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

Calculus Problem Solving Behavior of Mathematic Education Students

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Rizal, M.; Mansyur, J.

2017-04-01

The purpose of this study is to obtain a description of the problem-solving behaviour of mathematics education students. The attainment of the purpose consisted of several stages: (1) to gain the subject from the mathematic education of first semester students, each of them who has a high, medium, and low competence of mathematic case. (2) To give two mathematical problems with different characteristics. The first problem (M1), the statement does not lead to a resolution. The second problem (M2), a statement leads to problem-solving. (3) To explore the behaviour of problem-solving based on the step of Polya (Rizal, 2011) by way of thinking aloud and in-depth interviews. The obtained data are analysed as suggested by Miles and Huberman (1994) but at first, time triangulation is done or data’s credibility by providing equivalent problem contexts and at different times. The results show that the behavioral problem solvers (mathematic education students) who are capable of high mathematic competency (ST). In understanding M1, ST is more likely to pay attention to an image first, read the texts piecemeal and repeatedly, then as a whole and more focus to the sentences that contain equations, numbers or symbols. As a result, not all information can be received well. When understanding the M2, ST can link the information from a problem that is stored in the working memory to the information on the long-term memory. ST makes planning to the solution of M1 and M2 by using a formula based on similar experiences which have been ever received before. Another case when implementing the troubleshooting plans, ST complete the M1 according to the plan, but not all can be resolved correctly. In contrast to the implementation of the solving plan of M2, ST can solve the problem according to plan quickly and correctly. According to the solving result of M1 and M2, ST conducts by reading the job based on an algorithm and reasonability. Furthermore, when SS and SR understand the

How to solve applied mathematics problems

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Moiseiwitsch, B L

2011-01-01

This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

Analytical derivation: An epistemic game for solving mathematically based physics problems

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Bajracharya, Rabindra R.; Thompson, John R.

2016-06-01

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

Teaching Personal Finance Mathematical Problem Solving to Individuals with Moderate Intellectual Disability

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Root, Jenny; Saunders, Alicia; Spooner, Fred; Brosh, Chelsi

2017-01-01

The ability to solve mathematical problems related to purchasing and personal finance is important in promoting skill generalization and increasing independence for individuals with moderate intellectual disabilities (IDs). Using a multiple probe across participant design, this study investigated the effects of modified schema-based instruction…

Teaching Elementary Mathematics through Problem Solving and Its Relationship to Mathematics Achievement

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Bullock, Audrey N.

2017-01-01

Problem solving in mathematics has been a goal for students for decades. In the reviewed literature, problem solving was most often treated as the dependent variable and was defined very broadly; however, few studies were found that included problem solving as a treatment or independent variable. The purpose of this study was to investigate the…

A Metacognitive Profile of Vocational High School Student’s Field Independent in Mathematical Problem Solving

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Nugraheni, L.; Budayasa, I. K.; Suwarsono, S. T.

2018-01-01

The study was designed to discover examine the profile of metacognition of vocational high school student of the Machine Technology program that had high ability and field independent cognitive style in mathematical problem solving. The design of this study was exploratory research with a qualitative approach. This research was conducted at the Machine Technology program of the vocational senior high school. The result revealed that the high-ability student with field independent cognitive style conducted metacognition practices well. That involved the three types of metacognition activities, consisting of planning, monitoring, and evaluating at metacognition level 2 or aware use, 3 or strategic use, 4 or reflective use in mathematical problem solving. The applicability of the metacognition practices conducted by the subject was never at metacognition level 1 or tacit use. This indicated that the participant were already aware, capable of choosing strategies, and able to reflect on their own thinking before, after, or during the process at the time of solving mathematical problems.That was very necessary for the vocational high school student of Machine Technology program.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

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Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

Directory of Open Access Journals (Sweden)

Yinghui Lai

Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

Science.gov (United States)

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Original article Key factors for successful solving of mathematical word problems in fifth-grade learners

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Marija Kavkler

2014-05-01

Full Text Available BACKGROUND Difficulties in solving mathematical word problems (MWP are one of the most common reasons for weak mathematics performance, and poor mathematical literacy has important implications for an individual’s further education, employment opportunities, mental health and quality of life in today’s modern technological society. The purpose of the study was to examine whether Slovenian good and poor MWP solvers differ in arithmetic knowledge and skills, non-verbal reasoning, pupils’ self-evaluations of MWP abilities, teachers’ assessment of their mathematical knowledge and what strategies fifth- grade learners use in solving MWP. PARTICIPANTS AND PROCEDURE The larger sample included 233 pupils from 14 fifth-grade classes (mean age 10 years 3 months and 14 teachers. On the basis of the teachers’ opinions and the results of MWP solving two sub-samples of 24 students were formed, good and poor MWP solvers. Several tests were used to determine MWP solving ability, automation of arithmetic facts and procedures as well as Raven’s SPM. Questionnaires for pupils were used to assess pupils’ estimations of MWP tasks’ difficulty, their own ability to solve them and the strategies used. To assess pupils’ knowledge a questionnaire for teachers was used. RESULTS Slovenian 5 th graders in the larger sample generally used very few empirically proven effective cognitive and metacognitive strategies to solve MWP. Pupils with lower achievement in solving MWP, compared to pupils with higher achievement demonstrated significantly less automated arithmetic facts and procedures of the algorithm, less flexible use of arithmetic skills, as well as qualitatively different MWP solving, which is also related to their lower non-verbal reasoning. Teachers’ assessments and pupils’ self-assessments matched the achieved test results. CONCLUSIONS The results exposed important key factors for successful solving of mathematical word problems with

The Strategies of Mathematics Teachers When Solving Number Sense Problems

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Sare Şengül

2014-04-01

Full Text Available Number sense involves efficient strategies and the ability to think flexibly with numbers and number operations and flexible thinking ability and the inclination getting for making sound mathematical judgements. The aim of this study was to investigate the strategies used by mathematics teachers while solving number sense problems. Eleven mathematics teachers from a graduate program in education were the participants. A number sense test which has a total of 12 problems is used as the data gathering tool. Teachers’ responses and strategies were analyzed both qualitatively and quantitatively.First, participants’ responses were evaluated for correctness. Then the strategies teachers used were analyzed. The strategies were categorized as based on the use of number sense or rule based strategies. When the correct and incorrect responses were considered together, in the 46% of the responses number sense strategies were used and in 54% the rule-based strategies were used. The results of this study showed that even though teachers can use number sense strategies at some level, there is still room for development in teachers’ number sense.

Solicited versus Unsolicited Metacognitive Prompts for Fostering Mathematical Problem Solving Using Multimedia

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Kramarski, Bracha; Friedman, Sheli

2014-01-01

The study examined how student control over metacognitive prompts in a multimedia environment affects students' ability to solve mathematical problems in immediate comprehension tasks using a multimedia program and a delayed-transfer test. It also examined the effect on metacognitive discourse, mental effort, and engagement with multimedia-based…

Creativity in Unique Problem-Solving in Mathematics and Its Influence on Motivation for Learning

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Bishara, Saied

2016-01-01

This research study investigates the ability of students to tackle the solving of unique mathematical problems in the domain of numerical series, verbal and formal, and its influence on the motivation of junior high students with learning disabilities in the Arab sector. Two instruments were used to collect the data: mathematical series were…

Social problem solving ability predicts mental health among undergraduate students.

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Ranjbar, Mansour; Bayani, Ali Asghar; Bayani, Ali

2013-11-01

The main objective of this study was predicting student's mental health using social problem solving- ability. In this correlational. descriptive study, 369 (208 female and 161 male) from, Mazandaran University of Medical Science were selected through stratified random sampling method. In order to collect the data, the social problem solving inventory-revised and general health questionnaire were used. Data were analyzed through SPSS-19, Pearson's correlation, t test, and stepwise regression analysis. Data analysis showed significant relationship between social problem solving ability and mental health (P Social problem solving ability was significantly associated with the somatic symptoms, anxiety and insomnia, social dysfunction and severe depression (P social problem solving ability and mental health.

Exploring mathematics problem-solving and proof

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Grieser, Daniel

2018-01-01

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is requi...

Student’s thinking process in solving word problems in geometry

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Khasanah, V. N.; Usodo, B.; Subanti, S.

2018-05-01

This research aims to find out the thinking process of seventh grade of Junior High School in solve word problem solving of geometry. This research was descriptive qualitative research. The subject of the research was selected based on sex and differences in mathematical ability. Data collection was done based on student’s work test, interview, and observation. The result of the research showed that there was no difference of thinking process between male and female with high mathematical ability, and there were differences of thinking process between male and female with moderate and low mathematical ability. Also, it was found that male with moderate mathematical ability took a long time in the step of making problem solving plans. While female with moderate mathematical ability took a long time in the step of understanding the problems. The importance of knowing the thinking process of students in solving word problem solving were that the teacher knows the difficulties faced by students and to minimize the occurrence of the same error in problem solving. Teacher could prepare the right learning strategies which more appropriate with student’s thinking process.

Language and mathematical problem solving among bilinguals.

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Bernardo, Allan B I

2002-05-01

Does using a bilingual's 1st or 2nd language have an effect on problem solving in semantically rich domains like school mathematics? The author conducted a study to determine whether Filipino-English bilingual students' understanding and solving of word problems in arithmetic differed when the problems were in the students' 1st and 2nd languages. Two groups participated-students whose 1st language was Filipino and students whose 1st language was English-and easy and difficult arithmetic problems were used. The author used a recall paradigm to assess how students understood the word problems and coded the solution accuracy to assess problem solving. The results indicated a 1st-language advantage; that is, the students were better able to understand and solve problems in their 1st language, whether the 1st language was English or Filipino. Moreover, the advantage was more marked with the easy problems. The theoretical and practical implications of the results are discussed.

Problem Solving Frameworks for Mathematics and Software Development

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McMaster, Kirby; Sambasivam, Samuel; Blake, Ashley

2012-01-01

In this research, we examine how problem solving frameworks differ between Mathematics and Software Development. Our methodology is based on the assumption that the words used frequently in a book indicate the mental framework of the author. We compared word frequencies in a sample of 139 books that discuss problem solving. The books were grouped…

Students’ difficulties in probabilistic problem-solving

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Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

2018-03-01

There are many errors can be identified when students solving mathematics problems, particularly in solving the probabilistic problem. This present study aims to investigate students’ difficulties in solving the probabilistic problem. It focuses on analyzing and describing students errors during solving the problem. This research used the qualitative method with case study strategy. The subjects in this research involve ten students of 9th grade that were selected by purposive sampling. Data in this research involve students’ probabilistic problem-solving result and recorded interview regarding students’ difficulties in solving the problem. Those data were analyzed descriptively using Miles and Huberman steps. The results show that students have difficulties in solving the probabilistic problem and can be divided into three categories. First difficulties relate to students’ difficulties in understanding the probabilistic problem. Second, students’ difficulties in choosing and using appropriate strategies for solving the problem. Third, students’ difficulties with the computational process in solving the problem. Based on the result seems that students still have difficulties in solving the probabilistic problem. It means that students have not able to use their knowledge and ability for responding probabilistic problem yet. Therefore, it is important for mathematics teachers to plan probabilistic learning which could optimize students probabilistic thinking ability.

The Place of Problem Solving in Contemporary Mathematics Curriculum Documents

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Stacey, Kaye

2005-01-01

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

Investigating Mathematics Teachers Candidates' Knowledge about Problem Solving Strategies through Problem Posing

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Ünlü, Melihan

2017-01-01

The aim of the study was to determine mathematics teacher candidates' knowledge about problem solving strategies through problem posing. This qualitative research was conducted with 95 mathematics teacher candidates studying at education faculty of a public university during the first term of the 2015-2016 academic year in Turkey. Problem Posing…

Effects of the SOLVE Strategy on the Mathematical Problem Solving Skills of Secondary Students with Learning Disabilities

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Freeman-Green, Shaqwana M.; O'Brien, Chris; Wood, Charles L.; Hitt, Sara Beth

2015-01-01

This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic-based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe…

Glogs as Non-Routine Problem Solving Tools in Mathematics

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Devine, Matthew T.

2013-01-01

In mathematical problem solving, American students are falling behind their global peers because of a lack of foundational and reasoning skills. A specific area of difficulty with problem solving is working non-routine, heuristic-based problems. Many students are not provided with effective instruction and often grow frustrated and dislike math.…

Using Video Prompting to Teach Mathematical Problem Solving of Real-World Video-Simulation Problems

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Saunders, Alicia F.; Spooner, Fred; Ley Davis, Luann

2018-01-01

Mathematical problem solving is necessary in many facets of everyday life, yet little research exists on how to teach students with more severe disabilities higher order mathematics like problem solving. Using a multiple probe across participants design, three middle school students with moderate intellectual disability (ID) were taught to solve…

PEMBELAJARAN KONTEKSTUAL OPEN ENDED PROBLEM SOLVING DENGAN KOMIK MATEMATIKA UNTUK MENINGKATKAN KETERAMPILAN PEMECAHAN MASALAH

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Lenny Kurniati

2017-01-01

ABSTRACT The aim of this research to develop a mathematics learning instrument using contextual open ended problem solving with mathematic comic to increase the problem solving skill which valid, practical and effective. The type of research used in this study is development research using modification of Plomp model. Learning instrumen that have been develop are: syllabus, Lesson plan, worksheet, mathematics comic, and problem solving ability test. The results showed: (1 device developed valid; (2 practical learning is characterized by the positive response of students and good teachers ability, (3 Effectiveness characterized by (a problem solving ability score of the experimental class higher than minimum completeness criterion, (b learn interest and problem solving skill, both affected the problem solving ability positively,  (c problem solving ability of the experimental class score is higher than the control class, (d problem solving skill of the experimental class is increasing by 31%, the problem solving ability of the experimental class higher than the control class.. Because of the learning instrument develope are valid, practice and effective, it is shows that the research has ben reach out. Keywords: contextual teaching and learning, open ended problem solving, mathematics comic, problem solving.

Multi-representation ability of students on the problem solving physics

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Theasy, Y.; Wiyanto; Sujarwata

2018-03-01

Accuracy in representing knowledge possessed by students will show how the level of student understanding. The multi-representation ability of students on the problem solving of physics has been done through qualitative method of grounded theory model and implemented on physics education student of Unnes academic year 2016/2017. Multiforms of representation used are verbal (V), images/diagrams (D), graph (G), and mathematically (M). High and low category students have an accurate use of graphical representation (G) of 83% and 77.78%, and medium category has accurate use of image representation (D) equal to 66%.

Struggling Students' Use of Representation When Developing Number Sense and Problem Solving Abilities

OpenAIRE

Roxburgh, Allison L.

2016-01-01

Through my experience I have found students often rely on concrete or pictorial strategies to solve mathematical problems. These strategies are great to build an understanding in mathematical concepts. However, using these strategies becomes a tedious task when working with multi-digit numbers to solve problems involving mathematical operations. For example, a student who relies on drawing base ten blocks to solve three-digit addition problems may experience fatigue, as this is not the most e...

Self-directed questions to improve students' ability in solving chemical problems

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Sanjaya, Rahmat Eko; Muna, Khairiatul; Suharto, Bambang; Syahmani

2017-12-01

Students' ability in solving chemical problems is seen from their ability to solve chemicals' non-routine problems. It is due to learning faced directly on non-routine problems will generate a meaningful learning for students. Observations in Banjarmasin Public High School 1 (SMA Negeri 1 Banjarmasin) showed that students did not give the expected results when they were given the non-routine problems. Learning activities by emphasizing problem solving was implemented based on the existence of knowledge about cognition and regulation of cognition. Both of these elements are components of metacognition. The self-directed question is a strategy that involves metacognition in solving chemical problems. This research was carried out using classroom action research design in two cycles. Each cycle consists of four stages: planning, action, observation and reflection. The subjects were 34 students of grade XI-4 at majoring science (IPA) of SMA Negeri 1 Banjarmasin. The data were collected using tests of the students' ability in problem solving and non-tests instrument to know the process of implementation of the actions. Data were analyzed with descriptivequantitativeand qualitative analysis. The ability of students in solving chemical problems has increased from an average of 37.96 in cycle I became 61.83 in cycle II. Students' ability to solve chemical problems is viewed based on their ability to answer self-directed questions. Students' ability in comprehension questions increased from 73.04 in the cycle I became 96.32 in cycle II. Connection and strategic questions increased from 54.17 and 16.50 on cycle I became 63.73 and 55.23 on cycle II respectively. In cycle I, reflection questions were 26.96 and elevated into 36.27 in cycle II. The self-directed questions have the ability to help students to solve chemical problems through metacognition questions. Those questions guide students to find solutions in solving chemical problems.

Culture-Based Contextual Learning to Increase Problem-Solving Ability of First Year University Student

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Samo, Damianus Dao; Darhim; Kartasasmita, Bana G.

2018-01-01

The purpose of this study is to show the differences in problem-solving ability between first-year University students who received culture-based contextual learning and conventional learning. This research is a quantitative research using quasi-experimental research design. Samples were the First-year students of mathematics education department;…

Relationship between Problem-Solving Ability and Career Maturity ...

African Journals Online (AJOL)

This study investigated the relationship between problem-solving ability and career maturity of secondary school students in Ibadan, Oyo State, Nigeria. 230 final year secondary school students completed self-report measures of problem solving and career maturity. Multiple regression analysis was used to analyse the data ...

Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

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Takahashi, Akihiko

2016-01-01

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

The Geometric Construction Abilities Of Gifted Students In Solving Real - World Problems: A Case From Turkey

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Avni YILDIZ

2016-10-01

Full Text Available Geometric constructions have already been of interest to mathematicians. However, studies on geometric construction are not adequate in the relevant literature. Moreover, these studies generally focus on how secondary school gifted students solve non-routine mathematical problems. The present study aims to examine the geometric construction abilities of ninth-grade (15 years old gifted students in solving real-world geometry problems; thus a case study was conducted. Six gifted students participated in the study. The data consisted of voice records, solutions, and models made by the students on the GeoGebra screen. Results indicate that gifted students use their previous knowledge effectively during the process of geometric construction. They modeled the situations available in the problems through using mathematical concepts and the software in coordination. Therefore, it is evident that gifted students think more creatively while solving problems using GeoGebra.

Social problem solving ability predicts mental health among undergraduate students

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Mansour Ranjbar

2013-01-01

Methods : In this correlational- descriptive study, 369 (208 female and 161 male from, Mazandaran University of Medical Science were selected through stratified random sampling method. In order to collect the data, the social problem solving inventory-revised and general health questionnaire were used. Data were analyzed through SPSS-19, Pearson′s correlation, t test, and stepwise regression analysis. Results : Data analysis showed significant relationship between social problem solving ability and mental health (P < 0.01. Social problem solving ability was significantly associated with the somatic symptoms, anxiety and insomnia, social dysfunction and severe depression (P < 0.01. Conclusions: The results of our study demonstrated that there is a significant correlation between social problem solving ability and mental health.

The profile of conceptual comprehension of pre-service teacher in the mathematical problem solving with low emotional intelligence

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Prayitno, S. H.; Suwarsono, St.; Siswono, T. Y. E.

2018-03-01

Conceptual comprehension in this research is the ability to use the procedures that are owned by pre-service teachers to solve problems by finding the relation of the concept to another, or can be done by identifying the type of problem and associating it with a troubleshooting procedures, or connect the mathematical symbols with mathematical ideas and incorporate them into a series of logical reasoning, or by using prior knowledge that occurred directly, through its conceptual knowledge. The goal of this research is to describe the profile of conceptual comprehensin of pre-service teachers with low emotional intelligence in mathematical problems solving. Through observation and in-depth interview with the research subject the conclusion was that: pre-service teachers with low emotional intelligence pertained to the level of formal understanding in understanding the issues, relatively to the level of intuitive understanding in planning problem solving, to the level of relational understanding in implementing the relational problem solving plan, and pertained to the level of formal understanding in looking back to solve the problem.

Preservice Agricultural Education Teachers' Mathematics Ability

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Stripling, Christopher T.; Roberts, T. Grady

2012-01-01

The purpose of this study was to examine the mathematics ability of the nation's preservice agricultural education teachers. Based on the results of this study, preservice teachers were not proficient in solving agricultural mathematics problems, and agricultural teacher education programs require basic and intermediate mathematics as their…

Problem solving of student with visual impairment related to mathematical literacy problem

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Pratama, A. R.; Saputro, D. R. S.; Riyadi

2018-04-01

The student with visual impairment, total blind category depends on the sense of touch and hearing in obtaining information. In fact, the two senses can receive information less than 20%. Thus, students with visual impairment of the total blind categories in the learning process must have difficulty, including learning mathematics. This study aims to describe the problem-solving process of the student with visual impairment, total blind category on mathematical literacy issues based on Polya phase. This research using test method similar problems mathematical literacy in PISA and in-depth interviews. The subject of this study was a student with visual impairment, total blind category. Based on the result of the research, problem-solving related to mathematical literacy based on Polya phase is quite good. In the phase of understanding the problem, the student read about twice by brushing the text and assisted with information through hearing three times. The student with visual impairment in problem-solving based on the Polya phase, devising a plan by summoning knowledge and experience gained previously. At the phase of carrying out the plan, students with visual impairment implement the plan in accordance with pre-made. In the looking back phase, students with visual impairment need to check the answers three times but have not been able to find a way.

Block Model Approach in Problem Solving: Effects on Problem Solving Performance of the Grade V Pupils in Mathematics

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de Guzman, Niño Jose P.; Belecina, Rene R.

2012-01-01

The teaching of mathematics involves problem solving skills which prove to be difficult on the part of the pupils due to misrepresentation of the word problems. Oftentimes, pupils tend to represent the phrase "more than" as addition and the word difference as "- ". This paper aims to address the problem solving skills of grade…

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

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Aryani, F.; Amin, S. M.; Sulaiman, R.

2018-01-01

Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

The Motivation of Secondary School Students in Mathematical Word Problem Solving

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Gasco, Javier; Villarroel, Jose-Domingo

2014-01-01

Introduction: Motivation is an important factor in the learning of mathematics. Within this area of education, word problem solving is central in most mathematics curricula of Secondary School. The objective of this research is to detect the differences in motivation in terms of the strategies used to solve word problems. Method: It analyzed the…

Protocol Analysis of Group Problem Solving in Mathematics: A Cognitive-Metacognitive Framework for Assessment.

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Artzt, Alice F.; Armour-Thomas, Eleanor

The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each…

The Language Factor in Elementary Mathematics Assessments: Computational Skills and Applied Problem Solving in a Multidimensional IRT Framework

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Hickendorff, Marian

2013-01-01

The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and…

Comparison of mathematical problem solving strategies of primary school pupils

OpenAIRE

Wasilewská, Eliška

2016-01-01

The aim of this dissertation is to describe the role of educational strategy especially in field of the teaching of mathematics and to compare the mathematical problem solving strategies of primary school pupils which are taught by using different educational strategies. In the theoretical part, the main focus is on divergent educational strategies and their characteristics, next on factors affected teaching/learning process and finally on solving the problems. The empirical part of the disse...

The Effect of Dynamic and Interactive Mathematics Learning Environments (DIMLE), Supporting Multiple Representations, on Perceptions of Elementary Mathematics Pre-Service Teachers in Problem Solving Process

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Ozdemir, S.; Reis, Z. Ayvaz

2013-01-01

Mathematics is an important discipline, providing crucial tools, such as problem solving, to improve our cognitive abilities. In order to solve a problem, it is better to envision and represent through multiple means. Multiple representations can help a person to redefine a problem with his/her own words in that envisioning process. Dynamic and…

Working memory components as predictors of children's mathematical word problem solving.

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Zheng, Xinhua; Swanson, H Lee; Marcoulides, George A

2011-12-01

This study determined the working memory (WM) components (executive, phonological loop, and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy of elementary school children in Grades 2, 3, and 4 (N=310). A battery of tests was administered to assess problem-solving accuracy, problem-solving processes, WM, reading, and math calculation. Structural equation modeling analyses indicated that (a) all three WM components significantly predicted problem-solving accuracy, (b) reading skills and calculation proficiency mediated the predictive effects of the central executive system and the phonological loop on solution accuracy, and (c) academic mediators failed to moderate the relationship between the visual-spatial sketchpad and solution accuracy. The results support the notion that all components of WM play a major role in predicting problem-solving accuracy, but basic skills acquired in specific academic domains (reading and math) can compensate for some of the influence of WM on children's mathematical word problem solving. Copyright © 2011 Elsevier Inc. All rights reserved.

Strategies of solving arithmetic word problems in students with learning difficulties in mathematics

OpenAIRE

Kalan, Marko

2015-01-01

Problem solving as an important skill is, beside arithmetic, measure and algebra, included in standards of school mathematics (National Council of Teachers of Mathematics) (NCTM, 2000) and needed as a necessary skill for successfulness in science, technology, engineering and mathematics (STEM) (National Mathematics Advisory Panel, 2008). Since solving of human problems is connected to the real life, the arithmetic word problems (in short AWP) are an important kind of mathematics tasks in scho...

Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.

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Nunokawa, Kazuhiko

1996-01-01

The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)

Understanding and quantifying cognitive complexity level in mathematical problem solving items

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SUSAN E. EMBRETSON

2008-09-01

Full Text Available The linear logistic test model (LLTM; Fischer, 1973 has been applied to a wide variety of new tests. When the LLTM application involves item complexity variables that are both theoretically interesting and empirically supported, several advantages can result. These advantages include elaborating construct validity at the item level, defining variables for test design, predicting parameters of new items, item banking by sources of complexity and providing a basis for item design and item generation. However, despite the many advantages of applying LLTM to test items, it has been applied less often to understand the sources of complexity for large-scale operational test items. Instead, previously calibrated item parameters are modeled using regression techniques because raw item response data often cannot be made available. In the current study, both LLTM and regression modeling are applied to mathematical problem solving items from a widely used test. The findings from the two methods are compared and contrasted for their implications for continued development of ability and achievement tests based on mathematical problem solving items.

The Correlation Study of Interest at Physics and Knowledge of Mathematics Basic Concepts towards the Ability to Solve Physics Problems of 7th Grade Students at Junior High School in Ambon Maluku Province, Indonesia

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Izaak Hendrik Wenno

2015-01-01

Full Text Available The purpose of the study is to determine the relation between interest at Physics and knowledge of Mathematics basic concepts with the ability to solve Physics problems. The populations are all students in the 7th grade at the junior high school in Ambon, Maluku, Indonesia. The used sample schools are Junior High Schools 8, 9, and 10 during 2013/2014 academic year with 44 students per school. Two independent variables and one dependent variable are studied. The independent variables are the interest at Physics (X1 and the knowledge of Mathematics basic concepts (X2, while the dependent variable is the ability to solve Physics problems (Y. Data collection technique for X1 is an interview with questionnaire instrument, while for the X2 and Y is using the test technique with test items instrument. The obtained data from the measurements were analyzed with descriptive analysis and inferential analysis. The results show that there is a positive relation between interest at Physics and knowledge of Mathematics basic concepts with students’ ability to solve Physics problems.

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

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Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

Tracing for the problem-solving ability in advanced calculus class based on modification of SAVI model at Universitas Negeri Semarang

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Pujiastuti, E.; Waluya, B.; Mulyono

2018-03-01

There were many ways of solving the problem offered by the experts. The author combines various ways of solving the problem as a form of novelty. Among the learning model that was expected to support the growth of problem-solving skills was SAVI. The purpose, to obtain trace results from the analysis of the problem-solving ability of students in the Dual Integral material. The research method was a qualitative approach. Its activities include tests was filled with mathematical connections, observation, interviews, FGD, and triangulation. The results were: (1) some students were still experiencing difficulties in solving the problems. (2) The application of modification of SAVI learning model effective in supporting the growth of problem-solving abilities. (3) The strength of the students related to solving the problem, there were two students in the excellent category, there were three students in right classes and one student in the medium group.

Factors affecting the social problem-solving ability of baccalaureate nursing students.

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Lau, Ying

2014-01-01

The hospital environment is characterized by time pressure, uncertain information, conflicting goals, high stakes, stress, and dynamic conditions. These demands mean there is a need for nurses with social problem-solving skills. This study set out to (1) investigate the social problem-solving ability of Chinese baccalaureate nursing students in Macao and (2) identify the association between communication skill, clinical interaction, interpersonal dysfunction, and social problem-solving ability. All nursing students were recruited in one public institute through the census method. The research design was exploratory, cross-sectional, and quantitative. The study used the Chinese version of the Social Problem Solving Inventory short form (C-SPSI-R), Communication Ability Scale (CAS), Clinical Interactive Scale (CIS), and Interpersonal Dysfunction Checklist (IDC). Macao nursing students were more likely to use the two constructive or adaptive dimensions rather than the three dysfunctional dimensions of the C-SPSI-R to solve their problems. Multiple linear regression analysis revealed that communication ability (ß=.305, pproblem-solving after controlling for covariates. Macao has had no problem-solving training in its educational curriculum; an effective problem-solving training should be implemented as part of the curriculum. With so many changes in healthcare today, nurses must be good social problem-solvers in order to deliver holistic care. Copyright © 2012 Elsevier Ltd. All rights reserved.

Empowering Educationally Disadvantaged Mathematics Students through a Strategies-Based Problem Solving Approach

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Ramnarain, Umesh

2014-01-01

A major impediment to problem solving in mathematics in the great majority of South African schools is that disadvantaged students from seriously impoverished learning environments are lacking in the necessary informal mathematical knowledge to develop their own strategies for solving non-routine problems. A randomized pretest-posttest control…

A Rubric for Assessing Students' Experimental Problem-Solving Ability

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Shadle, Susan E.; Brown, Eric C.; Towns, Marcy H.; Warner, Don L.

2012-01-01

The ability to couple problem solving both to the understanding of chemical concepts and to laboratory practices is an essential skill for undergraduate chemistry programs to foster in our students. Therefore, chemistry programs must offer opportunities to answer real problems that require use of problem-solving processes used by practicing…

Assessing the Internal Dynamics of Mathematical Problem Solving in Small Groups.

Science.gov (United States)

Artzt, Alice F.; Armour-Thomas, Eleanor

The purpose of this exploratory study was to examine the problem-solving behaviors and perceptions of (n=27) seventh-grade students as they worked on solving a mathematical problem within a small-group setting. An assessment system was developed that allowed for this analysis. To assess problem-solving behaviors within a small group a Group…

The Effect of Problem Solving and Problem Posing Models and Innate Ability to Students Achievement

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Ratna Kartika Irawati

2015-04-01

Full Text Available Pengaruh Model Problem Solving dan Problem Posing serta Kemampuan Awal terhadap Hasil Belajar Siswa   Abstract: Chemistry concepts understanding features abstract quality and requires higher order thinking skills. Yet, the learning on chemistry has not boost the higher order thinking skills of the students. The use of the learning model of Problem Solving and Problem Posing in observing the innate ability of the student is expected to resolve the issue. This study aims to determine the learning model which is effective to improve the study of the student with different level of innate ability. This study used the quasi-experimental design. The research data used in this research is the quiz/test of the class which consist of 14 multiple choice questions and 5 essay questions. The data analysis used is ANOVA Two Ways. The results showed that Problem Posing is more effective to improve the student compared to Problem Solving, students with high level of innate ability have better outcomes in learning rather than the students with low level of innate ability after being applied with the Problem solving and Problem posing model, further, Problem Solving and Problem Posing is more suitable to be applied to the students with high level of innate ability. Key Words: problem solving, problem posing, higher order thinking skills, innate ability, learning outcomes   Abstrak: Pemahaman konsep-konsep kimia yang bersifat abstrak membutuhkan keterampilan berpikir tingkat tinggi. Pembelajaran kimia belum mendorong siswa melakukan keterampilan berpikir tingkat tinggi. Penggunaan model pembelajaran Problem Solving dan Problem Posing dengan memperhatikan kemampuan awal siswa diduga dapat mengatasi masalah tersebut. Penelitian ini bertujuan untuk mengetahui model pembelajaran yang efektif dalam meningkatkan hasil belajar dengan kemampuan awal siswa yang berbeda. Penelitian ini menggunakan rancangan eksperimen semu. Data penelitian menggunakan tes hasil belajar

The effects of stating problems in bilingual students' first and second languages on solving mathematical word problems.

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Bernardo, Allan B I; Calleja, Marissa O

2005-03-01

Researchers have suggested that among bilinguals, solving word problems in mathematics is influenced by linguistic factors (K. Durkin & B. Shire, 1991; L. Verschaffel, B. Greer, & E. De Corte, 2000). Others have suggested that students exhibit a strong tendency to exclude real-world constraints in solving mathematics word problems (L. Verschaffel, E. De Corte, & S. Lasure, 1994). In the present study, the authors explored the effects of stating word problems in either Filipino or English on how Filipino-English bilingual students solved word problems in which the solution required the application of real-world knowledge. The authors asked bilingual students to solve word problems in either their first or second language. For some of the word problems, real-life constraints prevented straightforward application of mathematical procedures. The authors analyzed the students' solutions to determine whether the language of the word problems affected the tendency to apply real-life constraints in the solution. Results showed that the bilingual students (a) rarely considered real-life constraints in their solutions, (b) were more successful in understanding and solving word problems that were stated in their first language, and (c) were more likely to experience failure in finding a solution to problems stated in their second language. The results are discussed in terms of the relationship between linguistic and mathematical problem-solving processes among bilinguals.

Investigation of Problem-Solving and Problem-Posing Abilities of Seventh-Grade Students

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Arikan, Elif Esra; Ünal, Hasan

2015-01-01

This study aims to examine the effect of multiple problem-solving skills on the problem-posing abilities of gifted and non-gifted students and to assess whether the possession of such skills can predict giftedness or affect problem-posing abilities. Participants' metaphorical images of problem posing were also explored. Participants were 20 gifted…

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

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Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

INVESTIGATING AND COMMUNICATING TECHNOLOGY MATHEMATICS PROBLEM SOLVING EXPERIENCE OF TWO PRESERVICE TEACHERS

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Ana Kuzle

2012-04-01

Full Text Available In this paper, I report on preservice teachers’ reflections and perceptions on theirproblem-solving process in a technological context. The purpose of the study was to to investigatehow preservice teachers experience working individually in a dynamic geometry environment andhow these experiences affect their own mathematical activity when integrating content (nonroutineproblems and context (technology environment. Careful analysis of participants’ perceptionsregarding their thinking while engaged in problem solving, provided an opportunity to explorehow they explain the emergence of problem solving when working in a dynamic geometryenvironment. The two participants communicated their experience both through the lenses ofthemselves as problem solvers and as future mathematics educators. Moreover, the results of thestudy indicated that problem solving in a technology environment does not necessarily allow focuson decision-making, reflection, and problem solving processes as reported by previous research.

Authentic assessment based showcase portfolio on learning of mathematical problem solving in senior high school

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Sukmawati, Zuhairoh, Faihatuz

2017-05-01

The purpose of this research was to develop authentic assessment model based on showcase portfolio on learning of mathematical problem solving. This research used research and development Method (R & D) which consists of four stages of development that: Phase I, conducting a preliminary study. Phase II, determining the purpose of developing and preparing the initial model. Phase III, trial test of instrument for the initial draft model and the initial product. The respondents of this research are the students of SMAN 8 and SMAN 20 Makassar. The collection of data was through observation, interviews, documentation, student questionnaire, and instrument tests mathematical solving abilities. The data were analyzed with descriptive and inferential statistics. The results of this research are authentic assessment model design based on showcase portfolio which involves: 1) Steps in implementing the authentic assessment based Showcase, assessment rubric of cognitive aspects, assessment rubric of affective aspects, and assessment rubric of skill aspect. 2) The average ability of the students' problem solving which is scored by using authentic assessment based on showcase portfolio was in high category and the students' response in good category.

Problem solving strategies integrated into nursing process to promote clinical problem solving abilities of RN-BSN students.

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Wang, Jing-Jy; Lo, Chi-Hui Kao; Ku, Ya-Lie

2004-11-01

A set of problem solving strategies integrated into nursing process in nursing core courses (PSNP) was developed for students enrolled in a post-RN baccalaureate nursing program (RN-BSN) in a university in Taiwan. The purpose of this study, therefore, was to evaluate the effectiveness of PSNP on students' clinical problem solving abilities. The one-group post-test design with repeated measures was used. In total 114 nursing students with 47 full-time students and 67 part-time students participated in this study. The nursing core courses were undertaken separately in three semesters. After each semester's learning, students would start their clinical practice, and were asked to submit three written nursing process recordings during each clinic. Assignments from the three practices were named post-test I, II, and III sequentially, and provided the data for this study. The overall score of problem solving indicated that score on the post-test III was significantly better than that on post-test I and II, meaning both full-time and part-time students' clinical problem solving abilities improved at the last semester. In conclusion, problem-solving strategies integrated into nursing process designed for future RN-BSN students are recommendable.

Robotic Toys as a Catalyst for Mathematical Problem Solving

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Highfield, Kate

2010-01-01

Robotic toys present unique opportunities for teachers of young children to integrate mathematics learning with engaging problem-solving tasks. This article describes a series of tasks using Bee-bots and Pro-bots, developed as part a larger project examining young children's use of robotic toys as tools in developing mathematical and metacognitive…

The effects of presenting multidigit mathematics problems in a realistic context on sixth graders' problem solving

NARCIS (Netherlands)

Hickendorff, M.

2013-01-01

Mathematics education and assessments increasingly involve arithmetic problems presented in context: a realistic situation that requires mathematical modeling. This study assessed the effects of such typical school mathematics contexts on two aspects of problem solving: performance and strategy use.

Problem solving as a challenge for mathematics education in The Netherlands

NARCIS (Netherlands)

Doorman, M.; Drijvers, P.; Dekker, T.; Heuvel-Panhuizen, T. van; Lange, J. de; Wijers, M.

2007-01-01

This paper deals with the challenge to establish problem solving as a living domain in mathematics education in The Netherlands. While serious attempts are made to implement a problem-oriented curriculum based on principles of realistic mathematics education with room for modelling and with

University Students' Problem Posing Abilities and Attitudes towards Mathematics.

Science.gov (United States)

Grundmeier, Todd A.

2002-01-01

Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)

Developing a pedagogical problem solving view for mathematics teachers with two reflection programs

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Bracha KRAMARSKI

2009-10-01

Full Text Available The study investigated the effects of two reflection support programs on elementary school mathematics teachers’ pedagogical problem solving view. Sixty-two teachers participated in a professional development program. Thirty teachers were assigned to the self-questioning (S_Q training and thirty two teachers were assigned to the reflection discourse (R_D training. The S_Q program was based on the IMPROVE self-questioning approach which emphasizes systematic discussion along the phases of mathematical or pedagogical problem solving as student and teacher. The R_D program emphasized discussion of standard based teaching and learning principles. Findings indicated that systematic reflection support (S_Q is effective for developing mathematics PCK, and strengthening metacognitive knowledge of mathematics teachers, more than reflection discourse (R_D. No differences were found between the groups in developing beliefs about teaching mathematics in using problem solving view.

Students’ conceptions and problem-solving ability on topic chemical thermodynamics

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Diawati, Chansyanah, E-mail: chansyanahd@yahoo.com [Program Studi Pendidikan Kimia Jurusan PMIPA FKIP, Universitas Lampung, Jl. Prof. Dr. Soemantri Brodjonegoro No. 1 Gedung Meneng, Bandar Lampung35145 (Indonesia)

2016-02-08

The enthalpy concept and its change were introduced to describe the forms of internal energy transfer in chemical reactions. Likewise, the concepts of exothermic and endothermic reactions introduced as a consequence of heat transfer form. In the heat measurement process at constant pressure, work is often ignored. The exothermic or endothermic reactions, usually only based on the increase or decrease of the reaction temperature, without associated with the internal energy. Depictions of enthalpy and its change assumed closely related to students’ problem-solving ability. Therefore, the study to describe pre-service chemistry teacher student’s conceptions and problem-solving ability on topic chemical thermodynamics has been done. This research was a case study of chemical education course in Provinsi Lampung. The subjects of this study were 42 students who attend the chemical thermodynamics course. Questions about exothermic and endothermic reactions, enthalpy and its change, as well as internal energy and its change were given in the form of an essay exam questions. Answers related to conception qualitatively categorized, while problem solving answers were scored and assessed. The results showed that, in general, students were having problems in enthalpy and describe the changes in the form of heat and work. The highest value of problem solving ability obtained 26.67 from the maximum value of 100. The lowest value was 0, and the average value was 14.73. These results show that the problem-solving ability of pre-service chemistry teacher students was low. The results provide insight to researchers, and educators to develop learning or lab work on this concept.

Students’ conceptions and problem-solving ability on topic chemical thermodynamics

International Nuclear Information System (INIS)

Diawati, Chansyanah

2016-01-01

The enthalpy concept and its change were introduced to describe the forms of internal energy transfer in chemical reactions. Likewise, the concepts of exothermic and endothermic reactions introduced as a consequence of heat transfer form. In the heat measurement process at constant pressure, work is often ignored. The exothermic or endothermic reactions, usually only based on the increase or decrease of the reaction temperature, without associated with the internal energy. Depictions of enthalpy and its change assumed closely related to students’ problem-solving ability. Therefore, the study to describe pre-service chemistry teacher student’s conceptions and problem-solving ability on topic chemical thermodynamics has been done. This research was a case study of chemical education course in Provinsi Lampung. The subjects of this study were 42 students who attend the chemical thermodynamics course. Questions about exothermic and endothermic reactions, enthalpy and its change, as well as internal energy and its change were given in the form of an essay exam questions. Answers related to conception qualitatively categorized, while problem solving answers were scored and assessed. The results showed that, in general, students were having problems in enthalpy and describe the changes in the form of heat and work. The highest value of problem solving ability obtained 26.67 from the maximum value of 100. The lowest value was 0, and the average value was 14.73. These results show that the problem-solving ability of pre-service chemistry teacher students was low. The results provide insight to researchers, and educators to develop learning or lab work on this concept

Are middle school mathematics teachers able to solve word problems without using variable?

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Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tuğba; Soylu, Yasin

2018-01-01

Many people consider problem solving as a complex process in which variables such as x, y are used. Problems may not be solved by only using 'variable.' Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is obvious that mathematics teachers should solve problems through concrete processes. In this context, middle school mathematics teachers' skills to solve word problems without using variables were examined in the current study. Through the case study method, this study was conducted with 60 middle school mathematics teachers who have different professional experiences in five provinces in Turkey. A test consisting of five open-ended word problems was used as the data collection tool. The content analysis technique was used to analyze the data. As a result of the analysis, it was seen that the most of the teachers used trial-and-error strategy or area model as the solution strategy. On the other hand, the teachers who solved the problems using variables such as x, a, n or symbols such as Δ, □, ○, * and who also felt into error by considering these solutions as without variable were also seen in the study.

Is There a Causal Relation between Mathematical Creativity and Mathematical Problem-Solving Performance?

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Tyagi, Tarun Kumar

2016-01-01

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

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Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

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Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

PROBLEM SOLVING IN SCHOOL MATHEMATICS BASED ON HEURISTIC STRATEGIES

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NOVOTNÁ, Jarmila

2014-03-01

Full Text Available The paper describes one of the ways of developing pupils’ creative approach to problem solving. The described experiment is a part of a longitudinal research focusing on improvement of culture of problem solving by pupils. It deals with solving of problems using the following heuristic strategies: Analogy, Guess – check – revise, Systematic experimentation, Problem reformulation, Solution drawing, Way back and Use of graphs of functions. Most attention is paid to the question whether short-term work, in this case only over the period of three months, can result in improvement of pupils’ abilities to solve problems whose solving algorithms are easily accessible. It also answers the question which strategies pupils will prefer and with what results. The experiment shows that even short-term work can bear positive results as far as pupils’ approach to problem solving is concerned.

Strategies That Help Learning-Disabled Students Solve Verbal Mathematical Problems.

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Giordano, Gerard

1990-01-01

Strategies are presented for dealing with factors that can be responsible for failure in mathematical problem solving. The suggestions include personalization of verbal problems, thematic strands based on student interests, visual representation, a laboratory approach, and paraphrasing. (JDD)

The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

Science.gov (United States)

Träff, Ulf

2013-10-01

This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

The Investigation of Elementary Mathematics Teacher Candidates' Problem Solving Skills According to Various Variables

Science.gov (United States)

Kaya, Deniz; Izgiol, Dilek; Kesan, Cenk

2014-01-01

The aim was to determine elementary mathematics teacher candidates' problem solving skills and analyze problem solving skills according to various variables. The data were obtained from total 306 different grade teacher candidates receiving education in Department of Elementary Mathematics Education, Buca Faculty of Education, Dokuz Eylul…

Towards efficient measurement of metacognition in mathematical problem solving

NARCIS (Netherlands)

Jacobse, Annemieke E.; Harskamp, Egbert G.

Metacognitive monitoring and regulation play an essential role in mathematical problem solving. Therefore, it is important for researchers and practitioners to assess students' metacognition. One proven valid, but time consuming, method to assess metacognition is by using think-aloud protocols.

Problem-solving rubrics revisited: Attending to the blending of informal conceptual and formal mathematical reasoning

Science.gov (United States)

Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew

2013-06-01

Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.

Development of syntax of intuition-based learning model in solving mathematics problems

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Yeni Heryaningsih, Nok; Khusna, Hikmatul

2018-01-01

The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and

Obstacles Related to Structuring for Mathematization Encountered by Students when Solving Physics Problems

DEFF Research Database (Denmark)

Niss, Martin

2017-01-01

This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called structuring for mathematization, where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report...

Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability

Science.gov (United States)

Maslukha, M.; Lukito, A.; Ekawati, R.

2018-01-01

Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.

The Construction of Mathematical Literacy Problems for Geometry

Science.gov (United States)

Malasari, P. N.; Herman, T.; Jupri, A.

2017-09-01

The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.

Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom

Science.gov (United States)

Fletcher, Nicole

2014-01-01

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

Examination Of Gifted Students’ Probability Problem Solving Process In Terms Of Mathematical Thinking

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Serdal BALTACI

2016-10-01

Full Text Available It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students’ probability problem-solving process related to daily life in terms of mathematical thinking skills. In this regard, a case study was used in the study. The participants of the study were six students at 8th grade (four girls and two boys from the Science and Art Center. One of the purposeful sampling methods, maximum variation sampling was used for selecting the participants. Clinical interview and problems were used as a data collection tool. As a results of the study, it was determined that gifted students use reasoning and strategies skill, which is one of the mathematical thinking skills, mostly on the process of probability problem solving, and communication skills at least.

Promoting students’ mathematical problem-solving skills through 7e learning cycle and hypnoteaching model

Science.gov (United States)

Saleh, H.; Suryadi, D.; Dahlan, J. A.

2018-01-01

The aim of this research was to find out whether 7E learning cycle under hypnoteaching model can enhance students’ mathematical problem-solving skill. This research was quasi-experimental study. The design of this study was pretest-posttest control group design. There were two groups of sample used in the study. The experimental group was given 7E learning cycle under hypnoteaching model, while the control group was given conventional model. The population of this study was the student of mathematics education program at one university in Tangerang. The statistical analysis used to test the hypothesis of this study were t-test and Mann-Whitney U. The result of this study show that: (1) The students’ achievement of mathematical problem solving skill who obtained 7E learning cycle under hypnoteaching model are higher than the students who obtained conventional model; (2) There are differences in the students’ enhancement of mathematical problem-solving skill based on students’ prior mathematical knowledge (PMK) category (high, middle, and low).

Enhancing Learners' Problem Solving Performance in Mathematics: A Cognitive Load Perspective

Science.gov (United States)

Dhlamini, Joseph J.

2016-01-01

This paper reports on a pilot study that investigated the effect of implementing a context-based problem solving instruction (CBPSI) to enhance the problem solving performance of high school mathematics learners. Primarily, the pilot study aimed: (1) to evaluate the efficiency of data collection instruments; and, (2) to test the efficacy of CBPSI…

Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students' mathematical literacy

Directory of Open Access Journals (Sweden)

Sunisa Sumirattana

2017-09-01

This study was based on research and development design. The main purposes of this study were to develop an instructional process for enhancing mathematical literacy among students in secondary school and to study the effects of the developed instructional process on mathematical literacy. The instructional process was developed by analyzing and synthesizing realistic mathematics education and the DAPIC problem-solving process. The developed instructional process was verified by experts and was trialed. The designated pre-test/post-test control method was used to study the effectiveness of the developed instructional process on mathematical literacy. The sample consisted of 104 ninth grade students from a secondary school in Bangkok, Thailand. The developed instructional process consisted of five steps, namely (1 posing real life problems, (2 solving problems individually or in a group, (3 presenting and discussing, (4 developing formal mathematics, and (5 applying knowledge. The mathematical literacy of the experimental group was significantly higher after being taught through the instructional process. The same results were obtained when comparing the results of the experimental group with the control group.

Attitude and practice of physical activity and social problem-solving ability among university students.

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Sone, Toshimasa; Kawachi, Yousuke; Abe, Chihiro; Otomo, Yuki; Sung, Yul-Wan; Ogawa, Seiji

2017-04-04

Effective social problem-solving abilities can contribute to decreased risk of poor mental health. In addition, physical activity has a favorable effect on mental health. These previous studies suggest that physical activity and social problem-solving ability can interact by helping to sustain mental health. The present study aimed to determine the association between attitude and practice of physical activity and social problem-solving ability among university students. Information on physical activity and social problem-solving was collected using a self-administered questionnaire. We analyzed data from 185 students who participated in the questionnaire surveys and psychological tests. Social problem-solving as measured by the Social Problem-Solving Inventory-Revised (SPSI-R) (median score 10.85) was the dependent variable. Multiple logistic regression analysis was employed to calculate the odds ratios (ORs) and 95% confidence intervals (CIs) for higher SPSI-R according to physical activity categories. The multiple logistic regression analysis indicated that the ORs (95% CI) in reference to participants who said they never considered exercising were 2.08 (0.69-6.93), 1.62 (0.55-5.26), 2.78 (0.86-9.77), and 6.23 (1.81-23.97) for participants who did not exercise but intended to start, tried to exercise but did not, exercised but not regularly, and exercised regularly, respectively. This finding suggested that positive linear association between physical activity and social problem-solving ability (p value for linear trend social problem-solving ability.

The effect of problem posing and problem solving with realistic mathematics education approach to the conceptual understanding and adaptive reasoning

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Mahendra, Rengga; Slamet, Isnandar; Budiyono

2017-12-01

One of the difficulties of students in learning mathematics is on the subject of geometry that requires students to understand abstract things. The aim of this research is to determine the effect of learning model Problem Posing and Problem Solving with Realistic Mathematics Education Approach to conceptual understanding and students' adaptive reasoning in learning mathematics. This research uses a kind of quasi experimental research. The population of this research is all seventh grade students of Junior High School 1 Jaten, Indonesia. The sample was taken using stratified cluster random sampling technique. The test of the research hypothesis was analyzed by using t-test. The results of this study indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students' conceptual understanding significantly in mathematics learning. In addition tu, the results also showed that the model of Problem Solving learning with Realistic Mathematics Education Approach can improve students' adaptive reasoning significantly in learning mathematics. Therefore, the model of Problem Posing and Problem Solving learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on the subject of geometry so as to improve conceptual understanding and students' adaptive reasoning. Furthermore, the impact can improve student achievement.

Investigating and developing engineering students' mathematical modelling and problem-solving skills

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Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-09-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

The Use of a Bar Model Drawing to Teach Word Problem Solving to Students with Mathematics Difficulties

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Morin, Lisa L.; Watson, Silvana M. R.; Hester, Peggy; Raver, Sharon

2017-01-01

For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based…

Investigating Pre-service Mathematics Teachers’ Geometric Problem Solving Process in Dynamic Geometry Environment

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Deniz Özen

2013-03-01

Full Text Available The aim of this study is to investigate pre-service elementary mathematics teachers’ open geometric problem solving process in a Dynamic Geometry Environment. With its qualitative inquiry based research design employed, the participants of the study are three pre-service teachers from 4th graders of the Department of Elementary Mathematics Teaching. In this study, clinical interviews, screencaptures of the problem solving process in the Cabri Geomery Environment, and worksheets included 2 open geometry problems have been used to collect the data. It has been investigated that all the participants passed through similar recursive phases as construction, exploration, conjecture, validate, and justification in the problem solving process. It has been thought that this study provide a new point of view to curriculum developers, teachers and researchers

Modeling Students' Problem Solving Performance in the Computer-Based Mathematics Learning Environment

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Lee, Young-Jin

2017-01-01

Purpose: The purpose of this paper is to develop a quantitative model of problem solving performance of students in the computer-based mathematics learning environment. Design/methodology/approach: Regularized logistic regression was used to create a quantitative model of problem solving performance of students that predicts whether students can…

Encouraging Sixth-Grade Students' Problem-Solving Performance by Teaching through Problem Solving

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Bostic, Jonathan D.; Pape, Stephen J.; Jacobbe, Tim

2016-01-01

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

Social Problem Solving Ability Predicts Mental Health Among Undergraduate Students

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Ranjbar, Mansour; Bayani, Ali Asghar; Bayani, Ali

2013-01-01

Background : The main objective of this study was predicting student′s mental health using social problem solving- ability . Methods : In this correlational- descriptive study, 369 (208 female and 161 male) from, Mazandaran University of Medical Science were selected through stratified random sampling method. In order to collect the data, the social problem solving inventory-revised and general health questionnaire were used. Data were analyzed through SPSS-19, Pearson′s correlation, t tes...

Critical Thinking and Problem Solving Skills in Mathematics of Grade-7 Public Secondary Students

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Emil C. Alcantara

2017-11-01

Full Text Available The study aimed to assess the academic performance, critical thinking skills, and problem solving skills in mathematics of Grade-7 students in the five central public secondary schools of Area 2, Division of Batangas, Philippines. This study utilized descriptive method of research. Three hundred forty one (341 students of the public secondary schools out of the total of 2,324 Grade-7 students were selected through systematic random sampling as the subjects of the study. It was found out that the level of performance in Mathematics of the Grade-7 students is proficient. The level of critical thinking skills of students from the different schools is above average as well as their level of problem solving skills. The mathematics performance of the students is positively correlated to their level of critical thinking skills and problem solving skills. Students considered the following learning competencies in the different content areas of Grade-7 Mathematics as difficult to master: solving problems involving sets, describing the development of measurement from the primitive to the present international system of units, finding a solution of an equation or inequality involving one variable, using compass and straightedge to bisect line segments and angles, and analyzing, interpreting accurately and drawing conclusions from graphic and tabular presentations of statistical data.

Addressing Mathematization Obstacles with Unformalized Problems in Physics Education

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Niss, Martin

2018-01-01

Abstract: Solving a physics problem requires that the problem solver either implicitly or explicitly structure the problem situation in such a way that she can set up the mathematical equations based on the relevant physics. This part of the mathematization process has been shown to cause obstacles...... for students (Niss, 2016). In the paper, we show how the students’ ability to perform this mathematization process can be trained by using so-called unformalized physics problems. Some examples of how this training can be done are provided from a course on problem solving in physics taught at Roskilde...

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

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Kim-Leong Lai

2009-07-01

Full Text Available This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while

Diagrams benefit symbolic problem-solving.

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Chu, Junyi; Rittle-Johnson, Bethany; Fyfe, Emily R

2017-06-01

The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic equations can benefit problem-solving performance as well. We tested the impact of diagram presence on students' performance on algebra equation problems to determine whether diagrams increase problem-solving success. We also examined the influence of item- and student-level factors to test the robustness of the diagram effect. We worked with 61 seventh-grade students who had received 2 months of pre-algebra instruction. Students participated in an experimenter-led classroom session. Using a within-subjects design, students solved algebra problems in two matched formats (equation and equation-with-diagram). The presence of diagrams increased equation-solving accuracy and the use of informal strategies. This diagram benefit was independent of student ability and item complexity. The benefits of diagrams found previously for story problems generalized to symbolic problems. The findings are consistent with cognitive models of problem-solving and suggest that diagrams may be a useful additional representation of symbolic problems. © 2017 The British Psychological Society.

How Cognitive Style and Problem Complexity Affect Preservice Agricultural Education Teachers' Abilities to Solve Problems in Agricultural Mechanics

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Blackburn, J. Joey; Robinson, J. Shane; Lamm, Alexa J.

2014-01-01

The purpose of this experimental study was to determine the effects of cognitive style and problem complexity on Oklahoma State University preservice agriculture teachers' (N = 56) ability to solve problems in small gasoline engines. Time to solution was operationalized as problem solving ability. Kirton's Adaption-Innovation Inventory was…

Helping Students with Emotional and Behavioral Disorders Solve Mathematics Word Problems

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Alter, Peter

2012-01-01

The author presents a strategy for helping students with emotional and behavioral disorders become more proficient at solving math word problems. Math word problems require students to go beyond simple computation in mathematics (e.g., adding, subtracting, multiplying, and dividing) and use higher level reasoning that includes recognizing relevant…

A case study of analyzing 11th graders’ problem solving ability on heat and temperature topic

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Yulianawati, D.; Muslim; Hasanah, L.; Samsudin, A.

2018-05-01

Problem solving ability must be owned by students after the process of physics learning so that the concept of physics becomes meaningful. Consequently, the research aims to describe their problem solving ability. Metacognition is contributed to physics learning to the success of students in solving problems. This research has already been implemented to 37 science students (30 women and 7 men) of eleventh grade from one of the secondary schools in Bandung. The research methods utilized the single case study with embedded research design. The instrument is Heat and Temperature Problem Solving Ability Test (HT-PSAT) which consists of twelve questions from three context problems. The result shows that the average value of the test is 8.27 out of the maximum total value of 36. In conclusion, eleventh graders’ problem-solving ability is still under expected. The implication of the findings is able to create learning situations which are probably developing students to embrace better problem solving ability.

Teacher Formation in the Mathematical Thinking through Problem Solving in the Second Phase of the CCyM Network of Reading Comprehension and Mathematics

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LUZ STELLA LÓPEZ

2008-12-01

Full Text Available This article shares the design, implementation, and evaluation of theLesson Study process used for the professional development of teachers of mathematics, through the Red de Comprensión Lectora y Matemáticas – CCyM Network, in ways to teach mathematics through problem solving. The program began with a course on the implementation of the Thinking Classroom, followed by the semi-presencial Lesson Study process. An analysis of teacher interactions during the Lesson Study process yielded these categories of study: Group Collective Thinking, Mathematical Pedagogical Content Knowledge, Subject Matter Knowledge, Knowledge about Technology, and Expert Support. The analysis reflected variations in group interactions, in the command of concepts, in reflective practice, in the ability to make arguments and to propose changes in practice, and in the ability to self-regulate.

Write Is Right: Using Graphic Organizers to Improve Student Mathematical Problem Solving

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Zollman, Alan

2012-01-01

Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…

Fluid Ability (Gf and Complex Problem Solving (CPS

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Patrick Kyllonen

2017-07-01

Full Text Available Complex problem solving (CPS has emerged over the past several decades as an important construct in education and in the workforce. We examine the relationship between CPS and general fluid ability (Gf both conceptually and empirically. A review of definitions of the two factors, prototypical tasks, and the information processing analyses of performance on those tasks suggest considerable conceptual overlap. We review three definitions of CPS: a general definition emerging from the human problem solving literature; a more specialized definition from the “German School” emphasizing performance in many-variable microworlds, with high domain-knowledge requirements; and a third definition based on performance in Minimal Complex Systems (MCS, with fewer variables and reduced knowledge requirements. We find a correlation of 0.86 between expert ratings of the importance of CPS and Gf across 691 occupations in the O*NET database. We find evidence that employers value both Gf and CPS skills, but CPS skills more highly, even after controlling for the importance of domain knowledge. We suggest that this may be due to CPS requiring not just cognitive ability but additionally skill in applying that ability in domains. We suggest that a fruitful future direction is to explore the importance of domain knowledge in CPS.

Intuitive physics knowledge, physics problem solving and the role of mathematical equations

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Laura Buteler

2012-09-01

Full Text Available The present work explores the role that mathematical equations play in modifying students’ physical intuition (diSessa, 1993. The work is carried out assuming that students achieve a great deal of the refinement in their physical intuitions during problem solving (Sherin, 2006. The study is guided by the question of how the use of mathematical equations contributes to this refinement. The authors aim at expanding on Sherin´s (2006 hypothesis, suggesting a more bounding relation between physical intuitions and mathematics. In this scenario, intuitions play a more compelling role in “deciding” which equations are acceptable and which are not. Our hypothesis is constructed on the basis of three cases: the first published by Sherin (2006 and two more from registries of our own. The three cases are compared and analyzed in relation to the role of mathematical equations in refining – or not – the intuitive knowledge students bring to play during problem solving.

LEVELING STUDENTS’ CREATIVE THINKING IN SOLVING AND POSING MATHEMATICAL PROBLEM

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Tatag Yuli Eko Siswono

2010-07-01

Full Text Available Many researchers assume that people are creative, but their degree ofcreativity is different. The notion of creative thinking level has beendiscussed .by experts. The perspective of mathematics creative thinkingrefers to a combination of logical and divergent thinking which is basedon intuition but has a conscious aim. The divergent thinking is focusedon flexibility, fluency, and novelty in mathematical problem solving andproblem posing. As students have various backgrounds and differentabilities, they possess different potential in thinking patterns,imagination, fantasy and performance; therefore, students have differentlevels of creative thinking. A research study was conducted in order todevelop a framework for students’ levels of creative thinking inmathematics. This research used a qualitative approach to describe thecharacteristics of the levels of creative thinking. Task-based interviewswere conducted to collect data with ten 8thgrade junior secondary schoolstudents. The results distinguished five levels of creative thinking,namely level 0 to level 4 with different characteristics in each level.These differences are based on fluency, flexibility, and novelty inmathematical problem solving and problem posing.Keywords: student’s creative thinking, problem posing, flexibility,fluency, novelty DOI: http://dx.doi.org/10.22342/jme.1.1.794.17-40

Assessing the Relation between Seventh-Grade Students' Engagement and Mathematical Problem Solving Performance

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Lein, Amy E.; Jitendra, Asha K.; Starosta, Kristin M.; Dupuis, Danielle N.; Hughes-Reid, Cheyenne L.; Star, Jon R.

2016-01-01

In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger…

The Different Patterns of Gesture between Genders in Mathematical Problem Solving of Geometry

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Harisman, Y.; Noto, M. S.; Bakar, M. T.; Amam, A.

2017-02-01

This article discusses about students’ gesture between genders in answering problems of geometry. Gesture aims to check students’ understanding which is undefined from their writings. This study is a qualitative research, there were seven questions given to two students of eight grade Junior High School who had the equal ability. The data of this study were collected from mathematical problem solving test, videoing students’ presentation, and interviewing students by asking questions to check their understandings in geometry problems, in this case the researchers would observe the students’ gesture. The result of this study revealed that there were patterns of gesture through students’ conversation and prosodic cues, such as tones, intonation, speech rate and pause. Female students tended to give indecisive gestures, for instance bowing, hesitating, embarrassing, nodding many times in shifting cognitive comprehension, forwarding their body and asking questions to the interviewer when they found tough questions. However, male students acted some gestures such as playing their fingers, focusing on questions, taking longer time to answer hard questions, staying calm in shifting cognitive comprehension. We suggest to observe more sample and focus on students’ gesture consistency in showing their understanding to solve the given problems.

Mathematical enculturation from the students' perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme

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Perrenet, J.C.; Taconis, R.

2009-01-01

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as

Students’ mathematical representations on secondary school in solving trigonometric problems

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Istadi; Kusmayadi, T. A.; Sujadi, I.

2017-06-01

This research aimed to analyse students’ mathematical representations on secondary school in solving trigonometric problems. This research used qualitative method. The participants were 4 students who had high competence of knowledge taken from 20 students of 12th natural-science grade SMAN-1 Kota Besi, Central Kalimantan. Data validation was carried out using time triangulation. Data analysis used Huberman and Miles stages. The results showed that their answers were not only based on the given figure, but also used the definition of trigonometric ratio on verbal representations. On the other hand, they were able to determine the object positions to be observed. However, they failed to determine the position of the angle of depression at the sketches made on visual representations. Failure in determining the position of the angle of depression to cause an error in using the mathematical equation. Finally, they were unsuccessful to use the mathematical equation properly on symbolic representations. From this research, we could recommend the importance of translations between mathematical problems and mathematical representations as well as translations among mathematical representaions (verbal, visual, and symbolic) in learning mathematics in the classroom.

Exploring a Structure for Mathematics Lessons That Foster Problem Solving and Reasoning

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Sullivan, Peter; Walker, Nadia; Borcek, Chris; Rennie, Mick

2015-01-01

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks…

The Enhancement of Mathematical Reasoning Ability of Junior High School Students by Applying Mind Mapping Strategy

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Ayal, Carolina S.; Kusuma, Yaya S.; Sabandar, Jozua; Dahlan, Jarnawi Afgan

2016-01-01

Mathematical reasoning ability, are component that must be governable by the student. Mathematical reasoning plays an important role, both in solving problems and in conveying ideas when learning mathematics. In fact there ability are not still developed well, even in middle school. The importance of mathematical reasoning ability (KPM are…

Student Teachers’ Self-Appraised Problem-Solving Ability and Willingness to Engage in Troubleshooting Activities

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Benedict Iorzer Labe

2015-07-01

Full Text Available The purpose of this research was to determine the extent of student teachers’ willingness to engage in troubleshooting activities and their technological problem-solving self-appraised ability. The study used a cross-sectional descriptive correlational design to collect data from 310 purposively random sampled students from three universities in Northern Nigeria. Results of data analyses indicated that student teachers from the universities surveyed reported a moderate willingness to engage in troubleshooting activities as well as a moderately positive self-appraisal of their problem-solving ability. The student teachers’ willingness to engage in troubleshooting activities was also significantly related to the pattern of their self-appraised problem-solving ability. It was therefore concluded that the findings from this research do not support the pedestrian view that students from Nigerian universities are reluctant to engage in problem-solving activities.

Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story

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Gunbas, N.

2015-01-01

The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…

The development of a professional development intervention for mathematical problem-solving pedagogy in a localised context

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Brantina Chirinda

2017-06-01

Full Text Available This article reports on the design and findings of the first iteration of a classroom-based design research project which endeavours to design a professional development intervention for teachers’ mathematical problem-solving pedagogy. The major outcome of this study is the generation of design principles that can be used by other researchers developing a professional development (PD intervention for mathematical problem-solving pedagogy. This study contributes to the mathematical problem-solving pedagogy and PD body of knowledge by working with teachers in an under-researched environment (an informal settlement in Gauteng, South Africa. In this iteration, two experienced Grade 9 mathematics teachers and their learners at a public secondary school in Gauteng, South Africa, participated in a 6-month intervention. Findings from the data are discussed in light of their implications for the next cycle and other PD studies.

Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

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Winda, A.; Sufyani, P.; Elah, N.

2018-05-01

Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

The Effect of Learning Environments Based on Problem Solving on Students' Achievements of Problem Solving

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Karatas, Ilhan; Baki, Adnan

2013-01-01

Problem solving is recognized as an important life skill involving a range of processes including analyzing, interpreting, reasoning, predicting, evaluating and reflecting. For that reason educating students as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum.…

The Effect of Using an Explicit General Problem Solving Teaching Approach on Elementary Pre-Service Teachers' Ability to Solve Heat Transfer Problems

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Mataka, Lloyd M.; Cobern, William W.; Grunert, Megan L.; Mutambuki, Jacinta; Akom, George

2014-01-01

This study investigate the effectiveness of adding an "explicit general problem solving teaching strategy" (EGPS) to guided inquiry (GI) on pre-service elementary school teachers' ability to solve heat transfer problems. The pre-service elementary teachers in this study were enrolled in two sections of a chemistry course for pre-service…

Mathematical Enculturation from the Students' Perspective: Shifts in Problem-Solving Beliefs and Behaviour during the Bachelor Programme

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Perrenet, Jacob; Taconis, Ruurd

2009-01-01

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill…

Student’s mathematical understanding ability based on self-efficacy

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Ramdhani, M. R.; Usodo, B.; Subanti, S.

2017-11-01

Materials in mathematics are provided not only as an ability to memorize, but also to train the ability of mathematical understanding. Students’ mathematical understanding ability is influenced by the students’ belief in solving the given problems. This research aim to determine the mathematical understanding ability of junior high school students. This research is descriptive qualitative research. Data collection was done through a test, questionnaire, and interview. The result showed that students with high self-efficacy category could master the three indicators of students’ mathematical understanding ability well, namely translation, interpretation, and exploration. Students with moderate self-efficacy category can master translation indicator and able to achieve interpretation indicator but they unable to reach exploration indicator. Students with low self-efficacy category only master the translation, but they cannot achieve the interpretation and exploration indicators. So, the students who have high, moderate or low self-efficacy master the indicator of mathematical understanding based on the level of understanding capabilities on each student.

Metacognitive experience of mathematics education students in open start problem solving based on intrapersonal intelligence

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Sari, D. P.; Usodo, B.; Subanti, S.

2018-04-01

This research aims to describe metacognitive experience of mathematics education students with strong, average, and weak intrapersonal intelligence in open start problem solving. Type of this research was qualitative research. The research subject was mathematics education students in Muhammadiyah University of Surakarta in academic year 2017/2018. The selected students consisted of 6 students with details of two students in each intrapersonal intelligence category. The research instruments were questionnaire, open start problem solving task, and interview guidelines. Data validity used time triangulation. Data analyses were done through data collection, data reduction, data presentation, and drawing conclusion. Based on findings, subjects with strong intrapersonal intelligence had high self confidence that they were able to solve problem correctly, able to do planning steps and able to solve the problem appropriately. Subjects with average intrapersonal intelligence had high self-assessment that they were able to solve the problem, able to do planning steps appropriately but they had not maximized in carrying out the plan so that it resulted incorrectness answer. Subjects with weak intrapersonal intelligence had high self confidence in capability of solving math problem, lack of precision in taking plans so their task results incorrectness answer.

Working Memory, Attention, and Mathematical Problem Solving: A Longitudinal Study of Elementary School Children

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Swanson, H. Lee

2011-01-01

The role of working memory (WM) in children's growth in mathematical problem solving was examined in a longitudinal study of children (N = 127). A battery of tests was administered that assessed problem solving, achievement, WM, and cognitive processing (inhibition, speed, phonological coding) in Grade 1 children, with follow-up testing in Grades…

Find the Dimensions: Students Solving a Tiling Problem

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Obara, Samuel

2018-01-01

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

The Effect of Contextual and Conceptual Rewording on Mathematical Problem-Solving Performance

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Haghverdi, Majid; Wiest, Lynda R.

2016-01-01

This study shows how separate and combined contextual and conceptual problem rewording can positively influence student performance in solving mathematical word problems. Participants included 80 seventh-grade Iranian students randomly assigned in groups of 20 to three experimental groups involving three types of rewording and a control group. All…

Metacognition, Motivation and Emotions: Contribution of Self-Regulated Learning to Solving Mathematical Problems

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Meirav Tzohar-Rozen

2014-11-01

Full Text Available Mathematical problem solving is among the most valuable aspects of mathematics education. It is also the hardest for elementary school students (Verschaffel, Greer & De Corte, 2000. Students experience cognitive and metacognitive difficulties in this area and develop negative emotions and poor motivation which hamper their efforts (Kramarski, Weiss, & Kololshi-Minsker, 2010. 9–11 seems the critical stage for developing attitudes and emotional reactions towards mathematics (Artino, 2009. These metacognitive and motivational-emotional factors are fundamental components of Self-Regulated Learning (SRL, a non-innate process requiring systematic, explicit student training (Pintrich, 2000; Zimmerman, 2000. Most self-regulation studies relating to problem-solving focus on metacognition. Few explore the motivational-emotional component. This study aimed to develop, examine, and compare two SRL interventions dealing with two additional components of self-regulation: metacognitive regulation (MC and motivational-emotional regulation (ME. It also sought to examine the significance of these components and their contribution to learners' problem-solving achievements and self-regulation. The study examined 118 fifth grade students, randomly assigned to two groups. Pre- and post-intervention, the two groups completed self-regulation questionnaires relating to metacognition, motivation, and emotion. They also solved arithmetic series problems presented in two ways (verbal form and numeric form. After intervention we also examined a novel transfer problem. The intervention consisted of 10 hours for 5 weeks. Following the intervention the groups exhibited similar improvements across all the problems. The MC group performed best in metacognitive self-regulation and the ME group performed best in certain motivational-emotional aspects of self-regulation. Research implications are discussed.

Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems

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Mokos, Evagelos; Kafoussi, Sonia

2013-01-01

Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky & Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity has been focused on the area of mathematics problem solving. This study…

Elementary Teachers' Perspectives of Mathematics Problem Solving Strategies

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Bruun, Faye

2013-01-01

Participants in this study were asked to report what strategies were most often used in their attempts to foster their students' problem solving abilities. Participants included 70 second through fifth-grade elementary teachers from 42 schools in a large state of the south central region in the U.S. Data analyses of the interviews revealed that…

Metacognition, Motivation, and Emotions: Contribution of Self-Regulated Learning to Solving Mathematical Problems

Science.gov (United States)

Tzohar-Rozen, Meirav; Kramarski, Bracha

2014-01-01

Mathematical problem solving is one of the most valuable aspects of mathematics education. It is also the most difficult for elementary-school students (Verschaffel, Greer, & De Corte, 2000). Students experience cognitive and metacognitive difficulties in this area and develop negative emotions and poor motivation, which hamper their efforts…

The Relationship Between Problem-Solving Ability and Self-Harm Amongst People with Mild Intellectual Disabilities.

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Rees, Joanna; Langdon, Peter E

2016-07-01

The purpose of this study was to investigate the relationship between depression, hopelessness, problem-solving ability and self-harming behaviours amongst people with mild intellectual disabilities (IDs). Thirty-six people with mild IDs (77.9% women, Mage  = 31.77, SD = 10.73, MIQ  = 62.65, SD = 5.74) who had a history of self-harm were recruited. Participants were asked to complete measures of depression, hopelessness and problem-solving ability. Cutting was most frequently observed, and depression was prevalent amongst the sample. There was a significant positive relationship between depression and hopelessness, while there was no significant relationship between self-harm and depression or hopelessness. Problem-solving ability explained 15% of the variance in self-harm scores. Problem-solving ability appears to be associated with self-harming behaviours in people with mild IDs. © 2015 John Wiley & Sons Ltd.

The profile of problem-solving ability of students of distance education in science learning

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Widiasih; Permanasari, A.; Riandi; Damayanti, T.

2018-05-01

This study aims to analyze the students' problem-solving ability in science learning and lesson-planning ability. The method used is descriptive-quantitative. The subjects of the study were undergraduate students of Distance Higher Education located in Serang, majoring in Primary Teacher Education in-service training. Samples were taken thoroughly from 2 groups taking the course of Science Learning in Primary School in the first term of 2017, amounted to 39 students. The technique of data collection used is essay test of problem solving from case study done at the beginning of lecture in February 2017. The results of this research can be concluded that In-service Training of Primary School Teacher Education Program are categorized as quite capable (score 66) in solving science learning problem and planning science lesson. Therefore, efforts need to be done to improve the ability of students in problem solving, for instance through online tutorials with the basis of interactive discussions.

Effects of Problem-Solving, Guided-Discovery and Expository ...

African Journals Online (AJOL)

This study investigated the relative effectiveness of problem-solving, guideddiscovery, and expository methods of instruction on students performance in redox reaction, considering their mathematics ability. It was a quasiexperimental research using non-randomized-pre-test post-test control group design with expository ...

Review of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan

OpenAIRE

Thomas J. Pfaff

2015-01-01

Mahajan, Sanjoy. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving (The MIT Press, Cambridge, Massachusetts, 2010). 152 pp. ISBN 978--0--262--51429--3 Street-Fighting Mathematics is an engaging collection of problem-solving techniques. The book is not for a general audience, as it requires a significant level of mathematical and scientific background knowledge. In particular, most of the book requires knowledge of Calculus I and there are examples ...

Enhancement of problem solving ability of high school students through learning with real engagement in active problem solving (REAPS) model on the concept of heat transfer

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Yulindar, A.; Setiawan, A.; Liliawati, W.

2018-05-01

This study aims to influence the enhancement of problem solving ability before and after learning using Real Engagement in Active Problem Solving (REAPS) model on the concept of heat transfer. The research method used is quantitative method with 35 high school students in Pontianak as sample. The result of problem solving ability of students is obtained through the test in the form of 3 description questions. The instrument has tested the validity by the expert judgment and field testing that obtained the validity value of 0.84. Based on data analysis, the value of N-Gain is 0.43 and the enhancement of students’ problem solving ability is in medium category. This was caused of students who are less accurate in calculating the results of answers and they also have limited time in doing the questions given.

Fluid Ability (Gf) and Complex Problem Solving (CPS)

OpenAIRE

Patrick Kyllonen; Cristina Anguiano Carrasco; Harrison J. Kell

2017-01-01

Complex problem solving (CPS) has emerged over the past several decades as an important construct in education and in the workforce. We examine the relationship between CPS and general fluid ability (Gf) both conceptually and empirically. A review of definitions of the two factors, prototypical tasks, and the information processing analyses of performance on those tasks suggest considerable conceptual overlap. We review three definitions of CPS: a general definition emerging from the human pr...

Analitycal Descriptive Study of Students' Critical Mathematic Thinking Ability Through Graded Response Model (Grm)

OpenAIRE

nurul, didin; zahra anasha, zara

2013-01-01

Critical mathematic thinking ability is very important to solve daily problems. But in reality, junior high school students' critical mathematic thinking ability is still low. Ability measurement such as measurement of critical mathematic thinking ability cannot be measured through multiple choices test. In that case, an essay test in which graded scoring is used as scoring technique more suitable than multiple choices test. The result of the essay test will be analyzed to describe...

The Relationship between 8th Grade Students’ Opinions about Problem Solving, Beliefs about Mathematics, Learned Hopelessness and Academics Success

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Agaç, Gülay; MASAL, Ercan

2017-01-01

Related literature emphasizes that affective factors are impactful on cognitive factors. For this reason, this study aims at revealing the relationship between problem solving,  which is one of metacognitive characteristics, beliefs about mathematics and learned hopelessness, which are two affective characteristics. Therefore, addressing emotional aspects together with cognitive abilities will give rise to understanding of the students’ current situation and predicting ab...

Problem solving and problem strategies in the teaching and learning ...

African Journals Online (AJOL)

Perennial poor performance recorded annually in both internal and external examinations in Mathematics has been a great concern for the Mathematics Educators in Nigeria. This paper discusses problem-solving and influence of problem-solving strategies on students' performance in mathematics. The concept of ...

Solving a bi-objective mathematical programming model for bloodmobiles location routing problem

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Masoud Rabbani

2017-01-01

Full Text Available Perishability of platelets, uncertainty of donors’ arrival and conflicting views in platelet supply chain have made platelet supply chain planning a problematic issue. In this paper, mobile blood collection system for platelet production is investigated. Two mathematical models are presented to cover the bloodmobile collection planning problem. The first model is a multi-objective fuzzy mathematical programming in which the bloodmobiles locations are considered with the aim of maximizing potential amount of blood collection and minimizing the operational cost. The second model is a vehicle routing problem with time windows which studies the shuttles routing problem. To tackle the first model, it is reformulated as a crisp multi objective linear programming model and then solved through a fuzzy multi objective programming approach. Several sensitivity analysis are conducted on important parameters to demonstrate the applicability of the proposed model. The proposed model is then solved by using a tailored Simulated Annealing (SA algorithm. The numerical results demonstrate promising efficiency of the proposed solution method.

KEEFEKTIFAN PENDEKATAN OPEN-ENDED DAN PROBLEM SOLVING PADA PEMBELAJARAN BANGUN RUANG SISI DATAR DI SMP

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Nuning Melianingsih

2015-11-01

Full Text Available Penelitian ini bertujuan untuk menentukan keefektifan dan perbandingan keefektifan dari pendekatan open-ended dan problem solving pada pembelajaran bangun ruang sisi datar ditinjau dari pencapaian kemampuan penalaran, pemecahan masalah, dan komunikasi matematis. Penelitian ini adalah quasi experiment dengan desain pretest-posttest nonequivalent group design. Populasi penelitian mencakup seluruh siswa kelas VIII SMP Negeri 1 Pandak, Bantul, Yogyakarta. Selanjutnya dengan memilih secara acak dari keseluruhan kelas tersebut, terpilih kelas VIII F dan VIII G sebagai sampel penelitian. Untuk menguji keefektifan masing-masing pendekatan pembelajaran digunakan uji one sample t-test. Untuk menguji bahwa pendekatan open-ended lebih efektif daripada pendekatan problem solving, data dianalisis menggunakan MANOVA yang dilanjutkan dengan uji t-Bonferroni. Hasil penelitian menunjukkan bahwa kedua pendekatan pembelajaran efektif ditinjau dari masing-masing aspek, dan pendekatan open-ended lebih efektif daripada pendekatan problem solving pada pembelajaran bangun ruang sisi datar ditinjau dari pencapaian kemampuan penalaran, pemecahan masalah, dan komunikasi matematis di SMP. Kata Kunci: pendekatan open-ended, pendekatan problem solving, kemampuan penalaran, kemampuan pemecahan masalah, kemampuan komunikasi matematis   THE EFFECTIVENESS OF OPEN-ENDED AND PROBLEM SOLVING APPROACH IN MATTER OF FLAT SIDE CONSTRUCT IN JUNIOR HIGH SCHOOL Abstract The aims of this research are to decide the effectiveness and the comparison of the effectiveness of open-ended and problem solving approach toward matter of flat side construct lesson viewed from achivement of reasoning ability, problem solving and mathematics communication. This study was a quasi experimental study using the pretest-posttest nonequivalent group design. The research population covered the entire VIII class students’ of SMP Negeri 1 Pandak, Bantul, Yogyakarta. From the population, classes of VIII F and

Mathematical problem solving in primary school

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Kolovou, A.

2011-01-01

A student is engaged in (non-routine) problem solving when there is no clear pathway to the solution. In contrast to routine problems, non-routine ones cannot be solved through the direct application of a standard procedure. Consider the following problem: In a quiz you get two points for each

Enabling Metacognitive Skills for Mathematics Problem Solving: A Collective Case Study of Metacognitive Reflection and Awareness

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Jagals, Divan; van der Walt, Marthie

2016-01-01

Metacognition encompasses knowledge and regulation that, through reflection, sustain problem solving behaviour. How metacognitive awareness is constructed from reflection on metacognitive knowledge and regulation and how these reflections enable metacognitive skills for Mathematics problem solving remain unclear. Three secondary schools…

Methods of solving nonstandard problems

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Grigorieva, Ellina

2015-01-01

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.   It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions.  The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem.  Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems.   Over 360 problems are included with hints, ...

Students' Ability to Solve Process-Diagram Problems in Secondary Biology Education

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Kragten, Marco; Admiraal, Wilfried; Rijlaarsdam, Gert

2015-01-01

Process diagrams are important tools in biology for explaining processes such as protein synthesis, compound cycles and the like. The aim of the present study was to measure the ability to solve process-diagram problems in biology and its relationship with prior knowledge, spatial ability and working memory. For this purpose, we developed a test…

The effects of imagery on problem-solving ability and autobiographical memory.

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Dennis, Ashley A; Astell, Arlene; Dritschel, Barbara

2012-12-01

Williams et al. (2006) found that increased imageability of cue words during an autobiographical memory task increased specificity of autobiographical memory (ABM) and improved subsequent social problem-solving (SPS). This study explored whether imagery during SPS improved SPS skill, perceived SPS ability, and the specificity of ABMs retrieved in the process of SPS in dysphoric students. Additionally, this study hypothesised that both memory specificity and perceived SPS ability would positively correlate with SPS skill. Dysphoric and non-dysphoric students solved hypothetical social problems on a modified version of the Means-End Problem-Solving task with a verbal or an imagery focus. Participants also completed a questionnaire about ABMs retrieved during SPS and rated their perceived effectiveness of their solutions. Contrary to Williams et al. (2006), the imagery focus did not improve SPS skill or influence perceived effectiveness. Additionally, in contrast to the hypothesis, the imagery group retrieved more overgeneral memories. Finally, ABM specificity did not correlate with SPS skill. However, dysphoric participants perceived specific memories to be significantly less helpful to SPS whereas non-dysphoric participants perceived specific memories to be helpful potentially supporting work on overgeneral ABM and functional avoidance. Copyright © 2011 Elsevier Ltd. All rights reserved.

Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

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Artzt, Alice F.; Armour-Thomas, Eleanor

1998-01-01

Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…

Effects of "Handep" Cooperative Learning Based on Indigenous Knowledge on Mathematical Problem Solving Skill

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Demitra; Sarjoko

2018-01-01

Indigenous people of Dayak tribe in Kalimantan, Indonesia have traditionally relied on a system of mutual cooperation called "handep." The cultural context has an influence on students mathematics learning. The "handep" system might be suitable for modern learning situations to develop mathematical problem-solving skill. The…

Math Teachers' Attitudes towards Photo Math Application in Solving Mathematical Problem Using Mobile Camera

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Hamadneh, Iyad M.; Al-Masaeed, Aslan

2015-01-01

This study aimed at finding out mathematics teachers' attitudes towards photo math application in solving mathematical problems using mobile camera; it also aim to identify significant differences in their attitudes according to their stage of teaching, educational qualifications, and teaching experience. The study used judgmental/purposive…

Development of Finnish Elementary Pupils’ Problem-Solving Skills in Mathematics

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Anu Laine

2014-09-01

Full Text Available The purpose of this study is to determine how Finnish pupils’ problemsolving skills develop from the 3rd to 5th grade. As research data, we use one non-standard problem from pre- and post-test material from a three-year follow-up study, in the area of Helsinki, Finland. The problems in both tests consisted of four questions related to each other. The purpose of the formulation of the problem was to help the pupils to find how many solutions for a certain answer exist. The participants in the study were 348 third-graders and 356 fifth-graders. Pupils’ fluency, i.e. ability to develop different solutions, was found to correlate with their ability to solve the problem. However, the proportions of the pupils (17% of the 3rd graders and 21% of the 5th graders who answered that there were an infinite number of solutions are of the same magnitude. Thus, the pupils’ ability to solve this kind of problem does not seem to have developed from the 3rd to the 5th grade. The lack and insufficiency of pupils’ justifications reveal the importance of the teacher carefully listening to the pupils’ ideas in order to be able to promote pupils’ understanding of the concept of infinity, as well as the basic calculations.

The Impact of Problem-Based Learning Approach to Senior High School Students’ Mathematics Critical Thinking Ability

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Reviandari Widyatiningtyas

2015-07-01

Full Text Available The study was report the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students’ prior mathematical ability to student’s mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from excellent and moderate school level. The research instruments a set of mathematical critical thinking ability test, and the data were analyzed by using two ways ANOVA and t-test. The research found that the problem based learning approach has significant impact to the ability of students’ mathematics critical thinking in terms of school level and students’ prior mathematical abilities. Furthermore. This research also found that there is no interaction between learning approach and school level, and learning approach and students’ prior mathematics ability to students’ mathematics critical thinking ability.

Academic Motivation Maintenance for Students While Solving Mathematical Problems in the Middle School

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M. Rodionov; Z. Dedovets

2015-01-01

The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.

Impact of the Curriculum Reform on Problem Solving Ability in ...

African Journals Online (AJOL)

An ex post facto study was conducted to examine the effect of the curriculum reform on 60 Dilla University chemistry education students' problem solving ability. The study shows that the curriculum reform that shifted university introductory courses of the old curriculum into preparatory school levels in the new curriculum ...

The development and nature of problem-solving among first-semester calculus students

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Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving

Study of Scientific Problem-Solving Abilities Based on Scientific Knowledge about Atmosphere and Weather for Seventh Grade Students

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Phoorin Thaengnoi

2017-06-01

Full Text Available The purposes of this research were: 1 to develop scientific problem-solving abilities test based on scientific knowledge about atmosphere and weather for seventh grade students and 2 to study the scientific problem-solving abilities of seventh grade students. The samples used in this study were 47 students who were studying in seventh grade in academic year 2015 of a school in Chai Nat province, Thailand. Purposive sampling was applied for identifying the samples. The research instrument of this study was the scientific problem-solving abilities test developed by the researcher. The research data was analyzed by comparing students’ scores with the criteria and considering students’ answers in each element of scientific problem-solving abilities. The results of the study were as follows: The scientific problem-solving abilities test composed of 2 parts. The first part was multiple-choice questions which was composed of 4 situations, a total of 20 questions. The Index of Item Objective Congruence of this part was varied in the range between 0.67 – 1.00. The difficulty and the discrimination level were in the range between 0.33 – 0.63 and 0.27 – 0.67, respectively. The reliability levels of this part was equal to 0.81. The second part of the test was subjective questions which composed of 2 situations, a total of 10 questions. The Index of Item Objective Congruence of this part was varied in the range between 0.67 – 1.00. The reliability level of this part was equal to 0.83. Besides, all questions in the test were covered all elements of scientific problem-solving abilities ; 1 identifying the problem 2 making the hypothesis 3 collecting data and knowledge to solve the problem 4 identifying problem-solving method and 5 predicting the characteristics of the results. The problem-solving abilities of the students revealed that 40.43% of students (n=19 were in a moderate level and 59.57% of students (n=28 were in a low level with the

Turkish Primary School Students' Strategies in Solving a Non-Routine Mathematical Problem and Some Implications for the Curriculum Design and Implementation

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Erdogan, Abdulkadir

2015-01-01

Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

The Prevalent Rate of Problem-Solving Approach in Teaching Mathematics in Ghanaian Basic Schools

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Nyala, Joseph; Assuah, Charles; Ayebo, Abraham; Tse, Newel

2016-01-01

Stakeholders of mathematics education decry the rate at which students' performance are falling below expectation; they call for a shift to practical methods of teaching the subject in Ghanaian basic schools. The study explores the extent to which Ghanaian basic school mathematics teachers use problem-solving approach in their lessons. The…

Teacher-Student Interaction in Joint Word Problem Solving. The Role of Situational and Mathematical Knowledge in Mainstream Classrooms

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Rosales, Javier; Vicente, Santiago; Chamoso, Jose M.; Munez, David; Orrantia, Josetxu

2012-01-01

Word problem solving involves the construction of two different mental representations, namely, mathematical and situational. Although educational research in word problem solving has documented different kinds of instruction at these levels, less is known about how both representational levels are evoked during word problem solving in day-to-day…

Behaviour of mathematics and physics students in solving problem of Vector-Physics context

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Sardi; Rizal, M.; Mansyur, J.

2018-04-01

This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.

Improvement of Word Problem Solving and Basic Mathematics Competencies in Students with Attention Deficit/Hyperactivity Disorder and Mathematical Learning Difficulties

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González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios

2016-01-01

Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…

The ABCs of Math: A Genetic Analysis of Mathematics and Its Links With Reading Ability and General Cognitive Ability

Science.gov (United States)

Hart, Sara A.; Petrill, Stephen A.; Thompson, Lee A.; Plomin, Robert

2009-01-01

The goal of this first major report from the Western Reserve Reading Project Math component is to explore the etiology of the relationship among tester-administered measures of mathematics ability, reading ability, and general cognitive ability. Data are available on 314 pairs of monozygotic and same-sex dizygotic twins analyzed across 5 waves of assessment. Univariate analyses provide a range of estimates of genetic (h2 = .00 –.63) and shared (c2 = .15–.52) environmental influences across math calculation, fluency, and problem solving measures. Multivariate analyses indicate genetic overlap between math problem solving with general cognitive ability and reading decoding, whereas math fluency shares significant genetic overlap with reading fluency and general cognitive ability. Further, math fluency has unique genetic influences. In general, math ability has shared environmental overlap with general cognitive ability and decoding. These results indicate that aspects of math that include problem solving have different genetic and environmental influences than math calculation. Moreover, math fluency, a timed measure of calculation, is the only measured math ability with unique genetic influences. PMID:20157630

Students’ Relational Thinking of Impulsive and Reflective in Solving Mathematical Problem

Science.gov (United States)

Satriawan, M. A.; Budiarto, M. T.; Siswono, T. Y. E.

2018-01-01

This is a descriptive research which qualitatively investigates students’ relational thinking of impulsive and reflective cognitive style in solving mathematical problem. The method used in this research are test and interview. The data analyzed by reducing, presenting and concluding the data. The results of research show that the students’ reflective cognitive style can possibly help to find out important elements in understanding a problem. Reading more than one is useful to identify what is being questioned and write the information which is known, building relation in every element and connecting information with arithmetic operation, connecting between what is being questioned with known information, making equation model to find out the value by using substitution, and building a connection on re-checking, re-reading, and re-counting. The impulsive students’ cognitive style supports important elements in understanding problems, building a connection in every element, connecting information with arithmetic operation, building a relation about a problem comprehensively by connecting between what is being questioned with known information, finding out the unknown value by using arithmetic operation without making any equation model. The result of re-checking problem solving, impulsive student was only reading at glance without re-counting the result of problem solving.

Problem Solving Strategies of Girls and Boys in Single-Sex Mathematics Classrooms

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Che, Megan; Wiegert, Elaine; Threlkeld, Karen

2012-01-01

This study examines patterns in middle-grade boys' and girls' written problem solving strategies for a mathematical task involving proportional reasoning. The students participating in this study attend a coeducational charter middle school with single-sex classrooms. One hundred nineteen sixth-grade students' responses are analyzed by gender…

Assessing Algebraic Solving Ability: A Theoretical Framework

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Lian, Lim Hooi; Yew, Wun Thiam

2012-01-01

Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

Concept mapping learning strategy to enhance students' mathematical connection ability

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Hafiz, M.; Kadir, Fatra, Maifalinda

2017-05-01

The concept mapping learning strategy in teaching and learning mathematics has been investigated by numerous researchers. However, there are still less researchers who have scrutinized about the roles of map concept which is connected to the mathematical connection ability. Being well understood on map concept, it may help students to have ability to correlate one concept to other concept in order that the student can solve mathematical problems faced. The objective of this research was to describe the student's mathematical connection ability and to analyze the effect of using concept mapping learning strategy to the students' mathematical connection ability. This research was conducted at senior high school in Jakarta. The method used a quasi-experimental with randomized control group design with the total number was 72 students as the sample. Data obtained through using test in the post-test after giving the treatment. The results of the research are: 1) Students' mathematical connection ability has reached the good enough level category; 2) Students' mathematical connection ability who had taught with concept mapping learning strategy is higher than who had taught with conventional learning strategy. Based on the results above, it can be concluded that concept mapping learning strategycould enhance the students' mathematical connection ability, especially in trigonometry.

An investigation of the effects of interventions on problem-solving strategies and abilities

Science.gov (United States)

Cox, Charles Terrence, Jr.

Problem-solving has been described as being the "heart" of the chemistry classroom, and students' development of problem-solving skills is essential for their success in chemistry. Despite the importance of problem-solving, there has been little research within the chemistry domain, largely because of the lack of tools to collect data for large populations. Problem-solving was assessed using a software package known as IMMEX (for Interactive Multimedia Exercises) which has an HTML tracking feature that allows for collection of problem-solving data in the background as students work the problems. The primary goal of this research was to develop methods (known as interventions) that could promote improvements in students' problem-solving and most notably aid in their transition from the novice to competent level. Three intervention techniques that were incorporated within the chemistry curricula: collaborative grouping (face-to-face and distance), concept mapping, and peer-led team learning. The face-to-face collaborative grouping intervention was designed to probe the factors affecting the quality of the group interaction. Students' logical reasoning abilities were measured using the Group Assessment of Logical Thinking (GALT) test which classifies students as formal, transitional, or concrete. These classifications essentially provide a basis for identifying scientific aptitude. These designations were used as the basis for forming collaborative groups of two students. The six possibilities (formal-formal, formal-transitional, etc.) were formed to determine how the group composition influences the gains in student abilities observed from collaborative grouping interventions. Students were given three assignments (an individual pre-collaborative, an individual post collaborative, and a collaborative assignment) each requiring them to work an IMMEX problem set. Similar gains in performance of 10% gains were observed for each group with two exceptions. The

Determining the Effects of Cognitive Style, Problem Complexity, and Hypothesis Generation on the Problem Solving Ability of School-Based Agricultural Education Students

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Blackburn, J. Joey; Robinson, J. Shane

2016-01-01

The purpose of this experimental study was to assess the effects of cognitive style, problem complexity, and hypothesis generation on the problem solving ability of school-based agricultural education students. Problem solving ability was defined as time to solution. Kirton's Adaption-Innovation Inventory was employed to assess students' cognitive…

A Further Study of Productive Failure in Mathematical Problem Solving: Unpacking the Design Components

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Kapur, Manu

2011-01-01

This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:10.1007/s11251-009-9093-x, 2009). One hundred and nine, seventh-grade mathematics students taught by the same teacher from a Singapore school experienced one of three learning designs: (a) traditional lecture and practice (LP), (b)…

Reflective Learning and Prospective Teachers' Conceptual Understanding, Critical Thinking, Problem Solving, and Mathematical Communication Skills

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Junsay, Merle L.

2016-01-01

This is a quasi-experimental study that explored the effects of reflective learning on prospective teachers' conceptual understanding, critical thinking, problem solving, and mathematical communication skills and the relationship of these variables. It involved 60 prospective teachers from two basic mathematics classes of an institution of higher…

Developing material for promoting problem-solving ability through bar modeling technique

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Widyasari, N.; Rosiyanti, H.

2018-01-01

This study aimed at developing material for enhancing problem-solving ability through bar modeling technique with thematic learning. Polya’s steps of problem-solving were chosen as the basis of the study. The methods of the study were research and development. The subject of this study were five teen students of the fifth grade of Lab-school FIP UMJ elementary school. Expert review and student’ response analysis were used to collect the data. Furthermore, the data were analyzed using qualitative descriptive and quantitative. The findings showed that material in theme “Selalu Berhemat Energi” was categorized as valid and practical. The validity was measured by using the aspect of language, contents, and graphics. Based on the expert comments, the materials were easy to implement in the teaching-learning process. In addition, the result of students’ response showed that material was both interesting and easy to understand. Thus, students gained more understanding in learning problem-solving.

VStops: A Thinking Strategy and Visual Representation Approach in Mathematical Word Problem Solving toward Enhancing STEM Literacy

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Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi

2014-01-01

This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…

Comparison of student's learning achievement through realistic mathematics education (RME) approach and problem solving approach on grade VII

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Ilyas, Muhammad; Salwah

2017-02-01

The type of this research was experiment. The purpose of this study was to determine the difference and the quality of student's learning achievement between students who obtained learning through Realistic Mathematics Education (RME) approach and students who obtained learning through problem solving approach. This study was a quasi-experimental research with non-equivalent experiment group design. The population of this study was all students of grade VII in one of junior high school in Palopo, in the second semester of academic year 2015/2016. Two classes were selected purposively as sample of research that was: year VII-5 as many as 28 students were selected as experiment group I and VII-6 as many as 23 students were selected as experiment group II. Treatment that used in the experiment group I was learning by RME Approach, whereas in the experiment group II by problem solving approach. Technique of data collection in this study gave pretest and posttest to students. The analysis used in this research was an analysis of descriptive statistics and analysis of inferential statistics using t-test. Based on the analysis of descriptive statistics, it can be concluded that the average score of students' mathematics learning after taught using problem solving approach was similar to the average results of students' mathematics learning after taught using realistic mathematics education (RME) approach, which are both at the high category. In addition, It can also be concluded that; (1) there was no difference in the results of students' mathematics learning taught using realistic mathematics education (RME) approach and students who taught using problem solving approach, (2) quality of learning achievement of students who received RME approach and problem solving approach learning was same, which was at the high category.

The main problem solving differences between high school and university in mathematical beliefs and professional behavior

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Reza Akhlaghi Garmjani

2016-10-01

Full Text Available Teaching science and math has been underdeveloped in nurturing the talents and motivations of young people who are in search of professions in these fields. Identifying and strengthening the students' problem solving beliefs and behaviors, can be a great help to those involved in teaching mathematics. This study investigates on the university and high school students, teachers and professors' problem solving beliefs and behaviors. Considering the research method, this study is a field research in which questionnaire is used. Participants in this research were senior high school and university students, math teachers and math professors. Data collection method for beliefs and behavior variables was via the use of a questionnaire. The Mann-Whitney test results showed that problem solving in high school and university was different and the main difference was in mathematical professional beliefs and behaviors.

Critical Thinking Skills Of Junior High School Female Students With High Mathematical Skills In Solving Contextual And Formal Mathematical Problems

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Ismail; Suwarsono, St.; Lukito, A.

2018-01-01

Critical thinking is one of the most important skills of the 21st century in addition to other learning skills such as creative thinking, communication skills and collaborative skills. This is what makes researchers feel the need to conduct research on critical thinking skills in junior high school students. The purpose of this study is to describe the critical thinking skills of junior high school female students with high mathematical skills in solving contextual and formal mathematical problems. To achieve this is used qualitative research. The subject of the study was a female student of eight grade junior high school. The students’ critical thinking skills are derived from in-depth problem-based interviews using interview guidelines. Interviews conducted in this study are problem-based interviews, which are done by the subject given a written assignment and given time to complete. The results show that critical thinking skills of female high school students with high math skills are as follows: In solving the problem at the stage of understanding the problem used interpretation skills with sub-indicators: categorization, decode, and clarify meaning. At the planning stage of the problem-solving strategy is used analytical skills with sub-indicators: idea checking, argument identification and argument analysis and evaluation skills with sub indicators: assessing the argument. In the implementation phase of problem solving, inference skills are used with subindicators: drawing conclusions, and problem solving and explanatory skills with sub-indicators: problem presentation, justification procedures, and argument articulation. At the re-checking stage all steps have been employed self-regulatory skills with sub-indicators: self-correction and selfstudy.

Assessment of students' critical-thinking and problem-solving abilities across a 6-year doctor of pharmacy program.

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Gleason, Brenda L; Gaebelein, Claude J; Grice, Gloria R; Crannage, Andrew J; Weck, Margaret A; Hurd, Peter; Walter, Brenda; Duncan, Wendy

2013-10-14

To determine the feasibility of using a validated set of assessment rubrics to assess students' critical-thinking and problem-solving abilities across a doctor of pharmacy (PharmD) curriculum. Trained faculty assessors used validated rubrics to assess student work samples for critical-thinking and problem-solving abilities. Assessment scores were collected and analyzed to determine student achievement of these 2 ability outcomes across the curriculum. Feasibility of the process was evaluated in terms of time and resources used. One hundred sixty-one samples were assessed for critical thinking, and 159 samples were assessed for problem-solving. Rubric scoring allowed assessors to evaluate four 5- to 7-page work samples per hour. The analysis indicated that overall critical-thinking scores improved over the curriculum. Although low yield for problem-solving samples precluded meaningful data analysis, it was informative for identifying potentially needed curricular improvements. Use of assessment rubrics for program ability outcomes was deemed authentic and feasible. Problem-solving was identified as a curricular area that may need improving. This assessment method has great potential to inform continuous quality improvement of a PharmD program.

Assessing metacognition of grade 2 and grade 4 students using an adaptation of multi-method interview approach during mathematics problem-solving

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Kuzle, A.

2018-06-01

The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during mathematics problem-solving, (2) to describe their multi-method interview approach developed to study student mathematical metacognition, and (3) to empirically evaluate the utility of their model and the adaptation of their approach in the context of grade 2 and grade 4 mathematics problem-solving. The results are discussed not only with regard to further development of the adapted multi-method interview approach, but also with regard to their theoretical and practical implications.

High profile students’ growth of mathematical understanding in solving linier programing problems

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Utomo; Kusmayadi, TA; Pramudya, I.

2018-04-01

Linear program has an important role in human’s life. This linear program is learned in senior high school and college levels. This material is applied in economy, transportation, military and others. Therefore, mastering linear program is useful for provision of life. This research describes a growth of mathematical understanding in solving linear programming problems based on the growth of understanding by the Piere-Kieren model. Thus, this research used qualitative approach. The subjects were students of grade XI in Salatiga city. The subjects of this study were two students who had high profiles. The researcher generally chose the subjects based on the growth of understanding from a test result in the classroom; the mark from the prerequisite material was ≥ 75. Both of the subjects were interviewed by the researcher to know the students’ growth of mathematical understanding in solving linear programming problems. The finding of this research showed that the subjects often folding back to the primitive knowing level to go forward to the next level. It happened because the subjects’ primitive understanding was not comprehensive.

Teaching Problem Solving without Modeling through "Thinking Aloud Pair Problem Solving."

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Pestel, Beverly C.

1993-01-01

Reviews research relevant to the problem of unsatisfactory student problem-solving abilities and suggests a teaching strategy that addresses the issue. Author explains how she uses teaching aloud problem solving (TAPS) in college chemistry and presents evaluation data. Among the findings are that the TAPS class got fewer problems completely right,…

Perceptual Learning in Early Mathematics: Interacting with Problem Structure Improves Mapping, Solving and Fluency

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Thai, Khanh-Phuong; Son, Ji Y.; Hoffman, Jessica; Devers, Christopher; Kellman, Philip J.

2014-01-01

Mathematics is the study of structure but students think of math as solving problems according to rules. Students can learn procedures, but they often have trouble knowing when to apply learned procedures, especially to problems unlike those they trained with. In this study, the authors rely on the psychological mechanism of perceptual learning…

Pose and Solve Varignon Converse Problems

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Contreras, José N.

2014-01-01

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

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Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics

NARCIS (Netherlands)

Sweller, John; Clark, Richard; Kirschner, Paul A.

2010-01-01

Sweller, J., Clark, R., & Kirschner, P. A. (2010). Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics. Notices of the American Mathematical Society, 57, 1303-1304.

MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics

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Lalingkar, Aparna; Ramnathan, Chandrashekar; Ramani, Srinivasan

2015-01-01

The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…

The software package for solving problems of mathematical modeling of isothermal curing process

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S. G. Tikhomirov

2016-01-01

Full Text Available Summary. On the basis of the general laws of sulfur vulcanization diene rubbers the principles of the effective cross-linking using a multi-component agents was discussed. It is noted that the description of the mechanism of action of the complex cross-linking systems are complicated by the diversity of interactions of components and the influence of each of them on the curing kinetics, leading to a variety technological complications of real technology and affects on the quality and technical and economic indicators of the production of rubber goods. Based on the known theoretical approaches the system analysis of isothermal curing process was performed. It included the integration of different techniques and methods into a single set of. During the analysis of the kinetics of vulcanization it was found that the formation of the spatial grid parameters vulcanizates depend on many factors, to assess which requires special mathematical and algorithmic support. As a result of the stratification of the object were identified the following major subsystems. A software package for solving direct and inverse kinetic problems isothermal curing process was developed. Information support “Isothermal vulcanization” is a set of applications of mathematical modeling of isothermal curing. It is intended for direct and inverse kinetic problems. When solving the problem of clarifying the general scheme of chemical transformations used universal mechanism including secondary chemical reactions. Functional minimization algorithm with constraints on the unknown parameters was used for solving the inverse kinetic problem. Shows a flowchart of the program. An example of solving the inverse kinetic problem with the program was introduced. Dataware was implemented in the programming language C ++. Universal dependence to determine the initial concentration of the curing agent was applied . It allowing the use of a model with different properties of multicomponent

Personalized Computer-Assisted Mathematics Problem-Solving Program and Its Impact on Taiwanese Students

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Chen, Chiu-Jung; Liu, Pei-Lin

2007-01-01

This study evaluated the effects of a personalized computer-assisted mathematics problem-solving program on the performance and attitude of Taiwanese fourth grade students. The purpose of this study was to determine whether the personalized computer-assisted program improved student performance and attitude over the nonpersonalized program.…

Problem Solving Strategies of Selected Pre-Service Secondary School Mathematics Teachers in Malaysia

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Yew, Wun Theam; Zamri, Sharifah Norul Akmar Syed

2016-01-01

Problem solving strategies of eight pre-service secondary school mathematics teachers (PSSMTs) were examined in this study. A case study research design was employed and clinical interview technique was used to collect the data. Materials collected for analysis consisted of audiotapes and videotapes of clinical interviews, subjects' notes and…

Primary School Text Comprehension Predicts Mathematical Word Problem-Solving Skills in Secondary School

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Björn, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik

2016-01-01

This longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9-10 years old at the baseline). The children's text-reading fluency, text comprehension and basic calculation…

The Relationship between Mathematical Problem-Solving Skills and Self-Regulated Learning through Homework Behaviours, Motivation, and Metacognition

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Özcan, Zeynep Çigdem

2016-01-01

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students' self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving…

Research on a Unique Instructional Framework for Elevating Students’ Quantitative Problem Solving Abilities

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Prather, Edward E.; Wallace, Colin Scott

2018-06-01

We present an instructional framework that allowed a first time physics instructor to improve students quantitative problem solving abilities by more than a letter grade over what was achieved by students in an experienced instructor’s course. This instructional framework uses a Think-Pair-Share approach to foster collaborative quantitative problem solving during the lecture portion of a large enrollment introductory calculus-based mechanics course. Through the development of carefully crafted and sequenced TPS questions, we engage students in rich discussions on key problem solving issues that we typically only hear about when a student comes for help during office hours. Current work in the sophomore E&M course illustrates that this framework is generalizable to classes beyond the introductory level and for topics beyond mechanics.

Dimensional analysis and qualitative methods in problem solving: II

International Nuclear Information System (INIS)

Pescetti, D

2009-01-01

We show that the underlying mathematical structure of dimensional analysis (DA), in the qualitative methods in problem-solving context, is the algebra of the affine spaces. In particular, we show that the qualitative problem-solving procedure based on the parallel decomposition of a problem into simple special cases yields the new original mathematical concepts of special points and special representations of affine spaces. A qualitative problem-solving algorithm piloted by the mathematics of DA is illustrated by a set of examples.

The Effects of Group Monitoring on Fatigue-Related Einstellung during Mathematical Problem Solving

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Frings, Daniel

2011-01-01

Fatigue resulting from sleep deficit can lead to decreased performance in a variety of cognitive domains and can result in potentially serious accidents. The present study aimed to test whether fatigue leads to increased Einstellung (low levels of cognitive flexibility) in a series of mathematical problem-solving tasks. Many situations involving…

Comprehension and computation in Bayesian problem solving

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Eric D. Johnson

2015-07-01

Full Text Available Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages, both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on transparent Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point.

Threshold Effects of Creative Problem-Solving Attributes on Creativity in the Math Abilities of Taiwanese Upper Elementary Students

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Chia-Yi Lin

2017-01-01

Full Text Available This study aimed to help determine what the typology of math creative problem-solving is. Different from studies that have discussed the threshold effect between creativity and intelligence, this research investigated the threshold effect between creativity and other attributes. The typology of the math creative problem-solving abilities of 409 fifth- and sixth-grade Taiwanese students was identified and compared in this study. A Creative Problem-Solving Attribute Instrument was devised for this study, with the aim of measuring students’ perceptions on their motivation, knowledge, and skills, both in general and in specific domains. Divergent and convergent thinking were also measured. Cluster analyses yielded three creative problem-solving typologies: High, Medium, and Low. The High Attribute group scored significantly higher in the Math Creative Problem-Solving Ability Test than did the Medium Attribute and Low Attribute groups. The results suggest a threshold effect from several attributes—divergent thinking, convergent thinking, motivation, general knowledge and skills, domain-specific knowledge and skills, and environment—on students’ creative problem-solving abilities. Balanced development of attributes may be an important consideration in nurturing creativity in children.

impact of the curriculum reform on problem solving ability in ...

African Journals Online (AJOL)

unesco

that “learning is problem solving”. Therefore, teaching problem solving is teaching people how to learn, so is problem solving in chemistry education. Kalbag (4) states that problem solving orientation in chemistry education has an importance in that problem solving converts information into knowledge. Kalbag further states.

Pengaruh Pembelajaran Inquiry dan Problem Solving terhadap Motivasi dan Prestasi Belajar Matematika

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Henri Rianto

2014-06-01

This study aimed to describe the difference effect of inquiry approach and problem solving approach on motivations to learn mathematics and student mathematics achievement and the better  effect of inquiry approach and problem solving approach on motivations to learn mathematics and student mathematics achievement. This research was a quasi-experimental using nonrandomized control group, pretest-posttest design. The data were collected through non-test and test. The data were analyzed using the MANOVA test and independent sample t-test with significance level of 0,05. The results of the study show  the inquiry approach and problem solving approach was not effective to increase the student mathematics achievement, the inquiry approach and problem solving approach was not effective to increase the motivation to learn mathematics, and there is no difference effect between the inquiry approach and the problem solving approach on learning motivations and the student mathematics achievement. Keywords: inquiry approach, problem solving approach, motivations to learn mathematics, student mathematics achievement

Factors Affecting Differential Equation Problem Solving Ability of Students at Pre-University Level: A Conceptual Model

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Aisha, Bibi; Zamri, Sharifa NorulAkmar Syed; Abdallah, Nabeel; Abedalaziz, Mohammad; Ahmad, Mushtaq; Satti, Umbreen

2017-01-01

In this study, different factors affecting students' differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students' differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that…

Examination of Gifted Students' Probability Problem Solving Process in Terms of Mathematical Thinking

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Baltaci, Serdal

2016-01-01

It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students' probability…

Evaluation of Students' Mathematical Problem Solving Skills in Relation to Their Reading Levels

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Özsoy, Gökhan; Kuruyer, Hayriye Gül; Çakiroglu, Ahmet

2015-01-01

The purpose of the current study is to investigate the correlation between students' reading levels and mathematical problem solving skills. The present study was conducted in line with a qualitative research method, i.e., the phenomenological method. The study group of the current research is composed of six third grade students with different…

The Effects of Schema-Based Instruction on the Mathematical Problem Solving of Students with Emotional and Behavioral Disorders

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Peltier, Corey; Vannest, Kimberly J.

2018-01-01

The current study examines the effects of schema instruction on the problem-solving performance of four second-grade students with emotional and behavioral disorders. The existence of a functional relationship between the schema instruction intervention and problem-solving accuracy in mathematics is examined through a single case experiment using…

Schema-Based Strategy Instruction and the Mathematical Problem-Solving Performance of Two Students with Emotional or Behavioral Disorders

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Peltier, Corey; Vannest, Kimberly J.

2016-01-01

The purpose of this study was to analyze the effects of schema instruction on the mathematical problem solving of students with emotional or behavioral disorders (EBD). The participants were two fourth-grade students identified with EBD. The intervention package consisted of schema instruction, strategy instruction on problem-solving heuristics…

Analysis of students’ creative thinking level in problem solving based on national council of teachers of mathematics

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Hobri; Suharto; Rifqi Naja, Ahmad

2018-04-01

This research aims to determine students’ creative thinking level in problem solving based on NCTM in function subject. The research type is descriptive with qualitative approach. Data collection methods which were used are test and interview. Creative thinking level in problem solving based on NCTM indicators consists of (1) Make mathematical model from a contextual problem and solve the problem, (2) Solve problem using various possible alternatives, (3) Find new alternative(s) to solve the problem, (4) Determine the most efficient and effective alternative for that problem, (5) Review and correct mistake(s) on the process of problem solving. Result of the research showed that 10 students categorized in very satisfying level, 23 students categorized in satisfying level and 1 students categorized in less satisfying level. Students in very satisfying level meet all indicators, students in satisfying level meet first, second, fourth, and fifth indicator, while students in less satisfying level only meet first and fifth indicator.

The Problem-Solving Approach in the Teaching of Number Theory

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Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him

2014-01-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

Exploring students’ perceived and actual ability in solving statistical problems based on Rasch measurement tools

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Azila Che Musa, Nor; Mahmud, Zamalia; Baharun, Norhayati

2017-09-01

One of the important skills that is required from any student who are learning statistics is knowing how to solve statistical problems correctly using appropriate statistical methods. This will enable them to arrive at a conclusion and make a significant contribution and decision for the society. In this study, a group of 22 students majoring in statistics at UiTM Shah Alam were given problems relating to topics on testing of hypothesis which require them to solve the problems using confidence interval, traditional and p-value approach. Hypothesis testing is one of the techniques used in solving real problems and it is listed as one of the difficult concepts for students to grasp. The objectives of this study is to explore students’ perceived and actual ability in solving statistical problems and to determine which item in statistical problem solving that students find difficult to grasp. Students’ perceived and actual ability were measured based on the instruments developed from the respective topics. Rasch measurement tools such as Wright map and item measures for fit statistics were used to accomplish the objectives. Data were collected and analysed using Winsteps 3.90 software which is developed based on the Rasch measurement model. The results showed that students’ perceived themselves as moderately competent in solving the statistical problems using confidence interval and p-value approach even though their actual performance showed otherwise. Item measures for fit statistics also showed that the maximum estimated measures were found on two problems. These measures indicate that none of the students have attempted these problems correctly due to reasons which include their lack of understanding in confidence interval and probability values.

Error Patterns in Problem Solving.

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Babbitt, Beatrice C.

Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…

Tangram solved? Prefrontal cortex activation analysis during geometric problem solving.

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Ayaz, Hasan; Shewokis, Patricia A; Izzetoğlu, Meltem; Çakır, Murat P; Onaral, Banu

2012-01-01

Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.

Review of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan

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Thomas J. Pfaff

2015-07-01

Full Text Available Mahajan, Sanjoy. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving (The MIT Press, Cambridge, Massachusetts, 2010. 152 pp. ISBN 978--0--262--51429--3 Street-Fighting Mathematics is an engaging collection of problem-solving techniques. The book is not for a general audience, as it requires a significant level of mathematical and scientific background knowledge. In particular, most of the book requires knowledge of Calculus I and there are examples that will require knowledge of Physics. At the same time, there are parts of the book that don't require this much background. While the title of the book may be misleading, as it is really street-fighting mathematics for people with a fair amount of training in the subject, there is a lot to be gained from reading this book, and calculus teachers may find it to be a useful resource.

Much ado about aha!: Insight problem solving is strongly related to working memory capacity and reasoning ability.

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Chuderski, Adam; Jastrzębski, Jan

2018-02-01

A battery comprising 4 fluid reasoning tests as well as 13 working memory (WM) tasks that involved storage, recall, updating, binding, and executive control, was applied to 318 adults in order to evaluate the true relationship of reasoning ability and WM capacity (WMC) to insight problem solving, measured using 40 verbal, spatial, math, matchstick, and remote associates problems (insight problems). WMC predicted 51.8% of variance in insight problem solving and virtually explained its almost isomorphic link to reasoning ability (84.6% of shared variance). The strong link between WMC and insight pertained generally to most WM tasks and insight problems, was identical for problems solved with and without reported insight, was linear throughout the ability levels, and was not mediated by age, motivation, anxiety, psychoticism, and openness to experience. In contrast to popular views on the sudden and holistic nature of insight, the solving of insight problems results primarily from typical operations carried out by the basic WM mechanisms that are responsible for the maintenance, retrieval, transformation, and control of information in the broad range of intellectual tasks (including fluid reasoning). Little above and beyond WM is unique about insight. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Syntactic Awareness and Arithmetic Word Problem Solving in Children with and without Learning Disabilities

Science.gov (United States)

Peake, Christian; Jiménez, Juan E.; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca

2015-01-01

Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in…

Capturing Problem-Solving Processes Using Critical Rationalism

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Chitpin, Stephanie; Simon, Marielle

2012-01-01

The examination of problem-solving processes continues to be a current research topic in education. Knowing how to solve problems is not only a key aspect of learning mathematics but is also at the heart of cognitive theories, linguistics, artificial intelligence, and computers sciences. Problem solving is a multistep, higher-order cognitive task…

Modifying a Research-Based Problem-Solving Intervention to Improve the Problem-Solving Performance of Fifth and Sixth Graders With and Without Learning Disabilities.

Science.gov (United States)

Krawec, Jennifer; Huang, Jia

The purpose of the present study was to test the efficacy of a modified cognitive strategy instructional intervention originally developed to improve the mathematical problem solving of middle and high school students with learning disabilities (LD). Fifth and sixth grade general education mathematics teachers and their students of varying ability (i.e., average-achieving [AA] students, low-achieving [LA] students, and students with LD) participated in the research study. Several features of the intervention were modified, including (a) explicitness of instruction, (b) emphasis on meta-cognition, (c) focus on problem-solving prerequisites, (d) extended duration of initial intervention, and (e) addition of visual supports. General education math teachers taught all instructional sessions to their inclusive classrooms. Curriculum-based measures (CBMs) of math problem solving were administered five times over the course of the year. A multilevel model (repeated measures nested within students and students nested within schools) was used to analyze student progress on CBMs. Though CBM scores in the intervention group were initially lower than that of the comparison group, intervention students improved significantly more in the first phase, with no differences in the second phase. Implications for instruction are discussed as well as directions for future research.

The effect of Think Pair Share (TPS) using scientific approach on students’ self-confidence and mathematical problem-solving

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Rifa’i, A.; Lestari, H. P.

2018-03-01

This study was designed to know the effects of Think Pair Share using Scientific Approach on students' self-confidence and mathematical problem-solving. Quasi-experimental with pre-test post-test non-equivalent group method was used as a basis for design this study. Self-confidence questionnaire and problem-solving test have been used for measurement of the two variables. Two classes of the first grade in religious senior high school (MAN) in Indonesia were randomly selected for this study. Teaching sequence and series from mathematics book at control group in the traditional way and at experiment group has been in TPS using scientific approach learning method. For data analysis regarding students’ problem-solving skill and self-confidence, One-Sample t-Test, Independent Sample t-Test, and Multivariate of Variance (MANOVA) were used. The results showed that (1) TPS using a scientific approach and traditional learning had positive effects (2) TPS using scientific approach learning in comparative with traditional learning had a more significant effect on students’ self-confidence and problem-solving skill.

Analysis of difficulties in mathematics problem solving based on revised Bloom’s Taxonomy viewed from high self-efficacy

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Prismana, R. D. E.; Kusmayadi, T. A.; Pramudya, I.

2018-04-01

The ability of solving problem is a part of the mathematic curriculum that is very important. Problem solving prefers the process and strategy that is done by students in solving a problem rather than the result. This learning concept in accordance with the stages on the revised bloom’s taxonomy. The revised Bloom’s Taxonomy has two dimensions, namely the dimension of cognitive process and the dimension of knowledge. Dimension of knowledge has four categories, but this study only restricted on two knowledge, conceptual knowledge and procedural knowledge. Dimensions of cognitive processes are categorized into six kinds, namely remembering, understanding, applying, analyzing, evaluating, and creating. Implementation of learning more emphasis on the role of students. Students must have their own belief in completing tasks called self-efficacy. This research is a qualitative research. This research aims to know the site of the students’ difficulty based on revised Bloom’s Taxonomy viewed from high self-efficacy. The results of the study stated the students with high self efficacy have difficulties site. They are evaluating conceptual knowledge, evaluating procedural knowledge, creating conceptual knowledge, and creating procedural knowledge. It could be the consideration of teachers in the teaching, so as to reduce the difficulties of learning in students.

Best Known Problem Solving Strategies in "High-Stakes" Assessments

Science.gov (United States)

Hong, Dae S.

2011-01-01

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Using Problem-solving Therapy to Improve Problem-solving Orientation, Problem-solving Skills and Quality of Life in Older Hemodialysis Patients.

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Erdley-Kass, Shiloh D; Kass, Darrin S; Gellis, Zvi D; Bogner, Hillary A; Berger, Andrea; Perkins, Robert M

2017-08-24

To determine the effectiveness of Problem-Solving Therapy (PST) in older hemodialysis (HD) patients by assessing changes in health-related quality of life and problem-solving skills. 33 HD patients in an outpatient hemodialysis center without active medical and psychiatric illness were enrolled. The intervention group (n = 15) received PST from a licensed social worker for 6 weeks, whereas the control group (n = 18) received usual care treatment. In comparison to the control group, patients receiving PST intervention reported improved perceptions of mental health, were more likely to view their problems with a positive orientation and were more likely to use functional problem-solving methods. Furthermore, this group was also more likely to view their overall health, activity limits, social activities and ability to accomplish desired tasks with a more positive mindset. The results demonstrate that PST may positively impact mental health components of quality of life and problem-solving coping among older HD patients. PST is an effective, efficient, and easy to implement intervention that can benefit problem-solving abilities and mental health-related quality of life in older HD patients. In turn, this will help patients manage their daily living activities related to their medical condition and reduce daily stressors.

Exploring Teachers' Process of Change in Incorporating Problem Solving into the Mathematics Classroom

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Rutherford, Vanessa

2012-01-01

This study explores how a problem-solving based professional learning community (PLC) affects the beliefs, knowledge, and instructional practices of two sixth-grade mathematics teachers. An interview and two observations were conducted prior to beginning the year-long PLC in order to gather information about the participants' beliefs,…

Possibilities of mathematical models in solving flow problems in environmental protection and water architecture

Energy Technology Data Exchange (ETDEWEB)

1979-01-01

The booklet presents the full text of 13 contributions to a Colloquium held at Karlsruhe in Sept. 1979. The main topics of the papers are the evaluation of mathematical models to solve flow problems in tide water, seas, rivers, groundwater and in the earth atmosphere. See further hints under relevant topics.

The Influence of Self-Efficacy Beliefs and Metacognitive Prompting on Genetics Problem Solving Ability among High School Students in Kenya

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Aurah, Catherine Muhonja

Within the framework of social cognitive theory, the influence of self-efficacy beliefs and metacognitive prompting on genetics problem solving ability among high school students in Kenya was examined through a mixed methods research design. A quasi-experimental study, supplemented by focus group interviews, was conducted to investigate both the outcomes and the processes of students' genetics problem-solving ability. Focus group interviews substantiated and supported findings from the quantitative instruments. The study was conducted in 17 high schools in Western Province, Kenya. A total of 2,138 high school students were purposively sampled. A sub-sample of 48 students participated in focus group interviews to understand their perspectives and experiences during the study so as to corroborate the quantitative data. Quantitative data were analyzed through descriptive statistics, zero-order correlations, 2 x 2 factorial ANOVA,, and sequential hierarchical multiple regressions. Qualitative data were transcribed, coded, and reported thematically. Results revealed metacognitive prompts had significant positive effects on student problem-solving ability independent of gender. Self-efficacy and metacognitive prompting significantly predicted genetics problem-solving ability. Gender differences were revealed, with girls outperforming boys on the genetics problem-solving test. Furthermore, self-efficacy moderated the relationship between metacognitive prompting and genetics problem-solving ability. This study established a foundation for instructional methods for biology teachers and recommendations are made for implementing metacognitive prompting in a problem-based learning environment in high schools and science teacher education programs in Kenya.

The effect of creative problem solving on students’ mathematical adaptive reasoning

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Muin, A.; Hanifah, S. H.; Diwidian, F.

2018-01-01

This research was conducted to analyse the effect of creative problem solving (CPS) learning model on the students’ mathematical adaptive reasoning. The method used in this study was a quasi-experimental with randomized post-test only control group design. Samples were taken as many as two classes by cluster random sampling technique consisting of experimental class (CPS) as many as 40 students and control class (conventional) as many as 40 students. Based on the result of hypothesis testing with the t-test at the significance level of 5%, it was obtained that significance level of 0.0000 is less than α = 0.05. This shows that the students’ mathematical adaptive reasoning skills who were taught by CPS model were higher than the students’ mathematical adaptive reasoning skills of those who were taught by conventional model. The result of this research showed that the most prominent aspect of adaptive reasoning that could be developed through a CPS was inductive intuitive. Two aspects of adaptive reasoning, which were inductive intuitive and deductive intuitive, were mostly balanced. The different between inductive intuitive and deductive intuitive aspect was not too big. CPS model can develop student mathematical adaptive reasoning skills. CPS model can facilitate development of mathematical adaptive reasoning skills thoroughly.

The Impact of Problem-Based Learning Approach to Senior High School Students' Mathematics Critical Thinking Ability

Science.gov (United States)

Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua

2015-01-01

The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…

Conceptual problem solving in high school physics

OpenAIRE

Jennifer L. Docktor; Natalie E. Strand; José P. Mestre; Brian H. Ross

2015-01-01

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in w...

Investigasi Kemampuan Problem Solving dan Problem Posing Matematis Mahasiswa Via Pendekatan Realistic

OpenAIRE

Afriansyah, Ekasatya Aldila

2016-01-01

Mathematical problem solving and problem posing skill are the mathematical skills that need to be owned by students. By having this skill, students can be more creative in expressing ideas by connecting the knowledge that they held previously. But in reality, there are some students who are lack of problem solving skill; therefore it is really important to improve learning through appropriate approach. Realistic approach had been chosen as the learning theory to be applied in the class. This ...

Functional Thinking Profile of Junior High School Student in Solving Mathematical Problem Observed by Differences of Sex

Science.gov (United States)

Siregar, A. P.; Juniati, D.; Sulaiman, R.

2018-01-01

This study involving 2 grade VIII students was taken place in SMPK Anak Bangsa Surabaya. Subjects were selected using equal mathematics ability criteria. Data was collected using provision of problem-solving tasks and followed by a task-based interview. Obtained data was analysed through the following steps, which are data reduction, data presentation, and conclusions. Meanwhile, to obtain a valid data, in this study, researchers used data triangulation. The results indicated that in the problem number 1 about identifying patterns, the subjects of male and female show a tendency of similarities in stating what is known and asked the question. However, the male students provided a more specific answer in explaining the magnitude of the difference between the first quantity and the increased differences in the other quantities. Related the activities in determining the relationship between two quantities, male subjects and women subject tended to have similarities in the sense of using trial and error on existing mathematical operations. It can be concluded that the functional way of thinking both subjects is relatively identic. Nevertheless, the male subject showed the more specific answer in finding the difference between the two quantities and finding the correspondence relationship between the quantities.

Open-Start Mathematics Problems: An Approach to Assessing Problem Solving

Science.gov (United States)

Monaghan, John; Pool, Peter; Roper, Tom; Threlfall, John

2009-01-01

This article describes one type of mathematical problem, open-start problems, and discusses their potential for use in assessment. In open-start problems how one starts to address the problem can vary but they have a correct answer. We argue that the use of open-start problems in assessment could positively influence classroom mathematics…

Visuospatial Anatomy Comprehension: The Role of Spatial Visualization Ability and Problem-Solving Strategies

Science.gov (United States)

Nguyen, Ngan; Mulla, Ali; Nelson, Andrew J.; Wilson, Timothy D.

2014-01-01

The present study explored the problem-solving strategies of high- and low-spatial visualization ability learners on a novel spatial anatomy task to determine whether differences in strategies contribute to differences in task performance. The results of this study provide further insights into the processing commonalities and differences among…

Students’ difficulties in solving linear equation problems

Science.gov (United States)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Strategy Keys as Tools for Problem Solving

Science.gov (United States)

Herold-Blasius, Raja

2017-01-01

Problem solving is one of the main competences we seek to teach students at school for use in their future lives. However, when dealing with mathematical problems, teachers encounter a wide variety of difficulties. To foster students' problem-solving skills, the authors developed "strategy keys." Strategy keys can serve as material to…

MATHEMATICAL PROBLEMS OF INTEGRATIVE CONTENTS

Directory of Open Access Journals (Sweden)

V. Kushnir

2014-09-01

Full Text Available The tasks of integrative content requires the use of knowledge and skills on various themes both one discipline and different disciplines. Mostly in the classroom (or in homework the tasks on the properties absorption of different concepts using different theories are considered. Thus knowledge within only one discipline is formed, knowledge of the narrow sense (one subject. Such knowledge is "prescriptional", we call it idealized. After all, it is far from models of the real professional problems and problems of life in general, in order to solve them it is necessary to apply knowledge and skills acquired in different themes of the same objects,life experience. Practical formation of integrative knowledge requires statement of the educational problems before the subjects of studying, the problems within the "narrow objectivity" can not be resolved at all, or such kind of solving is too difficult to solve, for example, the nature and the context of solving problems (scientific approaches to solving problems, creating mathematical models, methods for solving such models, means of solving, application of methods, analysis of the models solution and the right choice, the inspection of solutions, etc. will sink in the conglomeration of technical operations. The problems with integrative content are usually more complicated than the problems of "narrow objectivity." In our problems the index of such difficulty is the essence of educational content, which is disclosed in the previous paragraph. The problems solution proposed in this article requires knowledge of the structural geometry (circle construction, touching two or three laps: with analytic geometry (method of coordinates on the plane; the distance between two points on the coordinate plane; algebra (system drawing irrational equations, method for solving such system, the solution of the system, analysis of the results and the right choose of the desired solution for found criterion, testing

Conceptual Problem Solving in High School Physics

Science.gov (United States)

Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.

2015-01-01

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an…

Pupils' Visual Representations in Standard and Problematic Problem Solving in Mathematics: Their Role in the Breach of the Didactical Contract

Science.gov (United States)

Deliyianni, Eleni; Monoyiou, Annita; Elia, Iliada; Georgiou, Chryso; Zannettou, Eleni

2009-01-01

This study investigated the modes of representations generated by kindergarteners and first graders while solving standard and problematic problems in mathematics. Furthermore, it examined the influence of pupils' visual representations on the breach of the didactical contract rules in problem solving. The sample of the study consisted of 38…

Threshold Effects of Creative Problem-Solving Attributes on Creativity in the Math Abilities of Taiwanese Upper Elementary Students

OpenAIRE

Lin, Chia-Yi

2017-01-01

This study aimed to help determine what the typology of math creative problem-solving is. Different from studies that have discussed the threshold effect between creativity and intelligence, this research investigated the threshold effect between creativity and other attributes. The typology of the math creative problem-solving abilities of 409 fifth- and sixth-grade Taiwanese students was identified and compared in this study. A Creative Problem-Solving Attribute Instrument was devised for t...

Quantitative Reasoning in Problem Solving

Science.gov (United States)

Ramful, Ajay; Ho, Siew Yin

2015-01-01

In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

Developing non-routine problems for assessing students’ mathematical literacy

Science.gov (United States)

Murdiyani, N. M.

2018-03-01

The purpose of this study is to develop non-routine problems for assessing the mathematics literacy skills of students, which is valid, practical, and effective. It is based on the previous research said that Indonesian students’ mathematical literacy is still low. The results of this study can be used as a guide in developing the evaluation questions that can train students to improve the ability of solving non-routine problems in everyday life. This research type is formative evaluation that consists of preliminary, self evaluation, expert reviews, one-to-one, small group, and field test. The sample of this research is grade 8 students at one of Junior High School in Yogyakarta. This study results in mathematics literacy problems prototype consisting of level 1 to level 6 problems similar to PISA problems. This study also discusses the examples of students’ answer and their reasoning.

Investigating Plane Geometry Problem-Solving Strategies of Prospective Mathematics Teachers in Technology and Paper-and-Pencil Environments

Science.gov (United States)

Koyuncu, Ilhan; Akyuz, Didem; Cakiroglu, Erdinc

2015-01-01

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies…

Do Students Trust in Mathematics or Intuition during Physics Problem Solving? An Epistemic Game Perspective

Science.gov (United States)

Yavuz, Ahmet

2015-01-01

This study aims to investigate (1) students' trust in mathematics calculation versus intuition in a physics problem solving and (2) whether this trust is related to achievement in physics in the context of epistemic game theoretical framework. To achieve this research objective, paper-pencil and interview sessions were conducted. A paper-pencil…

The effects of cumulative practice on mathematics problem solving.

Science.gov (United States)

Mayfield, Kristin H; Chase, Philip N

2002-01-01

This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.

Strategies, Not Solutions: Involving Students in Problem Solving.

Science.gov (United States)

Von Kuster, Lee N.

1984-01-01

Defines problem solving, discusses the use of problems developed by students that are relevant to their own lives, presents examples of practical mathematics problems that deal with local situations, discusses fringe benefits of this type of problem solving, and addresses teachers' concern that this method consumes too much time. (MBR)

Methods of solving sequence and series problems

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Grigorieva, Ellina

2016-01-01

This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions,Met...

The role of crossmodal interaction in psychological and brain organization of mathematical abilities

Directory of Open Access Journals (Sweden)

Nikita A. Khokhlov

2016-12-01

Full Text Available The paper analyzes the work of Russian and foreign scholars devoted to the role of cross analyzer cooperation in developing and implementing mathematical abilities.Crossmodal interaction is considered as an additional category of neuropsychological analysis that allows to extend the existing ideas about the psychological structure and brain providing the mathematical ability. There are data that confirm the relevance of studying the interaction of the senses. Many of the research on this issue are carried out using the synesthesia which is considered a rare phenomenon. However, both Russian and foreign works suggest that the interaction of analyzers is not characteristic only to those whose brain is synesthetic. The joint work of the senses is characteristic of every person since his/her childhood, and is an obligatory condition for cognitive processes. Cross analyzer synthesis is assumed to play an important role in producing spatial representations and the ability to intuitively perceive the notion of quantity (evolutionary foundations of mathematical ability. On the brain level, these processes are provided primarily by functioning of parietal and tertiary cortical areas located at the junctionof cortical analyzer areas and also temporal areas that border on the parahippocampal brain area. When dealing with school mathematics the structure of mathematical abilities is changing due to verbal and symbolic representations of numerical coding. Dealing with symbols opens up new opportunities, but it also narrows the spectrum of modalities involved in doing mathematical sums. Thus, the ability to re-encode information from one modality to another after school mathematics is perceived has an impact on the efficacy of mathematical activity. Doing mathematical sums is accompanied by crossmodal interaction that occurs on the unconscious level. Some problem conditions may be efficiently processed in one modality, others may be solved in other modality

The Effects of Problem-Based Learning on Pre-Service Teachers' Critical Thinking Dispositions and Perceptions of Problem-Solving Ability

Science.gov (United States)

Temel, Senar

2014-01-01

The aim of this study was two-fold. The first aim was to determine the levels of critical thinking disposition and perception of problem-solving ability of pre-service teachers. The second aim was to compare the effects of problem-based learning and traditional teaching methods on the critical thinking dispositions and perceptions of…

Students’ thinking preferences in solving mathematics problems based on learning styles: a comparison of paper-pencil and geogebra

Science.gov (United States)

Farihah, Umi

2018-04-01

The purpose of this study was to analyze students’ thinking preferences in solving mathematics problems using paper pencil comparing to geogebra based on their learning styles. This research employed a qualitative descriptive study. The subjects of this research was six of eighth grade students of Madrasah Tsanawiyah Negeri 2 Trenggalek, East Java Indonesia academic year 2015-2016 with their difference learning styles; two visual students, two auditory students, and two kinesthetic students.. During the interview, the students presented the Paper and Pencil-based Task (PBTs) and the Geogebra-based Task (GBTs). By investigating students’ solution methods and the representation in solving the problems, the researcher compared their visual and non-visual thinking preferences in solving mathematics problems while they were using Geogebra and without Geogebra. Based on the result of research analysis, it was shown that the comparison between students’ PBTs and GBTs solution either visual, auditory, or kinesthetic represented how Geogebra can influence their solution method. By using Geogebra, they prefer using visual method while presenting GBTs to using non-visual method.

Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

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Wesley Pacheco Calixto

2010-01-01

Full Text Available Having the property to modify only the geometry of a polygonal structure, preserving its physical magnitudes, the Conformal Mapping is an exceptional tool to solve electromagnetism problems with known boundary conditions. This work aims to introduce a new developed mathematical operator, based on polynomial extrapolation. This operator has the capacity to accelerate an optimization method applied in conformal mappings, to determinate the equipotential lines, the field lines, the capacitance, and the permeance of some polygonal geometry electrical devices with an inner dielectric of permittivity ε. The results obtained in this work are compared with other simulations performed by the software of finite elements method, Flux 2D.

Schema Knowledge for Solving Arithmetic Story Problems: Some Affective Components.

Science.gov (United States)

Marshall, Sandra P.

This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…

DEVELOPMENT OF LARSON’S PROBLEMS SOLVING PATTERNS WITH "IDEAL" STRATEGIES

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. Junarti

2018-01-01

Full Text Available Abstract: Mathematical Problem-solving is taught to improve students' high-order thinking skills. A heuristic problem-solving strategy is used to find different Problem-solving. This research is to: 1 describe the student's Problem-solving ability profile in finding the pattern of algebra solving through the "IDEAL" (Identify Define Explore Act Look back strategy by developing Larson’s Problem-solving pattern, 2 measuring the extent of the pattern can be formed by using " IDEAL". Finding patterns is part of the first heuristic strategy. The research method used a qualitative approach with descriptive analysis. Problems conveyed to students are done in pairs of two people, with the consideration that more discussion opportunities with friends make it possible to get more than five troubleshooting as Larson puts it. The results showed that: 1 profile Problem-solving ability found pattern with "IDEAL" strategy from student got result that from problem given to 20 student group can help solve algebra Problem-solving; 2 there are four kinds of Problem-solving patterns consisting of 3 Larson model Problem-solving patterns and one Problem-solving pattern using geometry sequence pattern. Keyword: Problem-solving Pattern, Heuristic, “IDEAL” Strategy Abstrak: Pemecahan masalah matematika diajarkan untuk meningkatkan kemampuan pemikiran tingkat tinggi mahasiswa.  Strategi pemecahan masalah heuristic digunakan untuk menemukan pemecahan masalah yang berbeda. Penelitian ini untuk: 1 menggambarkan profil kemampuan pemecahan masalah mahasiswa dalam menemukan pola pemecahan aljabar melalui strategi “IDEAL” (Identify Define Explore Act Look back dengan mengembangkan pola pemecahan masalah Larson, 2 mengukur sejauhmana pola yang dapat dibentuk mahasiswa dengan menggunakan strategi “IDEAL”. Menemukan Pola merupakan bagian dari strategi heuristik yang pertama. Metode penelitiannya menggunakan pendekatan kualitatif dengan  analisis deskriptif. Masalah

Solving Multiple Timetabling Problems at Danish High Schools

DEFF Research Database (Denmark)

Kristiansen, Simon

name; Elective Course Student Sectioning. The problem is solved using ALNS and solutions are proven to be close to optimum. The algorithm has been implemented and made available for the majority of the high schools in Denmark. The second Student Sectioning problem presented is the sectioning of each...... high schools. Two types of consultations are presented; the Parental Consultation Timetabling Problem (PCTP) and the Supervisor Consultation Timetabling Problem (SCTP). One mathematical model containing both consultation types has been created and solved using an ALNS approach. The received solutions...... problems as mathematical models and solve them using operational research techniques. Two of the models and the suggested solution methods have resulted in implementations in an actual decision support software, and are hence available for the majority of the high schools in Denmark. These implementations...

Kemampuan Berpikir Kritis dan Metakognisi Siswa dalam Menyelesaikan Masalah Matematika melalui Pendekatan Problem Solving

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Muhammad Ikhsan

2017-12-01

Full Text Available The aims of this study are to determine the improvement of critical thinking skills mathematical and metacognition of students who are taught with problem solving approach and the correlation between mathematical critical thinking and metacognition of students. This research is an experimental research with pretest-posttest control group design. The sample this research is the students of class VIII_2 and VIII_3 in SMP Negeri 1 Banda Aceh. Collecting data technique are test and nontest. Data were analyzed using t-test and correlation test. The result of the research shows 1 the critical thinking ability of the students who get the learning through problem solving approach is better than the students who get the conventional learning, 2 Metacognition of students who get the learning by using problem solving approach is better than the students who get the conventional learning, 3 a positive and significant relationship between students' metacognition and critical thinking skills.

Solving Out Loud : using discourse as a means to promote problem solving, motivation, and metacognition in a mathematics classroom

OpenAIRE

King, Megan E.

2011-01-01

Classroom communication can often be a teacher-centered discussion. Due to the teacher centered format of discussions students are not engaging in meaningful discourse in mathematics classroom, which is part of the NCTM 2000 Standards as well as a necessary component to learning. Students can only learn communication skills when discourse is a central feature from the classroom. In addition, students must explicitly learn problem-solving skills. Unfortunately, many of these features are absen...

Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

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Dewi, N. R.; Arini, F. Y.

2018-03-01

The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.

Using CAS to Solve Classical Mathematics Problems

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Burke, Maurice J.; Burroughs, Elizabeth A.

2009-01-01

Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

Evaluation of the Effectiveness of a Tablet Computer Application (App) in Helping Students with Visual Impairments Solve Mathematics Problems

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Beal, Carole R.; Rosenblum, L. Penny

2018-01-01

Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying prealgebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their…

High School Teachers' Problem Solving Activities to Review and Extend Their Mathematical and Didactical Knowledge

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Santos-Trigo, Manuel; Barrera-Mora, Fernando

2011-01-01

The study documents the extent to which high school teachers reflect on their need to revise and extend their mathematical and practicing knowledge. In this context, teachers worked on a set of tasks as a part of an inquiring community that promoted the use of different computational tools in problem solving approaches. Results indicated that the…

Cognitive Predictors of Everyday Problem Solving across the Lifespan.

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Chen, Xi; Hertzog, Christopher; Park, Denise C

2017-01-01

An important aspect of successful aging is maintaining the ability to solve everyday problems encountered in daily life. The limited evidence today suggests that everyday problem solving ability increases from young adulthood to middle age, but decreases in older age. The present study examined age differences in the relative contributions of fluid and crystallized abilities to solving problems on the Everyday Problems Test (EPT). We hypothesized that due to diminishing fluid resources available with advanced age, crystallized knowledge would become increasingly important in predicting everyday problem solving with greater age. Two hundred and twenty-one healthy adults from the Dallas Lifespan Brain Study, aged 24-93 years, completed a cognitive battery that included measures of fluid ability (i.e., processing speed, working memory, inductive reasoning) and crystallized ability (i.e., multiple measures of vocabulary). These measures were used to predict performance on EPT. Everyday problem solving showed an increase in performance from young to early middle age, with performance beginning to decrease at about age of 50 years. As hypothesized, fluid ability was the primary predictor of performance on everyday problem solving for young adults, but with increasing age, crystallized ability became the dominant predictor. This study provides evidence that everyday problem solving ability differs with age, and, more importantly, that the processes underlying it differ with age as well. The findings indicate that older adults increasingly rely on knowledge to support everyday problem solving, whereas young adults rely almost exclusively on fluid intelligence. © 2017 S. Karger AG, Basel.

Problem Solving, Scaffolding and Learning

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Lin, Shih-Yin

2012-01-01

Helping students to construct robust understanding of physics concepts and develop good solving skills is a central goal in many physics classrooms. This thesis examine students' problem solving abilities from different perspectives and explores strategies to scaffold students' learning. In studies involving analogical problem solving…

Analysis of critical thinking ability in direct current electrical problems solving

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Hartono; Sunarno, Widha; Sarwanto; Arya Nugraha, Dewanta

2017-11-01

This study concern on analyzing the ability of students in critical thinking skills on the subject matter of direct current electricity. Samples were taken using purposive random sampling consisted of 32 students of grade XI, Multimedia 1, SMK Negeri 3 Surakarta in academic year 2016/2017. This study used descriptive quantitative method. The data were collected using tests and interviews regarding the subject matter of direct current electricity. Based on the results, students are getting some difficulties in solving problem in indicator 4. The average of students’ correct answer is 62.8%.

Does Solving Insight-Based Problems Differ from Solving Learning-Based Problems? Some Evidence from an ERP Study

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