Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Improving mathematical problem solving skills through visual media

NASA Astrophysics Data System (ADS)

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.

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

ERIC Educational Resources Information Center

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…

Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students

ERIC Educational Resources Information Center

Budak, Ibrahim

2012-01-01

Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem…

Developing Instruction Materials Based on Joyful PBL to Improve Students Mathematical Representation Ability

ERIC Educational Resources Information Center

Minarni, Ani; Napitupulu, E. Elvis

2017-01-01

Solving problem either within mathematics or beyond is one of the ultimate goal students learn mathematics. It is since mathematics takes role tool as well as vehicle to develop problem solving ability. One of the supporting components to problem solving is mathematical representation ability (MRA). Nowadays, many teachers and researchers find out…

Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

Novita, Rita; 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…

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

ERIC Educational Resources Information Center

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…

Students' and Teachers' Conceptual Metaphors for Mathematical Problem Solving

ERIC Educational Resources Information Center

Yee, Sean P.

2017-01-01

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

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

NASA Astrophysics Data System (ADS)

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.

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

ERIC Educational Resources Information Center

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

ERIC Educational Resources Information Center

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…

Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

ERIC Educational Resources Information Center

Rasiman

2015-01-01

This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Categorization and analysis of explanatory writing in mathematics

NASA Astrophysics Data System (ADS)

Craig, Tracy S.

2011-10-01

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students' written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students' level of engagement with the mathematical material and with their stance towards knowledge.

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

NASA Astrophysics Data System (ADS)

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.

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

ERIC Educational Resources Information Center

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…

Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

ERIC Educational Resources Information Center

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

2017-01-01

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

ERIC Educational Resources Information Center

Mairing, Jackson Pasini

2017-01-01

Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

Prospective Elementary Teachers' Beliefs about Collaborative Problem Solving and Dialogue in Mathematics

ERIC Educational Resources Information Center

Xenofontos, Constantinos; Kyriakou, Artemis

2017-01-01

This study is concerned with prospective elementary teachers' beliefs about collaborative problem solving and dialogue in mathematics classrooms. Participants (n = 16) attended an undergraduate module titled "Problem Solving in Primary Mathematics", which was specifically designed to provide them with opportunities in collaborative…

Mathematical Problem Solving through Sequential Process Analysis

ERIC Educational Resources Information Center

Codina, A.; Cañadas, M. C.; Castro, E.

2015-01-01

Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

Collis-Romberg Mathematical Problem Solving Profiles.

ERIC Educational Resources Information Center

Collis, K. F.; Romberg, T. A.

Problem solving has become a focus of mathematics programs in Australia in recent years, necessitating the assessment of students' problem-solving abilities. This manual provides a problem-solving assessment and teaching resource package containing four elements: (1) profiles assessment items; (2) profiles diagnostic forms for recording individual…

"I Think I Can, but I'm Afraid to Try": The Role of Self-Efficacy Beliefs and Mathematics Anxiety in Mathematics Problem-Solving Efficiency

ERIC Educational Resources Information Center

Hoffman, Bobby

2010-01-01

This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for…

Mathematical Problem-Solving Styles in the Education of Deaf and Hard-of-Hearing Individuals

ERIC Educational Resources Information Center

Erickson, Elizabeth E. A.

2012-01-01

This study explored the mathematical problem-solving styles of middle school and high school deaf and hard-of-hearing students and the mathematical problem-solving styles of the mathematics teachers of middle school and high school deaf and hard-of-hearing students. The research involved 45 deaf and hard-of-hearing students and 19 teachers from a…

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

ERIC Educational Resources Information Center

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…

Mathematical Problem Solving. Issues in Research.

ERIC Educational Resources Information Center

Lester, Frank K., Jr., Ed.; Garofalo, Joe, Ed.

This set of papers was originally developed for a conference on Issues and Directions in Mathematics Problem Solving Research held at Indiana University in May 1981. The purpose is to contribute to the clear formulation of the key issues in mathematical problem-solving research by presenting the ideas of actively involved researchers. An…

The Place of Problem Solving in Contemporary Mathematics Curriculum Documents

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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.…

Kindergarten Students Solving Mathematical Word Problems

ERIC Educational Resources Information Center

Johnson, Nickey Owen

2013-01-01

The purpose of this study was to explore problem solving with kindergarten students. This line of inquiry is highly significant given that Common Core State Standards emphasize deep, conceptual understanding in mathematics as well as problem solving in kindergarten. However, there is little research on problem solving with kindergarten students.…

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

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

NASA Astrophysics Data System (ADS)

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 the borderland between mathematics and physics

NASA Astrophysics Data System (ADS)

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.

The Acquisition of Problem-Solving Skills in Mathematics: How Animations Can Aid Understanding of Structural Problem Features and Solution Procedures

ERIC Educational Resources Information Center

Scheiter, Katharina; Gerjets, Peter; Schuh, Julia

2010-01-01

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

ERIC Educational Resources Information Center

Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.

2016-01-01

Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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.…

A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance

NASA Technical Reports Server (NTRS)

Thomas, Valerie L.

2004-01-01

U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.

The relation between children’s constructive play activities, spatial ability, and mathematical word problem-solving performance: a mediation analysis in sixth-grade students

PubMed Central

Oostermeijer, Meike; Boonen, Anton J. H.; Jolles, Jelle

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 performance on mathematical word problems is, however, not reported yet. The aim of the present study was to investigate whether spatial ability acted as a mediator in the relation between constructive play and mathematical word problem-solving performance in 128 sixth-grade elementary school children. This mediating role of spatial ability was tested by utilizing the current mediation approaches suggested by Preacher and Hayes (2008). Results showed that 38.16% of the variance in mathematical word problem-solving performance is explained by children’s constructive play activities and spatial ability. More specifically, spatial ability acted as a partial mediator, explaining 31.58% of the relation between constructive play and mathematical word problem-solving performance. PMID:25101038

Socially Shared Metacognition of Dyads of Pupils in Collaborative Mathematical Problem-Solving Processes

ERIC Educational Resources Information Center

Iiskala, Tuike; Vauras, Marja; Lehtinen, Erno; Salonen, Pekka

2011-01-01

This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of…

Working Memory Components as Predictors of Children's Mathematical Word Problem Solving

ERIC Educational Resources Information Center

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

2011-01-01

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,…

Analyzing the Effects of a Mathematics Problem-Solving Program, Exemplars, on Mathematics Problem-Solving Scores with Deaf and Hard-of-Hearing Students

ERIC Educational Resources Information Center

Chilvers, Amanda Leigh

2013-01-01

Researchers have noted that mathematics achievement for deaf and hard-of-hearing (d/hh) students has been a concern for many years, including the ability to problem solve. This quasi-experimental study investigates the use of the Exemplars mathematics program with students in grades 2-8 in a school for the deaf that utilizes American Sign Language…

Student’s thinking process in solving word problems in geometry

NASA Astrophysics Data System (ADS)

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.

Tutoring Mathematical Word Problems Using Solution Trees: Text Comprehension, Situation Comprehension, and Mathematization in Solving Story Problems. Research Report No. 8.

ERIC Educational Resources Information Center

Reusser, Kurt; And Others

The main concern of this paper is on the psychological processes of how students understand and solve mathematical word problems, and on how this knowledge can be applied to computer-based tutoring. It is argued that only a better understanding of the psychological requirements for understanding and solving those problems will lead to…

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

NASA Astrophysics Data System (ADS)

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.

Effectiveness of discovery learning model on mathematical problem solving

NASA Astrophysics Data System (ADS)

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.

South African Grade 9 Mathematics Teachers' Views on the Teaching of Problem Solving

ERIC Educational Resources Information Center

Chirinda, Brantina; Barmby, Patrick

2018-01-01

The South African curriculum emphasizes the teaching of problem solving in mathematics. However, little is known about South African teachers' views on the teaching of mathematical problem solving (MPS). The purpose of this study was to establish Grade 9 South African teachers' views, teaching strategies and the support required in their teaching…

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

ERIC Educational Resources Information Center

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…

Model-Eliciting Activities (MEAs) as a Bridge between Engineering Education Research and Mathematics Education Research

ERIC Educational Resources Information Center

Hamilton, Eric; Lesh, Richard; Lester, Frank; Brilleslyper, Michael

2008-01-01

This article introduces Model-Eliciting Activities (MEAs) as a form of case study team problem-solving. MEA design focuses on eliciting from students conceptual models that they iteratively revise in problem-solving. Though developed by mathematics education researchers to study the evolution of mathematical problem-solving expertise in middle…

The Motivation of Secondary School Students in Mathematical Word Problem Solving

ERIC Educational Resources Information Center

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…

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

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

ERIC Educational Resources Information Center

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…

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

Pose and Solve Varignon Converse Problems

ERIC Educational Resources Information Center

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,…

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

ERIC Educational Resources Information Center

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…

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

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

NASA Astrophysics Data System (ADS)

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.

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

ERIC Educational Resources Information Center

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)

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

ERIC Educational Resources Information Center

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 Influence of Cognitive Abilities on Mathematical Problem Solving Performance

ERIC Educational Resources Information Center

Bahar, Abdulkadir

2013-01-01

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 students. The…

Embedding Game-Based Problem-Solving Phase into Problem-Posing System for Mathematics Learning

ERIC Educational Resources Information Center

Chang, Kuo-En; Wu, Lin-Jung; Weng, Sheng-En; Sung, Yao-Ting

2012-01-01

A problem-posing system is developed with four phases including posing problem, planning, solving problem, and looking back, in which the "solving problem" phase is implemented by game-scenarios. The system supports elementary students in the process of problem-posing, allowing them to fully engage in mathematical activities. In total, 92 fifth…

Problem Solvers: Problem--Jesse's Train

ERIC Educational Resources Information Center

James, Julie; Steimle, Alice

2014-01-01

Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…

Processes involved in solving mathematical problems

NASA Astrophysics Data System (ADS)

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.

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

ERIC Educational Resources Information Center

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…

Mathematical Word Problem Solving Ability of Children with Autism Spectrum Disorder and their Typically Developing Peers.

PubMed

Bae, Young Seh; Chiang, Hsu-Min; Hickson, Linda

2015-07-01

This study examined the difference between children with autism spectrum disorders (ASD) and children with typical development (TD) in mathematical word problem solving ability and the factors associated with these children's word problem-solving ability. A total of 20 children with ASD and 20 children with TD participated in this study. Independent sample t tests and Spearman's rho correlations were used for data analysis. This study found: (a) Children with TD had higher word problem solving ability than did children with ASD; (b) Sentence comprehension, math vocabulary, computation, and everyday mathematical knowledge were associated with word problem solving ability of children with ASD and children with TD; and (c) Children with TD had higher everyday mathematical knowledge than did children with ASD.

Characterising the Cognitive Processes in Mathematical Investigation

ERIC Educational Resources Information Center

Yeo, Joseph B. W.; Yeap, Ban Har

2010-01-01

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

The enhancement of students' mathematical problem solving ability through teaching with metacognitive scaffolding approach

NASA Astrophysics Data System (ADS)

Prabawanto, Sufyani

2017-05-01

This research aims to investigate the enhancement of students' mathematical problem solving through teaching with metacognitive scaffolding approach. This research used a quasi-experimental design with pretest-posttest control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 studentswho acquire teaching mathematicsunder metacognitive scaffolding approach, while the control group consists of 58 studentswho acquire teaching mathematicsunder direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical problem solving test instruments. By usingmean difference test, two conclusions of the research:(1) there is a significant difference in the enhancement of mathematical problem solving between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and(2) thereis no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students' mathematical problem solving.

Mathematical Problem Solving with Technology: The Techno-Mathematical Fluency of a Student-with-GeoGebra

ERIC Educational Resources Information Center

Jacinto, Hélia; Carreira, Susana

2017-01-01

This study offers a view on students' technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the…

Mathematics as a Course of Study in Problem Solving: Then and Now.

ERIC Educational Resources Information Center

Ellis, Wade, Jr.

The mathematics curriculum in the first 2 years of college is a tool created to assist in solving problems. The current mathematics curriculum has changed little; the same topics, tied to the engineering and science curriculum, are taught as they were being taught in 1945. The problems that students need to solve have changed however. Both the…

The Interrelationship of Sex, Visual Spatial Abilities, and Mathematical Problem Solving Ability in Grade Seven. Parts 1, 2, and 3.

ERIC Educational Resources Information Center

Schonberger, Ann Koch

This three-volume report deals with the hypothesis that males are more successful at solving mathematical and spatial problems than females. The general relationship between visual spatial abilities and mathematical problem-solving ability is also investigated. The research sample consisted of seventh graders. Each pupil took five spatial tests…

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

ERIC Educational Resources Information Center

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…

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Problem Solving in Swedish Mathematics Textbooks for Upper Secondary School

ERIC Educational Resources Information Center

Brehmer, Daniel; Ryve, Andreas; Van Steenbrugge, Hendrik

2016-01-01

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

Adolescent Mathematical Problem Solving: The Role of Metacognition, Strategies and Beliefs.

ERIC Educational Resources Information Center

Fitzpatrick, Corine

Mathematical problem solving has been the focus of much concern. This study investigated the relationship of various cognitive factors, attributions, and gender to the solution of mathematics problems by 100 high school seniors. The independent variables examined in this study included: (1) mathematics knowledge as measured by a score on the…

Mexican high school students' social representations of mathematics, its teaching and learning

NASA Astrophysics Data System (ADS)

Martínez-Sierra, Gustavo; Miranda-Tirado, Marisa

2015-07-01

This paper reports a qualitative research that identifies Mexican high school students' social representations of mathematics. For this purpose, the social representations of 'mathematics', 'learning mathematics' and 'teaching mathematics' were identified in a group of 50 students. Focus group interviews were carried out in order to obtain the data. The constant comparative style was the strategy used for the data analysis because it allowed the categories to emerge from the data. The students' social representations are: (A) Mathematics is…(1) important for daily life, (2) important for careers and for life, (3) important because it is in everything that surrounds us, (4) a way to solve problems of daily life, (5) calculations and operations with numbers, (6) complex and difficult, (7) exact and (6) a subject that develops thinking skills; (B) To learn mathematics is…(1) to possess knowledge to solve problems, (2) to be able to solve everyday problems, (3) to be able to make calculations and operations, and (4) to think logically to be able to solve problems; and (C) To teach mathematics is…(1) to transmit knowledge, (2) to know to share it, (3) to transmit the reasoning ability, and (4) to show how to solve problems.

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

ERIC Educational Resources Information Center

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),…

Latinas and Problem Solving: What They Say and What They Do

ERIC Educational Resources Information Center

Guerra, Paula; Lim, Woong

2014-01-01

In this article, the authors present three adolescent Latinas' perceptions of ideal mathematical competencies, their perception of their individual "abilities" in mathematics, and their work on a mathematics problem-solving task. Results indicate that these Latinas recognize flexible mathematics as the ideal mathematical competency in…

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

NASA Astrophysics Data System (ADS)

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.

Effectiveness of Small-Group Tutoring Interventions for Improving the Mathematical Problem-Solving Performance of Third-Grade Students with Mathematics Difficulties: A Randomized Experiment

ERIC Educational Resources Information Center

Jitendra, Asha K.; Dupuis, Danielle N.; Rodriguez, Michael C.

2012-01-01

The present research assessed the efficacy of two tutoring protocols for improving the mathematics outcomes of at-risk third-grade students. Results indicated that students in the schema-based instruction (SBI) group outperformed students in the control group on word problem solving performance after 30 hours of problem-solving experience, but the…

Examination of the Mathematical Problem-Solving Beliefs and Success Levels of Primary School Teacher Candidates through the Variables of Mathematical Success and Gender

ERIC Educational Resources Information Center

Bal, Ayten Pinar

2015-01-01

The aim of this study is to examine the mathematical problem-solving beliefs and problem-solving success levels of primary school teacher candidates through the variables of academic success and gender. The research was designed according to the mixed methods technique in which qualitative and quantitative methods are used together. The working…

Mathematics at Work in Alberta.

ERIC Educational Resources Information Center

Glanfield, Florence, Ed.; Tilroe, Daryle, Ed.

This document is designed to assist teachers by providing practical examples of real world applications of high school mathematics. Fifteen problems are presented that individuals in industry and business solve using mathematics. Each problem provides the contributor's name, suggested skills required to solve the problem, background information…

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

ERIC Educational Resources Information Center

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 the results of an analysis of four…

Different Procedures for Solving Mathematical Word Problems in High School

ERIC Educational Resources Information Center

Gasco, Javier; Villarroel, Jose Domingo; Zuazagoitia, Dani

2014-01-01

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

Assessing Mathematics 4. Problem Solving: The APU Approach.

ERIC Educational Resources Information Center

Foxman, Derek; And Others

1984-01-01

Presented are examples of problem-solving items from practical and written mathematics tests. These tests are part of an English survey designed to assess the mathematics achievement of students aged 11 and 15. (JN)

A Randomized Trial of the Effects of Schema-Based Instruction on Proportional Problem-Solving for Students with Mathematics Problem-Solving Difficulties

ERIC Educational Resources Information Center

Jitendra, Asha K.; Harwell, Michael R.; Dupuis, Danielle N.; Karl, Stacy R.

2016-01-01

This paper reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their…

A Randomized Trial of the Effects of Schema-Based Instruction on Proportional Problem-Solving for Students with Mathematics Problem-Solving Difficulties

ERIC Educational Resources Information Center

Jitendra, Asha K.; Harwell, Michael R.; Dupuis, Danielle N.; Karl, Stacy R.

2017-01-01

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and…

An Investigation of Construct Relevant and Irrelevant Features of Mathematics Problem-Solving Questions Using Comparative Judgement and Kelly's Repertory Grid

ERIC Educational Resources Information Center

Holmes, Stephen D.; He, Qingping; Meadows, Michelle

2017-01-01

The relationship between the characteristics of 33 mathematical problem-solving questions answered by 16-year-old students in England and the quality of problem-solving elicited was investigated in two studies. The first study used comparative judgement (CJ) to estimate the quality of the problem-solving elicited by each question, involving 33…

Glogs as Non-Routine Problem Solving Tools in Mathematics

ERIC Educational Resources Information Center

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 Problem Solving to Assess Young Children's Mathematics Knowledge

ERIC Educational Resources Information Center

Charlesworth, Rosalind; Leali, Shirley A.

2012-01-01

Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

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

NASA Astrophysics Data System (ADS)

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.

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Reading-Enhanced Word Problem Solving: A Theoretical Model

ERIC Educational Resources Information Center

Capraro, Robert M.; Capraro, Mary Margaret; Rupley, William H.

2012-01-01

There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…

Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

Student’s scheme in solving mathematics problems

NASA Astrophysics Data System (ADS)

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.

The Mathematical Preparation of Prospective Elementary Teachers: Reflections from Solving an "Interesting Problem"

ERIC Educational Resources Information Center

Ellis, Mark W.; Contreras, Jose; Martinez-Cruz, Armando M.

2009-01-01

Problem solving tasks offer valuable opportunities to strengthen prospective elementary teachers' knowledge of and disposition toward mathematics, providing them with new experiences doing mathematics. Mathematics educators can influence future instruction by modeling effective pedagogical strategies that engage students in making sense of…

Instructional Qualities of a Successful Mathematical Problem-Solving Class.

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

1998-01-01

Describes activities that have been successfully implemented by an expert during a mathematical problem-solving course. Focuses on the identification of the qualities of these problems used to promote the development of student strategies and values that reflect mathematical practice in the classroom. Contains 17 references. (ASK)

Students' Activity in Computer-Supported Collaborative Problem Solving in Mathematics

ERIC Educational Resources Information Center

Hurme, Tarja-riitta; Jarvela, Sanna

2005-01-01

The purpose of this study was to analyse secondary school students' (N = 16) computer-supported collaborative mathematical problem solving. The problem addressed in the study was: What kinds of metacognitive processes appear during computer-supported collaborative learning in mathematics? Another aim of the study was to consider the applicability…

Problem Solving and Computational Skill: Are They Shared or Distinct Aspects of Mathematical Cognition?

PubMed Central

Fuchs, Lynn S.; Fuchs, Douglas; Hamlett, Carol L.; Lambert, Warren; Stuebing, Karla; Fletcher, Jack M.

2009-01-01

The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed. PMID:20057912

Towards the Construction of a Framework to Deal with Routine Problems to Foster Mathematical Inquiry

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Camacho-Machin, Matias

2009-01-01

To what extent does the process of solving textbook problems help students develop a way of thinking that is consistent with mathematical practice? Can routine problems be transformed into problem solving activities that promote students' mathematical reflection? These questions are used to outline and discuss features of an inquiry framework…

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

NASA Astrophysics Data System (ADS)

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%).

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

The Influence of English-Korean Bilingualism in Solving Mathematics Word Problems.

ERIC Educational Resources Information Center

Whang, Woo-Hyung

1996-01-01

Purposeful sampling was used to select six English-Korean bilingual students to investigate language difficulties and cognitive processes in solving mathematics word problems. These six case studies revealed distinct patterns of difficulties in solving problems written in English and Korean, especially for students in transition stage. (Author/KMC)

Learning from Examples versus Verbal Directions in Mathematical Problem Solving

ERIC Educational Resources Information Center

Lee, Hee Seung; Fincham, Jon M.; Anderson, John R.

2015-01-01

This event-related fMRI study investigated the differences between learning from examples and learning from verbal directions in mathematical problem solving and how these instruction types affect the activity of relevant brain regions during instruction and solution periods within problem-solving trials. We identified distinct neural signatures…

Students' Use of Technological Features while Solving a Mathematics Problem

ERIC Educational Resources Information Center

Lee, Hollylynne Stohl; Hollebrands, Karen F.

2006-01-01

The design of technology tools has the potential to dramatically influence how students interact with tools, and these interactions, in turn, may influence students' mathematical problem solving. To better understand these interactions, we analyzed eighth grade students' problem solving as they used a java applet designed to specifically accompany…

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

NASA Astrophysics Data System (ADS)

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.

Collection of solved problems in physics

NASA Astrophysics Data System (ADS)

Koupilová, ZdeÅka; Mandíková, Dana; Snětinová, Marie

2017-01-01

To solve physics problems is a key ability which students should reach during their physics education. Ten years ago we started to develop a Collection of fully solved problems. The structure of problems' solutions is specially designed to substitute tutor's help during lesson and encourage students to solve at least some parts of a problem independently. Nowadays the database contains about 770 fully solved problems in physics in Czech, more than 100 problems in Polish and more than 140 problems in English. Other problems are still being translated. Except for physics problems, the Collection has also a mathematical part, which contains more than 300 fully solved problems in mathematics. This paper follows the presentation of the Collection of solved problems from previous years and introduces a new interface of the Collection, its enhanced functionality, new topics, newly created interface for teachers, user feedback and plans for future development. The database is placed at the website of the Department of Physics Education, Faculty of Mathematics and Physics, Charles University in Prague, the links are: http://reseneulohy.cz/fyzika (Czech version); http://www.physicstasks.eu/ (English version).

Mathematical Giftedness, Problem Solving, and the Ability To Formulate Generalizations: The Problem-Solving Experiences of Four Gifted Students.

ERIC Educational Resources Information Center

Sriraman, Bharath

2003-01-01

Nine freshmen in a ninth-grade accelerated algebra class were asked to solve five nonroutine combinatorial problems. The four mathematically gifted students were successful in discovering and verbalizing the generality that characterized the solutions to the five problems, whereas the five nongifted students were unable to discover the hidden…

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

How Young Students Communicate Their Mathematical Problem Solving in Writing

ERIC Educational Resources Information Center

Teledahl, Anna

2017-01-01

This study investigates young students' writing in connection to mathematical problem solving. Students' written communication has traditionally been used by mathematics teachers in the assessment of students' mathematical knowledge. This study rests on the notion that this writing represents a particular activity which requires a complex set of…

Enhancing Mathematical Problem Solving for Secondary Students with or at Risk of Learning Disabilities: A Literature Review

ERIC Educational Resources Information Center

Hwang, Jiwon; Riccomini, Paul J.

2016-01-01

Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as…

The Microevolution of Mathematical Representations in Children's Activity.

ERIC Educational Resources Information Center

Meira, Luciano

1995-01-01

Discusses children's design of mathematical representations on paper. Suggests that the design of displays during problem solving shapes one's mathematical activity and sense making in crucial ways, and that knowledge of mathematical representations is not simply recalled and applied to problem solving, but also emerges out of one's interactions…

Mathematical Problem Solving Ability of Eleventh Standard Students

ERIC Educational Resources Information Center

Priya, J. Johnsi

2017-01-01

There is a general assertion among mathematics instructors that learners need to acquire problem solving expertise, figure out how to communicate using mathematics knowledge and aptitude, create numerical reasoning and thinking, to see the interconnectedness amongst mathematics and other subjects. Based on this perspective, the present study aims…

Can goal-free problems facilitating students' flexible thinking?

NASA Astrophysics Data System (ADS)

Maulidya, Sity Rahmy; Hasanah, Rusi Ulfa; Retnowati, Endah

2017-08-01

Problem solving is the key of doing and also learning mathematics. It takes also the fundamental role of developing mathematical knowledge. Responding to the current reform movement in mathematics, students are expected to learn to be a flexible thinker. The ability to think flexible is challenged by the globalisation, hence influence mathematics education. A flexible thinking includes ability to apply knowledge in different contexts rather than simply use it in similar context when it is studied. Arguably problem solving activities can contribute to the development of the ability to apply skills to unfamiliar situations. Accordingly, an appropriate classroom instructional strategy must be developed. A cognitive load theory suggests that by reducing extraneous cognitive load during learning could enhance transfer learning. A goal-free problem strategy that is developed based in cognitive load theory have been showed to be effective for transfer learning. This strategy enables students to learn a large numbers of problem solving moves from a mathematics problem. The instruction in a goal-free problem directs students to `calculate as many solution as you can' rather than to calculate a single given goal. Many experiment research evident goal-free problem enhance learning. This literature review will discuss evidence goal-free problem facilitate students to solve problems flexibly and thus enhance their problem solving skills, including how its implication in the classroom.

The Effect of Cognitive- and Metacognitive-Based Instruction on Problem Solving by Elementary Students with Mathematical Learning Difficulties

ERIC Educational Resources Information Center

Grizzle-Martin, Tamieka

2014-01-01

Children who struggle in mathematics may also lack cognitive awareness in mathematical problem solving. The cognitively-driven program IMPROVE, a multidimensional method for teaching mathematics, has been shown to be helpful for students with mathematical learning difficulties (MLD). Guided by cognitive theory, the purpose of this…

Constructive Metacognitive Activity Shift in Mathematical Problem Solving

ERIC Educational Resources Information Center

Hastuti, Intan Dwi; Nusantara, Toto; Subanji; Susanto, Hery

2016-01-01

This study aims to describe the constructive metacognitive activity shift of eleventh graders in solving a mathematical problem. Subjects in this study were 10 students in grade 11 of SMAN 1 Malang. They were divided into 4 groups. Three types of metacognitive activity undertaken by students when completing mathematical problem are awareness,…

Shifting College Students' Epistemological Framing Using Hypothetical Debate Problems

ERIC Educational Resources Information Center

Hu, Dehui; Rebello, N. Sanjay

2014-01-01

Developing expertise in physics problem solving requires the ability to use mathematics effectively in physical scenarios. Novices and experts often perceive the use of mathematics in physics differently. Students' perceptions and how they frame the use of mathematics in physics play an important role in their physics problem solving. In this…

Examining How Students with Diverse Abilities Use Diagrams to Solve Mathematics Word Problems

ERIC Educational Resources Information Center

van Garderen, Delinda; Scheuermann, Amy; Jackson, Christa

2013-01-01

This study examined students' understanding of diagrams and their use of diagrams as tools to solve mathematical word problems. Students with learning disabilities (LD), typically achieving students, and gifted students in Grades 4 through 7 ("N" = 95) participated. Students were presented with novel mathematical word problem-solving…

A Comparison of the Effects of LOGO Use and Teacher-Directed Problem-Solving Instruction on the Problem-Solving Skills, Achievement, and Attitudes of Low, Average, and High Achieving Junior High School Learners.

ERIC Educational Resources Information Center

Dalton, David W.

This comparison of the effects of LOGO use with the use of teacher-directed problem-solving instruction, and with conventional mathematics instruction, focused on the problem-solving ability, basic skills achievement, and attitudes of junior high school learners. Students (N=97) in five seventh grade mathematics classes were systematically…

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

ERIC Educational Resources Information Center

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…

Problem Solving Frameworks for Mathematics and Software Development

ERIC Educational Resources Information Center

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…

Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development

ERIC Educational Resources Information Center

Bae, Young Seh

2013-01-01

Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically…

Associations of Students' Beliefs with Self-Regulated Problem Solving in College Algebra

ERIC Educational Resources Information Center

Cifarelli, Victor; Goodson-Espy, Tracy; Chae, Jeong-Lim

2010-01-01

This paper reports results from a study of self-regulated problem solving actions of students enrolled in College Algebra (N = 139). The study examined the associations between the expressed mathematical beliefs of students and the students' self-regulated actions in solving mathematics problems. The research questions are: (a) What are some…

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

ERIC Educational Resources Information Center

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)…

Analytical Derivation: An Epistemic Game for Solving Mathematically Based Physics Problems

ERIC Educational Resources Information Center

Bajracharya, Rabindra R.; Thompson, John R.

2016-01-01

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…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

An Examination of the Relationship between Computation, Problem Solving, and Reading

ERIC Educational Resources Information Center

Cormier, Damien C.; Yeo, Seungsoo; Christ, Theodore J.; Offrey, Laura D.; Pratt, Katherine

2016-01-01

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide…

Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications

ERIC Educational Resources Information Center

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…

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

NASA Astrophysics Data System (ADS)

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.

Analysis of mathematical problem-solving ability based on metacognition on problem-based learning

NASA Astrophysics Data System (ADS)

Mulyono; Hadiyanti, R.

2018-03-01

Problem-solving is the primary purpose of the mathematics curriculum. Problem-solving abilities influenced beliefs and metacognition. Metacognition as superordinate capabilities can direct, regulate cognition and motivation and then problem-solving processes. This study aims to (1) test and analyzes the quality of problem-based learning and (2) investigate the problem-solving capabilities based on metacognition. This research uses mixed method study with The subject research are class XI students of Mathematics and Science at High School Kesatrian 2 Semarang which divided into tacit use, aware use, strategic use and reflective use level. The collecting data using scale, interviews, and tests. The data processed with the proportion of test, t-test, and paired samples t-test. The result shows that the students with levels tacit use were able to complete the whole matter given, but do not understand what and why a strategy is used. Students with aware use level were able to solve the problem, be able to build new knowledge through problem-solving to the indicators, understand the problem, determine the strategies used, although not right. Students on the Strategic ladder Use can be applied and adopt a wide variety of appropriate strategies to solve the issues and achieved re-examine indicators of process and outcome. The student with reflective use level is not found in this study. Based on the results suggested that study about the identification of metacognition in problem-solving so that the characteristics of each level of metacognition more clearly in a more significant sampling. Teachers need to know in depth about the student metacognitive activity and its relationship with mathematical problem solving and another problem resolution.

Fostering Modeling Competencies: Benefits of Worked Examples, Problems to Be Solved, and Fading Procedures

ERIC Educational Resources Information Center

Große, Cornelia S.

2015-01-01

The application of mathematics to real-world problems is moving more and more in the focus of attention of mathematics education; however, many learners experience huge difficulties in relating "pure" mathematics to everyday contents. In order to solve "modeling problems", it is first necessary to find a transition from a…

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

NASA Astrophysics Data System (ADS)

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).

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

ERIC Educational Resources Information Center

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…

Problem Solving in Technology Rich Contexts: Mathematics Sense Making in Out-of-School Environments

ERIC Educational Resources Information Center

Lowrie, Tom

2005-01-01

This investigation describes the way in which a case study participant (aged 7) represented, posed and solved problems in a technology game-based environment. The out-of-school problem-solving context placed numeracy demands on the participant that were more complex and sophisticated than the type of mathematics experiences he encountered in…

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

ERIC Educational Resources Information Center

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…

Mathematical Problem Solving among Latina/o Kindergartners: An Analysis of Opportunities to Learn

ERIC Educational Resources Information Center

Turner, Erin E.; Celedon-Pattichis, Sylvia

2011-01-01

This study explores opportunities to learn mathematics problem solving for Latina/o students in 3 kindergarten classrooms in the southwest. Mixed methods were used to examine teaching practices that engaged Latina/o students in problem solving and supported their learning. Findings indicate that although students in all 3 classrooms showed growth…

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

ERIC Educational Resources Information Center

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…

Survey of Mathematics Teachers' Static and Transformational Performance and Perspectives for Teaching Similarity

ERIC Educational Resources Information Center

Cunningham, Robert F.; Rappa, Anthony

2016-01-01

Surveys were used to examine mathematics teachers (15) on their ability to solve similarity problems and on their likely implementation of lesson objectives for teaching similarity. All correctly solved a similarity problem requiring a traditional static perspective, but 7 out of 15 failed to correctly solve a problem that required a more…

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

ERIC Educational Resources Information Center

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…

Solvers' Making of Drawings in Mathematical Problem Solving and Their Understanding of the Problem Situations

ERIC Educational Resources Information Center

Nunokawa, Kazuhiko

2004-01-01

The purpose of this paper was to investigate how it becomes possible for solvers to make drawings to advance their problem solving processes, in order to understand the use of drawings in mathematical problem solving more deeply. For this purpose, three examples in which drawings made by the solver played a critical role in the solutions have been…

Pattern of mathematic representation ability in magnetic electricity problem

NASA Astrophysics Data System (ADS)

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.

The Art of Problem Solving: A Resource for the Mathematics Teacher.

ERIC Educational Resources Information Center

Posamentier, Alfred S.; Schulz, Wolfgang

This book is designed to give mathematics teachers a host of interesting and useful ideas thereby raising their consciousness level and enabling an enrichment of the mathematics instruction program. The chapters in this book capture a broad spectrum of ideas in the area of mathematics problem solving. Chapters are: (1) "Strategies for Problem…

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

ERIC Educational Resources Information Center

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…

Impulsive-Analytic Disposition in Mathematical Problem Solving: A Survey and a Mathematics Test

ERIC Educational Resources Information Center

Lim, Kien H.; Wagler, Amy

2012-01-01

The Likelihood-to-Act (LtA) survey and a mathematics test were used in this study to assess students' impulsive-analytic disposition in the context of mathematical problem solving. The results obtained from these two instruments were compared to those obtained using two widely-used scales: Need for Cognition (NFC) and Barratt Impulsivity Scale…

Problem Solving in the Borderland between Mathematics and Physics

ERIC Educational Resources Information Center

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

Teacher Mathematical Literacy: Case Study of Junior High School Teachers in Pasaman

NASA Astrophysics Data System (ADS)

Ahmad, D.; Suherman, S.; Maulana, H.

2018-04-01

The aim of this paper was to examine the ability of junior high school mathematics teachers to solve mathematical literacy base Problems (PISA and PISA-like problems) for the case Pasaman regency. The data was collected by interviews and test. As the results of this study, teacher ability in solving mathematical literacy base problems for level 1 until 3 has been good, but for level 4 or above is still low. It is caused by teacher knowledge about mathematical literacy still few.

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics.

PubMed

DeCaro, Marci S

2016-10-01

An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

Connecting Mathematics in Primary Science Inquiry Projects

ERIC Educational Resources Information Center

So, Winnie Wing-mui

2013-01-01

Science as inquiry and mathematics as problem solving are conjoined fraternal twins attached by their similarities but with distinct differences. Inquiry and problem solving are promoted in contemporary science and mathematics education reforms as a critical attribute of the nature of disciplines, teaching methods, and learning outcomes involving…

Calculating Puddle Size

ERIC Educational Resources Information Center

Burton, Megan; Mims, Patricia

2012-01-01

Learning through meaningful problem solving is integral in any successful mathematics program (Carpenter et al. 1999). The National Council of Teachers of Mathematics (NCTM) promotes the use of problem solving as a means to deepen understanding of all content areas within mathematics (NCTM 2000). This article describes a first-grade lesson that…

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

ERIC Educational Resources Information Center

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)

An Investigation of Preservice Teachers' Use of Guess and Check in Solving a Semi Open-Ended Mathematics Problem

ERIC Educational Resources Information Center

Capraro, Mary Margaret; An, Song A.; Ma, Tingting; Rangel-Chavez, A. Fabiola; Harbaugh, Adam

2012-01-01

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a…

Investigating and analyzing prospective teacher's reflective thinking in solving mathematical problem: A case study of female-field dependent (FD) prospective teacher

NASA Astrophysics Data System (ADS)

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

2017-05-01

In the last few years, reflective thinking becomes very popular term in the world of education, especially in professional education of teachers. One of goals of the educational personnel and teacher institutions create responsible prospective teachers and they are able reflective thinking. Reflective thinking is a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. Reflective thinking can be applied in mathematics becauseby reflective thinking, students can improve theircuriosity to solve mathematical problem. In solving mathematical problem is assumed that cognitive style has an impact on prospective teacher's mental activity. As a consequence, reflective thinking and cognitive style are important things in solving mathematical problem. The subject, in this research paper, isa female-prospective teacher who has fielddependent cognitive style. The purpose of this research paperis to investigate the ability of prospective teachers' reflective thinking in solving mathematical problem. This research paper is a descriptive by using qualitativeapproach. To analyze the data related to prospectiveteacher's reflective thinking in solving contextual mathematicalproblem, the researchers focus in four main categories which describe prospective teacher's activities in 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.

Interleaved Practice Improves Mathematics Learning

ERIC Educational Resources Information Center

Rohrer, Doug; Dedrick, Robert F.; Stershic, Sandra

2015-01-01

A typical mathematics assignment consists primarily of practice problems requiring the strategy introduced in the immediately preceding lesson (e.g., a dozen problems that are solved by using the Pythagorean theorem). This means that students know which strategy is needed to solve each problem before they read the problem. In an alternative…

Mathematical Ability Relies on Knowledge, Too

ERIC Educational Resources Information Center

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

2011-01-01

Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…

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

ERIC Educational Resources Information Center

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"…

A Protocol-Analytic Study of Metacognition in Mathematical Problem Solving.

ERIC Educational Resources Information Center

Cai, Jinfa

1994-01-01

Metacognitive behaviors of subjects having high (n=2) and low (n=2) levels of mathematical experience were compared across four cognitive processes in mathematical problem solving: orientation, organization, execution, and verification. High-experience subjects engaged in self-regulation and spent more time on orientation and organization. (36…

Assessing Mathematical Problem Solving Using Comparative Judgement

ERIC Educational Resources Information Center

Jones, Ian; Swan, Malcolm; Pollitt, Alastair

2015-01-01

There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Mathematical Word Problem Solving Ability of Children with Autism Spectrum Disorder and Their Typically Developing Peers

ERIC Educational Resources Information Center

Bae, Young Seh; Chiang, Hsu-Min; Hickson, Linda

2015-01-01

This study examined the difference between children with autism spectrum disorders (ASD) and children with typical development (TD) in mathematical word problem solving ability and the factors associated with these children's word problem-solving ability. A total of 20 children with ASD and 20 children with TD participated in this study.…

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

NASA Astrophysics Data System (ADS)

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.

Mathematics Word Problem Solving: An Investigation into Schema-Based Instruction in a Computer-Mediated Setting and a Teacher-Mediated Setting with Mathematically Low-Performing Students

ERIC Educational Resources Information Center

Leh, Jayne

2011-01-01

Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to…

Proceedings of the China-Japan-U.S. Seminar on Mathematical Education.

ERIC Educational Resources Information Center

Zhang, Dianzhou, Ed.; And Others

This document contains the proceedings of the China-Japan-U.S. Seminar on Mathematical Education that was held in 1993 in China. The focus of the Seminar was problem solving in mathematics education. The main purposes of the seminar were: to examine the present states of problem solving in school mathematics in China, Japan, and the U.S.; to…

A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

NASA Astrophysics Data System (ADS)

Tuminaro, Jonathan

Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of mathematical use in the context physics, and (2) a detailed understanding, in terms of the proposed theoretical framework, of the errors that students make when using mathematics in the context of physics.

Using the concrete-representational-abstract approach to support students with intellectual disability to solve change-making problems.

PubMed

Bouck, Emily; Park, Jiyoon; Nickell, Barb

2017-01-01

The Concrete-Representational-Abstract (CRA) instructional approach supports students with disabilities in mathematics. Yet, no research explores the use of the CRA approach to teach functional-based mathematics for this population and limited research explores the CRA approach for students who have a disability different from a learning disability, such as an intellectual disability. This study investigated the effects of using the CRA approach to teach middle school students in a self-contained mathematics class focused on functional-based mathematics to solve making change problems. Researchers used a multiple probe across participants design to determine if a functional relation existed between the CRA strategy and students' ability to solve making change problems. The study of consisted of five-to-eight baseline sessions, 9-11 intervention sessions, and two maintenance sessions for each student. Data were collected on percentage of making change problems students solved correctly. The CRA instructional strategy was effective in teaching all four participants to correctly solve the problems; a functional relation between the CRA approach and solving making change with coins problems across all participants was found. The CRA instructional approach can be used to support students with mild intellectual disability or severe learning disabilities in learning functional-based mathematics, such as purchasing skills (i.e., making change). Copyright © 2016 Elsevier Ltd. All rights reserved.

The Effects of Using Drawings in Developing Young Children's Mathematical Word Problem Solving: A Design Experiment with Third-Grade Hungarian Students

ERIC Educational Resources Information Center

Csikos, Csaba; Szitanyi, Judit; Kelemen, Rita

2012-01-01

The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students' knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment…

Assessing the Effectiveness of STAD Model and Problem Based Learning in Mathematics Learning Achievement and Problem Solving Ability

ERIC Educational Resources Information Center

Rattanatumma, Tawachai; Puncreobutr, Vichian

2016-01-01

The objective of this study was to compare the effectiveness of teaching methods in improving Mathematics Learning Achievement and Problem solving ability of students at an international college. This is a Quasi-Experimental Research which was done the study with the first year students who have registered to study Mathematics subject at St.…

The Development of a Culture of Problem Solving with Secondary Students through Heuristic Strategies

ERIC Educational Resources Information Center

Eisenmann, Petr; Novotná, Jarmila; Pribyl, Jirí; Brehovský, Jirí

2015-01-01

The article reports the results of a longitudinal research study conducted in three mathematics classes in Czech schools with 62 pupils aged 12-18 years. The pupils were exposed to the use of selected heuristic strategies in mathematical problem solving for a period of 16 months. This was done through solving problems where the solution was the…

Procedural versus Content-Related Hints for Word Problem Solving: An Exploratory Study

ERIC Educational Resources Information Center

Kock, W. D.; Harskamp, E. G.

2016-01-01

For primary school students, mathematical word problems are often more difficult to solve than straightforward number problems. Word problems require reading and analysis skills, and in order to explain their situational contexts, the proper mathematical knowledge and number operations have to be selected. To improve students' ability in solving…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Robotic Toys as a Catalyst for Mathematical Problem Solving

ERIC Educational Resources Information Center

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…

Solving Common Mathematical Problems

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.

Metacognition and Meta-Affect in Young Students: Does It Make a Difference in Mathematical Problem Solving?

ERIC Educational Resources Information Center

Tzohar-Rozen, Meirav; Kramarski, Bracha

2017-01-01

Mathematical problem solving is one of the most valuable aspects of mathematics education and the most difficult for elementary school students. Cognitive and metacognitive difficulties in this area cause students to develop negative attitudes and emotions as affective reactions, hampering their efforts and achievements. These metacognitive and…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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

Future Primary and Preschool Pedagogy Specialization Students' Mathematical Problem Solving Competency

ERIC Educational Resources Information Center

Marchis, Iuliana

2013-01-01

Developing the problem solving competency is one of the main goals of school education, as it is a very important competency in someone's everyday life and career as well. Mathematics is highly appropriate for developing this competence. This research studies future Primary and Preschool Pedagogy specialization students' mathematical problem…

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

PubMed

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 Paper Folding

ERIC Educational Resources Information Center

Wares, Arsalan

2014-01-01

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

Math Is Not a Problem...When You Know How to Visualize It.

ERIC Educational Resources Information Center

Nelson, Dennis W.

1983-01-01

Visualization is an effective technique for determining exactly what students must do to solve a mathematics problem. Pictures and charts can be used to help children understand which mathematics facts are present and which are missing--an important step toward problem solving. (PP)

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

NASA Astrophysics Data System (ADS)

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.

Conceptualizing Perseverance in Problem Solving as Collective Enterprise

ERIC Educational Resources Information Center

Sengupta-Irving, Tesha; Agarwal, Priyanka

2017-01-01

Students are expected to learn mathematics such that when they encounter challenging problems they will persist. Creating opportunities for students to persist in problem solving is therefore argued as essential to effective teaching and to children developing positive dispositions in mathematical learning. This analysis takes a novel approach to…

Mathematical Problem Solving for Youth with ADHD, with and without Learning Disabilities.

ERIC Educational Resources Information Center

Zentall, Sydney S.; Ferkis, Mary Ann

1993-01-01

This review of research finds that, when IQ and reading ability are controlled, "true" math deficits of students with learning disabilities, attention deficit disorders, and attention deficit hyperactive disorders (ADHD) are specific to mathematical concepts and problem types. Slow computation affects problem solving by increasing attentional…

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

NASA Astrophysics Data System (ADS)

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.

Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students

NASA Astrophysics Data System (ADS)

Priyani, H. A.; Ekawati, R.

2018-01-01

Indonesian students’ competence in solving mathematical problems is still considered as weak. It was pointed out by the results of international assessment such as TIMSS. This might be caused by various types of errors made. Hence, this study aimed at identifying students’ errors in solving mathematical problems in TIMSS in the topic of numbers that considered as the fundamental concept in Mathematics. This study applied descriptive qualitative analysis. The subject was three students with most errors in the test indicators who were taken from 34 students of 8th graders. Data was obtained through paper and pencil test and student’s’ interview. The error analysis indicated that in solving Applying level problem, the type of error that students made was operational errors. In addition, for reasoning level problem, there are three types of errors made such as conceptual errors, operational errors and principal errors. Meanwhile, analysis of the causes of students’ errors showed that students did not comprehend the mathematical problems given.

The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving Framework

ERIC Educational Resources Information Center

Carlson, Marilyn P.; Bloom, Irene

2005-01-01

This paper describes the problem-solving behaviors of 12 mathematicians as they completed four mathematical tasks. The emergent problem-solving framework draws on the large body of research, as grounded by and modified in response to our close observations of these mathematicians. The resulting "Multidimensional Problem-Solving Framework" has four…

Mathematical Problem Solving: A Review of the Literature.

ERIC Educational Resources Information Center

Funkhouser, Charles

The major perspectives on problem solving of the twentieth century are reviewed--associationism, Gestalt psychology, and cognitive science. The results of the review on teaching problem solving and the uses of computers to teach problem solving are included. Four major issues related to the teaching of problem solving are discussed: (1)…

The Use of Mathematical Symbolism in Problem Solving: An Empirical Study Carried out in Grade One in the French Community of Belgium

ERIC Educational Resources Information Center

Fagnant, Annick

2005-01-01

This article relates to an empirical study based on the use of mathematical symbolism in problem solving, twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a…

Solving the water jugs problem by an integer sequence approach

NASA Astrophysics Data System (ADS)

Man, Yiu-Kwong

2012-01-01

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and lecturers involved in teaching mathematical problem solving, recreational mathematics, or elementary number theory.

Characteristics of Students at Risk for Mathematics Difficulties Predicting Arithmetic Word Problem Solving Performance: The Role of Attention, Behavior, and Reading

ERIC Educational Resources Information Center

Jitendra, Asha K.; Corroy, Kelly Cozine; Dupuis, Danielle N.

2013-01-01

The purposes of this study were (a) to evaluate differences in arithmetic word problem solving between high and low at-risk students for mathematics difficulties (MD) and (b) to assess the influence of attention, behavior, reading, and socio-economic status (SES) in predicting the word problem solving performance of third-grade students with MD.…

Students’ difficulties in probabilistic problem-solving

NASA Astrophysics Data System (ADS)

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 effect of mathematical model development on the instruction of acceleration to introductory physics students

NASA Astrophysics Data System (ADS)

Sauer, Tim Allen

The purpose of this study was to evaluate the effectiveness of utilizing student constructed theoretical math models when teaching acceleration to high school introductory physics students. The goal of the study was for the students to be able to utilize mathematical modeling strategies to improve their problem solving skills, as well as their standardized scientific and conceptual understanding. This study was based on mathematical modeling research, conceptual change research and constructivist theory of learning, all of which suggest that mathematical modeling is an effective way to influence students' conceptual connectiveness and sense making of formulaic equations and problem solving. A total of 48 students in two sections of high school introductory physics classes received constructivist, inquiry-based, cooperative learning, and conceptual change-oriented instruction. The difference in the instruction for the 24 students in the mathematical modeling treatment group was that they constructed every formula they needed to solve problems from data they collected. In contrast, the instructional design for the control group of 24 students allowed the same instruction with assigned problems solved with formulas given to them without explanation. The results indicated that the mathematical modeling students were able to solve less familiar and more complicated problems with greater confidence and mental flexibility than the control group students. The mathematical modeling group maintained fewer alternative conceptions consistently in the interviews than did the control group. The implications for acceleration instruction from these results were discussed.

Evaluating the Use of Problem-Based Video Podcasts to Teach Mathematics in Higher Education

ERIC Educational Resources Information Center

Kay, Robin; Kletskin, Ilona

2012-01-01

Problem-based video podcasts provide short, web-based, audio-visual explanations of how to solve specific procedural problems in subject areas such as mathematics or science. A series of 59 problem-based video podcasts covering five key areas (operations with functions, solving equations, linear functions, exponential and logarithmic functions,…

Modeling Scientific Processes with Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving

ERIC Educational Resources Information Center

Schuchardt, Anita M.; Schunn, Christian D.

2016-01-01

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…

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

ERIC Educational Resources Information Center

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…

Should Mathematics Be a Mandatory Fundamental Component of Any IT Discipline?

ERIC Educational Resources Information Center

Eid, Chaker; Millham, Richard

2013-01-01

In this paper, we investigate whether and how mathematics factors into students' performance in IT learning. The involved cognitive levels of students learning mathematics and hence problem solving, are correlated to how well they are able to transpose their knowledge and apply it to problem solving in the IT field(s). Our hypothesis is that if…

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

ERIC Educational Resources Information Center

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…

Impact of Teachers' Planned Questions on Opportunities for Students to Reason Mathematically in Whole-Class Discussions around Mathematical Problem-Solving Tasks

ERIC Educational Resources Information Center

Enoch, Sarah Elizabeth

2013-01-01

While professional developers have been encouraging teachers to plan for discourse around problem solving tasks as a way to orchestrate mathematically productive discourse (Stein, Engle, Smith, & Hughes, 2008; Stein, Smith, Henningsen, & Silver, 2009) no research has been conducted explicitly examining the relationship between the plans…

An Evaluation of Grades 9 and 10 Mathematics Textbooks vis-a-vis Fostering Problem Solving Skills

ERIC Educational Resources Information Center

Buishaw, Alemayehu; Ayalew, Assaye

2013-01-01

This study sought to evaluate the adequacy of integration of problematic situations and general problem-solving strategies (heuristics) in grades 9 and 10 mathematics textbooks. Grade 9 and grade 10 mathematics textbooks were used for analysis. Document analysis and interview were used as data gathering instruments. Document analysis was carried…

Mathematical Self-Efficacy and Understanding: Using Geographic Information Systems to Mediate Urban High School Students' Real-World Problem Solving

ERIC Educational Resources Information Center

DeBay, Dennis J.

2013-01-01

To explore student mathematical self-efficacy and understanding of graphical data, this dissertation examines students solving real-world problems in their neighborhood, mediated by professional urban planning technologies. As states and schools are working on the alignment of the Common Core State Standards for Mathematics (CCSSM), traditional…

Exploring the Effectiveness of Different Approaches to Teaching Finite Mathematics

ERIC Educational Resources Information Center

Smeal, Mary; Walker, Sandra; Carter, Jamye; Simmons-Johnson, Carolyn; Balam, Esenc

2013-01-01

Traditionally, mathematics has been taught using a very direct approach which the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of alternative approaches to mathematics have surfaced from a number of different directions. The purpose of this study was to examine the…

An Examination of Connections in Mathematical Processes in Students' Problem Solving: Connections between Representing and Justifying

ERIC Educational Resources Information Center

Stylianou, Despina A.

2013-01-01

Representation and justification are two central "mathematical practices". In the past, each has been examined to gain insights in the functions that they have in students' mathematical problem solving. Here, we examine the ways that representation and justification interact and influence the development of one another. We focus on the…

On Teaching Problem Solving in School Mathematics

ERIC Educational Resources Information Center

Pehkonen, Erkki; Näveri, Liisa; Laine, Anu

2013-01-01

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…

Secondary School Students' Construction and Use of Mathematical Models in Solving Word Problems

ERIC Educational Resources Information Center

Llinares, Salvador; Roig, Ana Isabel

2008-01-01

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Evaluation of the Effect of Mathematical Routines on the Development of Skills in Mathematical Problem Solving and School Motivation of Primary School Students in Abitibi-Témiscamingue

ERIC Educational Resources Information Center

Rajotte, Thomas; Marcotte, Christine; Bureau-Levasseur, Lisa

2016-01-01

In recent decades, the dropout rate in Abitibi-Témiscamingue is a worrying phenomenon. An analysis of ministerial examination results identifies that students in Abitibi-Témiscamingue have specific difficulties with mathematical problem solving tasks. Among the activities that develop those skills, the daily routines in mathematics seem to be a…

How to Solve Polyhedron Problem?

NASA Astrophysics Data System (ADS)

Wijayanti, A.; Kusumah, Y. S.; Suhendra

2017-09-01

The purpose of this research is to know the possible strategies to solve the problem in polyhedron topic with Knilsey’s Learning Model as scaffolding for the student. This research was conducted by using mixed method with sequential explanatory design. Researchers used purposive sampling technique to get two classes for Knisley class and conventional class and an extreme case sampling technique to get interview data. The instruments used are tests, observation sheets and interview guidelines. The result of the research shows that: (1) students’ strategies to solve polyhedron problem were grouped into two steps: by partitioning the problem to find out the solution and make a mathematical model of the mathematical sentence given and then connect it with the concept that the students already know; (2) students ‘mathematical problem solving ability in Knisley class is higher than those in conventional class.

Effects of the Problem-Posing Approach on Students' Problem Solving Skills and Metacognitive Awareness in Science Education

NASA Astrophysics Data System (ADS)

Akben, Nimet

2018-05-01

The interrelationship between mathematics and science education has frequently been emphasized, and common goals and approaches have often been adopted between disciplines. Improving students' problem-solving skills in mathematics and science education has always been given special attention; however, the problem-posing approach which plays a key role in mathematics education has not been commonly utilized in science education. As a result, the purpose of this study was to better determine the effects of the problem-posing approach on students' problem-solving skills and metacognitive awareness in science education. This was a quasi-experimental based study conducted with 61 chemistry and 40 physics students; a problem-solving inventory and a metacognitive awareness inventory were administered to participants both as a pre-test and a post-test. During the 2017-2018 academic year, problem-solving activities based on the problem-posing approach were performed with the participating students during their senior year in various university chemistry and physics departments throughout the Republic of Turkey. The study results suggested that structured, semi-structured, and free problem-posing activities improve students' problem-solving skills and metacognitive awareness. These findings indicated not only the usefulness of integrating problem-posing activities into science education programs but also the need for further research into this question.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

Students’ errors in solving combinatorics problems observed from the characteristics of RME modeling

NASA Astrophysics Data System (ADS)

Meika, I.; Suryadi, D.; Darhim

2018-01-01

This article was written based on the learning evaluation results of students’ errors in solving combinatorics problems observed from the characteristics of Realistic Mathematics Education (RME); that is modeling. Descriptive method was employed by involving 55 students from two international-based pilot state senior high schools in Banten. The findings of the study suggested that the students still committed errors in simplifying the problem as much 46%; errors in making mathematical model (horizontal mathematization) as much 60%; errors in finishing mathematical model (vertical mathematization) as much 65%; and errors in interpretation as well as validation as much 66%.

Flexibility in Mathematics Problem Solving Based on Adversity Quotient

NASA Astrophysics Data System (ADS)

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.

Interference thinking in constructing students’ knowledge to solve mathematical problems

NASA Astrophysics Data System (ADS)

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.

Helping Students with Emotional and Behavioral Disorders Solve Mathematics Word Problems

ERIC Educational Resources Information Center

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…

Factors Influencing Mathematic Problem-Solving Ability of Sixth Grade Students

ERIC Educational Resources Information Center

Pimta, Sakorn; Tayraukham, Sombat; Nuangchalerm, Prasart

2009-01-01

Problem statement: This study aims to investigate factors influencing mathematic problem-solving ability of sixth grade students. One thousand and twenty eight of sixth grade students, studying in the second semester of academic year 2007 were sampled by stratified random sampling technique. Approach: The research instruments used in the study…

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

ERIC Educational Resources Information Center

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…

Preservice Middle and High School Mathematics Teachers' Strategies When Solving Proportion Problems

ERIC Educational Resources Information Center

Arican, Muhammet

2018-01-01

The purpose of this study was to investigate eight preservice middle and high school mathematics teachers' solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers' (PSTs) reasoning about proportional…

Problem-Solving Attitudes and Gender as Predictors of Academic Achievement in Mathematics and Science for Canadian and Finnish Students in the PISA 2012 Assessment

ERIC Educational Resources Information Center

Cutumisu, Maria; Bulut, Okan

2017-01-01

This study aims to understand the predictive role of attitudes towards problem solving, such as perseverance and openness for problem solving, as well as of gender and country for Canadian and Finnish students' academic achievement in mathematics and science. We examined the data of students from Canada (n = 21,544) and Finland (n = 8,829) who…

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.

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Designing Opportunities to Learn Mathematics Theory-Building Practices

ERIC Educational Resources Information Center

Bass, Hyman

2017-01-01

Mathematicians commonly distinguish two modes of work in the discipline: "Problem solving," and "theory building." Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to…

How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

ERIC Educational Resources Information Center

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-01-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

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Handayani, I.; Januar, R. L.; Purwanto, S. E.

2018-01-01

This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.

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

ERIC Educational Resources Information Center

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)…

Effectiveness of Mathematical Word Problem Solving Interventions for Students with Learning Disabilities and Mathematics Difficulties: A Meta-Analysis

ERIC Educational Resources Information Center

Lein, Amy E.

2016-01-01

This meta-analysis synthesized the findings from 23 published and five unpublished experimental or quasi-experimental group design studies on word problem-solving instruction for K-12 students with learning disabilities (LD) and mathematics difficulties (MD). A secondary purpose of this meta-analysis was to analyze the relation between treatment…

THE CURRENT STATUS OF RESEARCH AND THEORY IN HUMAN PROBLEM SOLVING.

ERIC Educational Resources Information Center

DAVIS, GARY A.

PROBLEM-SOLVING THEORIES IN THREE AREAS - TRADITIONAL (STIMULUS-RESPONSE) LEARNING, COGNITIVE-GESTALT APPROACHES, AND COMPUTER AND MATHEMATICAL MODELS - WERE SUMMARIZED. RECENT EMPIRICAL STUDIES (1960-65) ON PROBLEM SOLVING WERE CATEGORIZED ACCORDING TO TYPE OF BEHAVIOR ELICITED BY PARTICULAR PROBLEM-SOLVING TASKS. ANAGRAM,…

Developing Creativity through Collaborative Problem Solving

ERIC Educational Resources Information Center

Albert, Lillie R.; Kim, Rina

2013-01-01

This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…

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

NASA Astrophysics Data System (ADS)

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 Integration of Mathematics in Physics Problem Solving: A Case Study of Greek Upper Secondary School Students

ERIC Educational Resources Information Center

Meli, Kalliopi; Zacharos, Konstantinos; Koliopoulos, Dimitrios

2016-01-01

This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…

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 problem of M1 and M2 similar to the ST’s, but both of the problem solvers read the questions with not complete so that they cannot pay attention to the questions of the problems. SS and SR create and execute M2 plan same as ST, but for M1, SS and SR cannot do it, but only active on reading the statement of the problem. On the checking of the M2 task, SS and SR retrace the task according to the used formula.

Designs of goal-free problems for trigonometry learning

NASA Astrophysics Data System (ADS)

Retnowati, E.; Maulidya, S. R.

2018-03-01

This paper describes the designs of goal-free problems particularly for trigonometry, which may be considered a difficult topic for high school students.Goal-free problem is an instructional design developed based on a Cognitive load theory (CLT). Within the design, instead of asking students to solve a specific goal of a mathematics problem, the instruction is to solve as many Pythagoras as possible. It was assumed that for novice students, goal-free problems encourage students to pay attention more to the given information and the mathematical principles that can be applied to reveal the unknown variables. Hence, students develop more structured knowledge while solving the goal-free problems. The resulted design may be used in regular mathematics classroom with some adjustment on the difficulty level and the allocated lesson time.

The errors of metacognitive evaluation on metacognitive failure of students in mathematical problem solving

NASA Astrophysics Data System (ADS)

Huda, Nizlel; Sutawidjaja, Akbar; Subanji; Rahardjo, Swasono

2018-04-01

Metacognitive activity is very important in mathematical problems solving. Metacognitive activity consists of metacognitive awareness, metacognitive evaluation and metacognitive regulation. This study aimed to reveal the errors of metacognitive evaluation in students’ metacognitive failure in solving mathematical problems. 20 students taken as research subjects were grouped into three groups: the first group was students who experienced one metacognitive failure, the second group was students who experienced two metacognitive failures and the third group was students who experienced three metacognitive failures. One person was taken from each group as the reasearch subject. The research data was collected from worksheets done using think aload then followed by interviewing the research subjects based on the results’ of subject work. The findings in this study were students who experienced metacognitive failure in solving mathematical problems tends to miscalculate metacognitive evaluation in considering the effectiveness and limitations of their thinking and the effectiveness of their chosen strategy of completion.

Students’ difficulties in solving linear equation problems

NASA Astrophysics Data System (ADS)

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.

An Exploration of Strategies Used by Students To Solve Problems with Multiple Ways of Solution.

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

1996-01-01

Describes a study that provides information about the extent to which students actually use their mathematical resources and strategies to solve problems. Interviews were used to analyze the problem solving abilities of high school students (N=35) as they solved five problems. (DDR)

Problem Solving. Research Brief

ERIC Educational Resources Information Center

Muir, Mike

2004-01-01

No longer solely the domain of Mathematics, problem solving permeates every area of today's curricula. Ideally students are applying heuristics strategies in varied contexts and novel situations in every subject taught. The ability to solve problems is a basic life skill and is essential to understanding technical subjects. Problem-solving is a…

Journey into Problem Solving: A Gift from Polya

ERIC Educational Resources Information Center

Lederman, Eric

2009-01-01

In "How to Solve It", accomplished mathematician and skilled communicator George Polya describes a four-step universal solving technique designed to help students develop mathematical problem-solving skills. By providing a glimpse at the grace with which experts solve problems, Polya provides definable methods that are not exclusive to…

Problem Solving in the General Mathematics Classroom

ERIC Educational Resources Information Center

Troutman, Andria Price; Lichtenberg, Betty Plunkett

1974-01-01

Five steps common to different problem solving models are listed. Next, seven specific abilities related to solving problems are discussed and examples given. Sample activities, appropriate to help in developing these specific abilities, are suggested. (LS)

Research Reporting Sections, Annual Meeting of the National Council of Teachers of Mathematics (57th, Boston, Massachusetts, April 18-21, 1979).

ERIC Educational Resources Information Center

Higgins, Jon L., Ed.

This document provides abstracts of 20 research reports. Topics covered include: children's comprehension of simple story problems; field independence and group instruction; problem-solving competence and memory; spatial visualization and the use of manipulative materials; effects of games on mathematical skills; problem-solving ability and right…

Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students' Proportional Reasoning: A Randomized Experiment

ERIC Educational Resources Information Center

Jitendra, Asha K.; Star, Jon R.; Dupuis, Danielle N.; Rodriguez, Michael C.

2013-01-01

This study examined the effect of schema-based instruction (SBI) on 7th-grade students' mathematical problem-solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a…

Children's Construction of Mathematical Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form.

ERIC Educational Resources Information Center

English, Lyn D.

1996-01-01

Presents case study data of low- and high-achieving nine-year olds focusing on construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in strategies for dealing with isomorphic combinatorial problems presented in hands-on and written form. Results showed that achievement level does not predict…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Investigation of the Effect of Assignment Projects on Mathematical Activity of Graduating Junior High School Students.

ERIC Educational Resources Information Center

Zehavi, Nurit

This study explored student mathematical activity in open problem-solving situations, derived from the work of Polya on problem solving and Skemp on intelligent learning and teaching. Assignment projects with problems for ninth-grade students were developed, whether they elicit the desired cognitive and cogno-affective goals was investigated, and…

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

ERIC Educational Resources Information Center

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…

Effect of the Presence of External Representations on Accuracy and Reaction Time in Solving Mathematical Double-Choice Problems by Students of Different Levels of Instruction

ERIC Educational Resources Information Center

Leikin, Roza; Leikin, Mark; Waisman, Ilana; Shaul, Shelley

2013-01-01

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

An Evaluation of Curriculum-Based Measurement of Mathematics Word Problem--Solving Measures for Monitoring Third-Grade Students' Mathematics Competence

ERIC Educational Resources Information Center

Leh, Jayne M.; Jitendra, Asha K.; Caskie, Grace I. L.; Griffin, Cynthia C.

2007-01-01

The purpose of this study was to examine the tenability of a curriculum-based mathematical word problem-solving (WPS) measure as a progress-monitoring tool to index students' rate of growth or slope of achievement over time. Participants consisted of 58 third-grade students, who were assessed repeatedly over 16 school weeks. Students were measured…

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

The Relationship between Students' Problem Posing and Problem Solving Abilities and Beliefs: A Small-Scale Study with Chinese Elementary School Children

ERIC Educational Resources Information Center

Limin, Chen; Van Dooren, Wim; Verschaffel, Lieven

2013-01-01

The goal of the present study is to investigate the relationship between pupils' problem posing and problem solving abilities, their beliefs about problem posing and problem solving, and their general mathematics abilities, in a Chinese context. Five instruments, i.e., a problem posing test, a problem solving test, a problem posing questionnaire,…

Generalised Assignment Matrix Methodology in Linear Programming

ERIC Educational Resources Information Center

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

Mathematics Anxiety and the Underprepared Student.

ERIC Educational Resources Information Center

Godbey, Cathy

This article discusses the symptoms and causes of math anxiety, and preventative measures that teachers can use to alleviate the stress some students experience in mathematics problem solving. Mathematics anxiety is defined as "feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems…

Restart Operator Meta-heuristics for a Problem-Oriented Evolutionary Strategies Algorithm in Inverse Mathematical MISO Modelling Problem Solving

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.

2017-02-01

This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.

On the Analysis of Two-Person Problem Solving Protocols.

ERIC Educational Resources Information Center

Schoenfeld, Alan H.

Methodological issues in the use of protocol analysis for research into human problem solving processes are examined through a case study in which two students were videotaped as they worked together to solve mathematical problems "out loud." The students' chosen strategic or executive behavior in examining and solving a problem was…

Sequenced Integration and the Identification of a Problem-Solving Approach through a Learning Process

ERIC Educational Resources Information Center

Cormas, Peter C.

2016-01-01

Preservice teachers (N = 27) in two sections of a sequenced, methodological and process integrated mathematics/science course solved a levers problem with three similar learning processes and a problem-solving approach, and identified a problem-solving approach through one different learning process. Similar learning processes used included:…

Capturing Problem-Solving Processes Using Critical Rationalism

ERIC Educational Resources Information Center

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…

ABC Problem in Elementary Mathematics Education: Arithmetic "before" Comprehension

ERIC Educational Resources Information Center

Boote, Stacy K.; Boote, David N.

2018-01-01

Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…

Categorization and Analysis of Explanatory Writing in Mathematics

ERIC Educational Resources Information Center

Craig, Tracy S.

2011-01-01

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to…

A Design To Improve Children's Competencies in Solving Mathematical Word Problems.

ERIC Educational Resources Information Center

Zimmerman, Helene

A discrepancy exists between children's ability to compute and their ability to solve mathematical word problems. The literature suggests a variety of methods that have been attempted to improve this skill with varying success. The utilization of manipulatives, visualization, illustration, and emphasis on improving listening skills all were…

Introducing Mathematics to Information Problem-Solving Tasks: Surface or Substance?

ERIC Educational Resources Information Center

Erickson, Ander

2017-01-01

This study employs a cross-case analysis in order to explore the demands and opportunities that arise when information problem-solving tasks are introduced into college mathematics classes. Professors at three universities collaborated with me to develop statistics-related activities that required students to engage in research outside the…

Modelling Mathematics Problem Solving Item Responses Using a Multidimensional IRT Model

ERIC Educational Resources Information Center

Wu, Margaret; Adams, Raymond

2006-01-01

This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring…

Problem-Solving Studies in Mathematics. Monograph Series.

ERIC Educational Resources Information Center

Harvey, John G., Ed.; Romberg, Thomas A., Ed.

This monograph focuses on educational research on the processes and natures of problem-solving activities in mathematics. The first chapter presents an overview to both the field and the document itself. All of the studies reported reflect interrelated investigations carried out at the University of Madison-Wisconsin, as partial fulfillments of…

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

ERIC Educational Resources Information Center

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…

Reversible Reasoning and the Working Backwards Problem Solving Strategy

ERIC Educational Resources Information Center

Ramful, Ajay

2015-01-01

Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

The Relationship of Drawing and Mathematical Problem Solving: "Draw for Math" Tasks

ERIC Educational Resources Information Center

Edens, Kellah; Potter, Ellen

2007-01-01

This study examines a series of children's drawings ("Draw for Math" tasks) to determine the relationship of students' spatial understanding and mathematical problem solving. Level of spatial understanding was assessed by applying the framework of central conceptual structures suggested by Case (1996), a cognitive developmental researcher.…

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 Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

The Relationship between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties

ERIC Educational Resources Information Center

Swanson, H. Lee; Beebe-Frankenberger, Margaret

2004-01-01

This study identified cognitive processes that underlie individual differences in working memory (WM) and mathematical problem-solution accuracy in elementary school children at risk and not at risk for serious math difficulties (SMD). A battery of tests was administered that assessed problem solving, achievement, and cognitive processing in…

Mathematical Problem Solving Project Technical Report III: Module Development and Formative Evaluation. Appendix B - "Organizing Lists" Quizzes and Data.

ERIC Educational Resources Information Center

Indiana Univ., Bloomington. Mathematics Education Development Center.

This appendix to the Mathematical Problem Solving Project "Module Development and Formative Evaluation" contains trials 1 and 2 of the Organizing Lists quiz. Editorial feedback from teachers on the Organizing Lists booklet is given for trials 1 and 2. Editorial feedback from teachers on the Organizing Lists problem deck is given for…

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

Detecting math problem solving strategies: an investigation into the use of retrospective self-reports, latency and fMRI data.

PubMed

Tenison, Caitlin; Fincham, Jon M; Anderson, John R

2014-02-01

This research explores how to determine when mathematical problems are solved by retrieval versus computation strategies. Past research has indicated that verbal reports, solution latencies, and neural imaging all provide imperfect indicators of this distinction. Participants in the current study solved mathematical problems involving two distinct problem types, called 'Pyramid' and 'Formula' problems. Participants were given extensive training solving 3 select Pyramid and 3 select Formula problems. Trained problems were highly practiced, whereas untrained problems were not. The distinction between untrained and trained problems was observed in the data. Untrained problems took longer to solve, more often used procedural strategies and showed a greater activation in the horizontal intraparietal sulcus (HIPS) when compared to trained problems. A classifier fit to the neural distinction between trained-untrained problems successfully predicted training within and between the two problem types. We employed this classifier to generate a prediction of strategy use. By combining evidence from the classifier, problem solving latencies, and retrospective reports, we predicted the strategy used to solve each problem in the scanner and gained unexpected insight into the distinction between different strategies. Copyright © 2013 Elsevier Ltd. All rights reserved.

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

PubMed

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.

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

PubMed Central

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

Problem-Solving Support for English Language Learners

ERIC Educational Resources Information Center

Wiest, Lynda R.

2008-01-01

Although word problems pose greater language demands, they also encourage more meaningful problem solving and mathematics understanding. With proper instructional support, a student-centered, investigative approach to contextualized problem solving benefits all students. This article presents a lesson built on an author-adapted version of the…

Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

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Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

2018-01-01

This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

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

PubMed

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.

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

PubMed

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.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

Problem-Solving Rubrics Revisited: Attending to the Blending of Informal Conceptual and Formal Mathematical Reasoning

ERIC Educational Resources Information Center

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

2013-01-01

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…

Problem Solving in the PISA and TIMSS 2003 Assessments. Technical Report. NCES 2007-049

ERIC Educational Resources Information Center

Dossey, John A.; McCrone, Sharon S.; O'Sullivan, Christine

2006-01-01

In 2003, the Program for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS) included a special focus on problem-solving. This report reviews the problem-solving aspects of each study in order to compare and contrast the nature of problem solving in each assessment. The report's authors develop…

Are Middle School Mathematics Teachers Able to Solve Word Problems without Using Variable?

ERIC Educational Resources Information Center

Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tugba; 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…

Using Coaching to Improve the Teaching of Problem Solving to Year 8 Students in Mathematics

ERIC Educational Resources Information Center

Kargas, Christine Anestis; Stephens, Max

2014-01-01

This study investigated how to improve the teaching of problem solving in a large Melbourne secondary school. Coaching was used to support and equip five teachers, some with limited experiences in teaching problem solving, with knowledge and strategies to build up students' problem solving and reasoning skills. The results showed increased…

Two Meanings of Algorithmic Mathematics.

ERIC Educational Resources Information Center

Maurer, Stephen B.

1984-01-01

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

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

ERIC Educational Resources Information Center

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…

Contribution of Equal-Sign Instruction beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty

ERIC Educational Resources Information Center

Powell, Sarah R.; Fuchs, Lynn S.

2010-01-01

Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for the development of higher order mathematics skills, including solving word problems. Research indicates equal-sign instruction…

Investigating and Communicating Technology Mathematics Problem Solving Experience of Two Preservice Teachers

ERIC Educational Resources Information Center

Kuzle, Ana

2012-01-01

In this paper, I report on preservice teachers' reflections and perceptions on their problem-solving process in a technological context. The purpose of the study was to investigate how preservice teachers experience working individually in a dynamic geometry environment and how these experiences affect their own mathematical activity when…

Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers

ERIC Educational Resources Information Center

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…

Exploring Gender Differences in Solving Open-Ended Mathematical Problems.

ERIC Educational Resources Information Center

Cai, Jinfa

Open-ended tasks were used to examine gender differences in complex mathematical problem solving. The results of this study suggest that, overall, males perform better than females, but the gender differences vary from task to task. A qualitative analysis of student responses to those tasks with gender differences showed that male and female…

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

ERIC Educational Resources Information Center

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…

A Naturalistic Study of Executive Function and Mathematical Problem-Solving

ERIC Educational Resources Information Center

Kotsopoulos, Donna; Lee, Joanne

2012-01-01

Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of…

From Number Lines to Graphs in the Coordinate Plane: Investigating Problem Solving across Mathematical Representations

ERIC Educational Resources Information Center

Earnest, Darrell

2015-01-01

This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Analyzing the Responses of 7-8 Year Olds When Solving Partitioning Problems

ERIC Educational Resources Information Center

Badillo, Edelmira; Font, Vicenç; Edo, Mequè

2015-01-01

We analyze the mathematical solutions of 7- to 8-year-old pupils while individually solving an arithmetic problem. The analysis was based on the "configuration of objects," an instrument derived from the onto-semiotic approach to mathematical knowledge. Results are illustrated through a number of cases. From the analysis of mathematical…

Exploration of Mathematics Problem Solving Process Based on the Thinking Level of Students in Junior High School

ERIC Educational Resources Information Center

Rahman, Abdul; Ahmar, Ansari Saleh

2016-01-01

Several studies suggest that most students are not in the same level of development (Slavin, 2008). From concrete operation level to formal operation level, students experience lateness in the transition phase. Consequently, students feel difficulty in solving mathematics problems. Method research is a qualitatively descriptive-explorative…

Prospective Teachers' Beliefs about Problem Solving in Multiple Ways

ERIC Educational Resources Information Center

Arikan, Elif Esra

2016-01-01

The purpose of this study is to analyze whether prospective teachers believe solving a mathematics problem involves in using different solution methods. 60 mathematics prospective teachers who take the pedagogic training program in a state university were participated in this study. Five open-ended questions were asked. The study was carried out…

Mathematical Language Development and Talk Types in Computer Supported Collaborative Learning Environments

ERIC Educational Resources Information Center

Symons, Duncan; Pierce, Robyn

2015-01-01

In this study we examine the use of cumulative and exploratory talk types in a year 5 computer supported collaborative learning environment. The focus for students in this environment was to participate in mathematical problem solving, with the intention of developing the proficiencies of problem solving and reasoning. Findings suggest that…

Transition Process of Procedural to Conceptual Understanding in Solving Mathematical Problems

ERIC Educational Resources Information Center

Fatqurhohman

2016-01-01

This article aims to describe the transition process from procedural understanding to conceptual understanding in solving mathematical problems. Subjects in this study were three students from 20 fifth grade students of SDN 01 Sumberberas Banyuwangi selected based on the results of the students' answers. The transition process from procedural to…

An Appropriate Prompts System Based on the Polya Method for Mathematical Problem-Solving

ERIC Educational Resources Information Center

Lee, Chien I.

2017-01-01

Current mathematics education emphasizes techniques, formulas, and procedures, neglecting the importance of understanding, presentation, and reasoning. This turns students into passive listeners that are well-practiced only in using formulas that they do not understand. We therefore adopted the Polya problem-solving method to provide students with…

Whole-Class Scaffolding for Learning to Solve Mathematics Problems Together in a Computer-Supported Environment

ERIC Educational Resources Information Center

Abdu, Rotem; Schwarz, Baruch; Mavrikis, Manolis

2015-01-01

We investigate teachers' practices in a whole-class context when they scaffold students' learning in situations where students use technologies that facilitate group learning to solve mathematical problems in small groups. We describe teachers' practices in order to evaluate their contribution to "Whole-Class Scaffolding" in the context…

Effects of Two Interventions on Solving Basic Fact Problems by Second Graders with Mathematics Learning Disabilities

ERIC Educational Resources Information Center

Dennis, Minyi Shih; Sorrells, Audrey McCray; Falcomata, Terry S.

2016-01-01

This study used a multiple probe across participants design, replicated across two interventions and counterbalanced across participant groups to examine the effects of number sense intervention and extensive practice intervention on strategy transformation when students with mathematics learning disabilities (MLD) solved basic fact problems. In…

The Effects of Feedback during Exploratory Mathematics Problem Solving: Prior Knowledge Matters

ERIC Educational Resources Information Center

Fyfe, Emily R.; Rittle-Johnson, Bethany; DeCaro, Marci S.

2012-01-01

Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain…

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

ERIC Educational Resources Information Center

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.…

Observing Student Working Styles when Using Graphic Calculators to Solve Mathematics Problems

ERIC Educational Resources Information Center

Berry, J.; Graham, E.; Smith, A.

2006-01-01

Some research studies, many of which used quantitative methods, have suggested that graphics calculators can be used to effectively enhance the learning of mathematics. More recently research studies have started to explore students' styles of working as they solve problems with technology. This paper describes the use of a software application…

The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

2016-01-01

The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

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

NASA Astrophysics Data System (ADS)

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.

Grasp of Consciousness and Performance in Mathematics Making Explicit the Ways of Thinking in Solving Cartesian Product Problems

ERIC Educational Resources Information Center

Soares, Maria Tereza Carneiro; Moro, Maria Lucia Faria; Spinillo, Alina Galvao

2012-01-01

This study examines the relationship between the grasp of consciousness of the reasoning process in Grades 5 and 8 pupils from a public and a private school, and their performance in mathematical problems of Cartesian product. Forty-two participants aged from 10 to 16 solved four problems in writing and explained their solution procedures by…

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

ERIC Educational Resources Information Center

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…

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training

PubMed Central

Boonen, Anton J. H.; de Koning, Björn B.; Jolles, Jelle; van der Schoot, Menno

2016-01-01

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME. PMID:26925012

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training.

PubMed

Boonen, Anton J H; de Koning, Björn B; Jolles, Jelle; van der Schoot, Menno

2016-01-01

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME.

Focus group discussion in mathematical physics learning

NASA Astrophysics Data System (ADS)

Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.

2018-03-01

The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.

[The application of new technologies to solving maths problems for students with learning disabilities: the 'underwater school'].

PubMed

Miranda-Casas, A; Marco-Taverner, R; Soriano-Ferrer, M; Melià de Alba, A; Simó-Casañ, P

2008-01-01

Different procedures have demonstrated efficacy to teach cognitive and metacognitive strategies to problem solving in mathematics. Some studies have used computer-based problem solving instructional programs. To analyze in students with learning disabilities the efficacy of a cognitive strategies training for problem solving, with three instructional delivery formats: a teacher-directed program (T-D), a computer-assisted instructional (CAI) program, and a combined program (T-D + CAI). Forty-four children with mathematics learning disabilities, between 8 and 10 years old participated in this study. The children were randomly assigned to one of the three instructional formats and a control group without cognitive strategies training. In the three instructional conditions which were compared all the students learnt problems solving linguistic and visual cognitive strategies trough the self-instructional procedure. Several types of measurements were used for analysing the possible differential efficacy of the three instructional methods implemented: solving problems tests, marks in mathematics, internal achievement responsibility scale, and school behaviours teacher ratings. Our findings show that the T-D training group and the T-D + CAI group improved significantly on math word problem solving and on marks in Maths from pre- to post-testing. In addition, the results indicated that the students of the T-D + CAI group solved more real-life problems and developed more internal attributions compared to both control and CAI groups. Finally, with regard to school behaviours, improvements in school adjustment and learning problems were observed in the students of the group with a combined instructional format (T-D + CAI).

Building a Career Mathematics File: Challenging Students to Find the Importance of Mathematics in a Variety of Occupations

ERIC Educational Resources Information Center

Keleher, Lori A.

2006-01-01

The Career Mathematics file is an occupational problem-solving system, which includes a wide range of mathematical problems and solutions, collected from various resources and helps students establish connections between mathematics and their environment. The study shows that the problems given can be used as realistic examples to study and…

The way adults with orientation to mathematics teaching cope with the solution of everyday real-world problems

NASA Astrophysics Data System (ADS)

Gazit, Avikam; Patkin, Dorit

2012-03-01

The article aims to check the way adults, some who are practicing mathematics teachers at elementary school, some who are academicians making a career change to mathematics teachers at junior high school and the rest who are pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of buying and selling. The findings show that even adults with mathematical background tend to make mistakes in solving everyday real-world problems. Only about 70% of the adults who have an orientation to mathematics solved the sample problem correctly. The lowest percentage of success was demonstrated by the academicians making a career change to junior high school mathematics teachers whereas the highest percentage of success was manifested by pre-service elementary school mathematics teachers. Moreover, the findings illustrate that life experience of the practicing mathematics teachers and, mainly, of the academicians making a career change, who were older than the pre-service teachers, did not facilitate the solution of such a real-world problem. Perhaps the reason resides in the process of mathematics teaching at school, which does not put an emphasis on the solution of everyday real-world problems.

Resource Letter RPS-1: Research in problem solving

NASA Astrophysics Data System (ADS)

Hsu, Leonardo; Brewe, Eric; Foster, Thomas M.; Harper, Kathleen A.

2004-09-01

This Resource Letter provides a guide to the literature on research in problem solving, especially in physics. The references were compiled with two audiences in mind: physicists who are (or might become) engaged in research on problem solving, and physics instructors who are interested in using research results to improve their students' learning of problem solving. In addition to general references, journal articles and books are cited for the following topics: cognitive aspects of problem solving, expert-novice problem-solver characteristics, problem solving in mathematics, alternative problem types, curricular interventions, and the use of computers in problem solving.

Problem Solving through an Optimization Problem in Geometry

ERIC Educational Resources Information Center

Poon, Kin Keung; Wong, Hang-Chi

2011-01-01

This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

Effects of a Research-Based Intervention to Improve Seventh-Grade Students' Proportional Problem Solving: A Cluster Randomized Trial

ERIC Educational Resources Information Center

Jitendra, Asha K.; Harwell, Michael R.; Dupuis, Danielle N.; Karl, Stacy R.; Lein, Amy E.; Simonson, Gregory; Slater, Susan C.

2015-01-01

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem-solving and metacognitive…

Effects of a Research-Based Intervention to Improve Seventh-Grade Students' Proportional Problem Solving: A Cluster Randomized Trial

ERIC Educational Resources Information Center

Jitendra, Asha K.; Harwell, Michael R.; Dupuis, Danielle N.; Karl, Stacy R.; Lein, Amy E.; Simonson, Gregory; Slater, Susan C.

2015-01-01

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem solving and metacognitive…

The Interference of Stereotype Threat with Women's Generation of Mathematical Problem-Solving Strategies.

ERIC Educational Resources Information Center

Quinn, Diane M.; Spencer, Steven J.

2001-01-01

Investigated whether stereotype threat would depress college women's math performance. In one test, men outperformed women when solving word problems, though women performed equally when problems were converted into numerical equivalents. In another test, participants solved difficult problems in high or reduced stereotype threat conditions. Women…

A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness

ERIC Educational Resources Information Center

Xin, Yan Ping; Zhang, Dake; Park, Joo Young; Tom, Kinsey; Whipple, Amanda; Si, Luo

2011-01-01

The authors compared a conceptual model-based problem-solving (COMPS) approach with a general heuristic instructional approach for teaching multiplication-division word-problem solving to elementary students with learning problems (LP). The results indicate that only the COMPS group significantly improved, from pretests to posttests, their…

Strategy Keys as Tools for Problem Solving

ERIC Educational Resources Information Center

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…

Perceptual support promotes strategy generation: Evidence from equation solving.

PubMed

Alibali, Martha W; Crooks, Noelle M; McNeil, Nicole M

2017-08-30

Over time, children shift from using less optimal strategies for solving mathematics problems to using better ones. But why do children generate new strategies? We argue that they do so when they begin to encode problems more accurately; therefore, we hypothesized that perceptual support for correct encoding would foster strategy generation. Fourth-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __) in a pre-test. They were then randomly assigned to one of three perceptual support conditions or to a Control condition. Participants in all conditions completed three mathematical equivalence problems with feedback about correctness. Participants in the experimental conditions received perceptual support (i.e., highlighting in red ink) for accurately encoding the equal sign, the right side of the equation, or the numbers that could be added to obtain the correct solution. Following this intervention, participants completed a problem-solving post-test. Among participants who solved the problems incorrectly at pre-test, those who received perceptual support for correctly encoding the equal sign were more likely to generate new, correct strategies for solving the problems than were those who received feedback only. Thus, perceptual support for accurate encoding of a key problem feature promoted generation of new, correct strategies. Statement of Contribution What is already known on this subject? With age and experience, children shift to using more effective strategies for solving math problems. Problem encoding also improves with age and experience. What the present study adds? Support for encoding the equal sign led children to generate correct strategies for solving equations. Improvements in problem encoding are one source of new strategies. © 2017 The British Psychological Society.

Increasing mathematical problem-solving performance through relaxation training

NASA Astrophysics Data System (ADS)

Sharp, Conni; Coltharp, Hazel; Hurford, David; Cole, Amykay

2000-04-01

Two intact classes of 30 undergraduate students enrolled in the same general education mathematics course were each administered the IPSP Mathematics Problem Solving Test and the Mathematics Anxiety Rating Scale at the beginning and end of the semester. Both groups experienced the same syllabus, lectures, course requirements, and assessment techniques; however, one group received relaxation training during an initial class meeting and during the first 5 to 7 minutes of each subsequent class. The group which had received relaxation training had significantly lower mathematics anxiety and significantly higher mathematics performance at the end of the course. The results suggest that relaxation training may be a useful tool for treating anxiety in undergraduate general education mathematics students.

Learning to Write about Mathematics

ERIC Educational Resources Information Center

Parker, Renee; Breyfogle, M. Lynn

2011-01-01

Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

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

NASA Astrophysics Data System (ADS)

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 Verification, (6) Closure with the review of students have learned or giving homework.

A Randomized Trial of the Effects of Schema-Based Instruction on Proportional Problem-Solving for Students With Mathematics Problem-Solving Difficulties.

PubMed

Jitendra, Asha K; Harwell, Michael R; Dupuis, Danielle N; Karl, Stacy R

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their students in the larger study were randomly assigned to an SBI or control condition and teachers in both conditions then provided instruction on the topics of ratio, proportion, and percent. We found that students with MD-PS in SBI classrooms scored on average higher than their counterparts in control classrooms on a posttest and delayed posttest administered 9 weeks later. Given students' difficulties with proportional problem-solving and the consequences of these difficulties, an important contribution of this research is the finding that when provided with appropriate instruction, students with MD-PS are capable of enhanced proportional problem-solving performance.

Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice

ERIC Educational Resources Information Center

Schoppek, Wolfgang; Tulis, Maria

2010-01-01

The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…

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

ERIC Educational Resources Information Center

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,…

Teaching Mathematics Problem Solving to Students with Limited English Proficiency through Nested Spiral Approach.

ERIC Educational Resources Information Center

Chyu, Chi-Oy W.

The Nested Spiral Approach (NSA) is an integrated instructional approach used to promote the motivated learning of mathematics problem solving in limited-English-proficient (LEP) students. The NSA is described and a trial use is discussed. The approach extends, elaborates, and supplements existing education and instruction theories to help LEP…

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

ERIC Educational Resources Information Center

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…

Using Confirmatory Factor Analysis to Validate the Chamberlin Affective Instrument for Mathematical Problem Solving with Academically Advanced Students

ERIC Educational Resources Information Center

Chamberlin, Scott A.; Moore, Alan D.; Parks, Kelly

2017-01-01

Background: Student affect plays a considerable role in mathematical problem solving performance, yet is rarely formally assessed. In this manuscript, an instrument and its properties are discussed to enable educational psychologists the opportunity to assess student affect. Aims: The study was conducted to norm the CAIMPS (instrument) with gifted…

The Role of Dynamic Software in the Identification and Construction of Mathematical Relationships

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

2004-01-01

What features of mathematical thinking do students exhibit when they use dynamic software in their problem solving approaches? To what extent does the systematic use of technology favour students' development of problem solving competences? What type of reasoning do students develop as a result of using a particular tool? This study documents…

Developing Physics E-Scaffolding Teaching Media to Increase the Eleventh-Grade Students' Problem Solving Ability and Scientific Attitude

ERIC Educational Resources Information Center

Saputri, Affa Ardhi; Wilujeng, Insih

2017-01-01

This research aims at revealing (1) the suitability of physics e-scaffolding teaching media with mathematical and image/diagrammatic representation, as well as (2) the effectiveness of the e-scaffolding teaching media with mathematical and image/diagrammatic representation to improve students' problem solving ability and scientific attitude. It is…

Applying Computerized Concept Maps in Guiding Pupils to Reason and Solve Mathematical Problems: The Design Rationale and Effect

ERIC Educational Resources Information Center

Chen, I-Ching; Hu, Shueh-Cheng

2013-01-01

The capability of solving fundamental mathematical problems is essential to elementary school students; however instruction based on ordinary narration usually perplexes students. Concept mapping is well known for its effectiveness on assimilating and organizing knowledge, which is essential to meaningful learning. A variety of concept map-based…

Problem Solving and the Use of Math in Physics Courses

ERIC Educational Resources Information Center

Redish, Edward F.

2006-01-01

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are…

Visualization of Problem Solving Related to the Quantitative Composition of Solutions in the Dynamic "GeoGebra" Environment

ERIC Educational Resources Information Center

Kostic, V. Dj.; Jovanovic, V. P. Stankov; Sekulic, T. M.; Takaci, Dj. B.

2016-01-01

Problem solving in the field of quantitative composition of solutions (QCS), expressed as mass share and molar concentration, is essential for chemistry students. Since successful chemistry education is based on different mathematical contents, it is important to be proficient in both mathematical and chemistry concepts as well as interconnections…

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

ERIC Educational Resources Information Center

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 Embodiment of Cases as Alternative Perspective in a Mathematics Hypermedia Learning Environment

ERIC Educational Resources Information Center

Valentine, Keri D.; Kopcha, Theodore J.

2016-01-01

This paper presents a design framework for cases as alternative perspectives (Jonassen in Learning to solve problems: a handbook for designing problem-solving learning environments, 2011a) in the context of K-12 mathematics. Using the design-based research strategy of conjecture mapping, the design of cases for a hypermedia site is described…

Problem Solving as a Professional Development Strategy for Teachers: A Case Study with Fractions

ERIC Educational Resources Information Center

Perdomo-Díaz, Josefa; Felmer, Patricio; Randolph, Valeria; González, Guillermo

2017-01-01

In this paper we present a professional development course designed to impact on teachers' mathematical knowledge for teaching fractions. The main features of the course are the use of i) problem solving activities related with mathematical knowledge for teaching fractions ii) peer discussions and iii) monitor's interventions focused on answering…

An Onto-Semiotic Analysis of Combinatorial Problems and the Solving Processes by University Students

ERIC Educational Resources Information Center

Godino, Juan D.; Batanero, Carmen; Roa, Rafael

2005-01-01

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…

Learning by Preparing to Teach: Fostering Self-Regulatory Processes and Achievement during Complex Mathematics Problem Solving

ERIC Educational Resources Information Center

Muis, Krista R.; Psaradellis, Cynthia; Chevrier, Marianne; Di Leo, Ivana; Lajoie, Susanne P.

2016-01-01

We developed an intervention based on the learning by teaching paradigm to foster self-regulatory processes and better learning outcomes during complex mathematics problem solving in a technology-rich learning environment. Seventy-eight elementary students were randomly assigned to 1 of 2 conditions: learning by preparing to teach, or learning for…

Tracing the Building of Robert's Connections in Mathematical Problem Solving: A Sixteen-Year Study

ERIC Educational Resources Information Center

Ahluwalia, Anoop

2011-01-01

This research analyzes how external representations created by a student, Robert, helped him in building mathematical understanding over a sixteen-year period. Robert (also known as Bobby), was an original participant of the Rutgers longitudinal study where students were encouraged to work on problem-solving tasks with minimum intervention (Maher,…

Adapting Experiential Learning to Develop Problem-Solving Skills in Deaf and Hard-of-Hearing Engineering Students

ERIC Educational Resources Information Center

Marshall, Matthew M.; Carrano, Andres L.; Dannels, Wendy A.

2016-01-01

Individuals who are deaf and hard-of-hearing (DHH) are underrepresented in science, technology, engineering, and mathematics (STEM) professions, and this may be due in part to their level of preparation in the development and retention of mathematical and problem-solving skills. An approach was developed that incorporates experiential learning and…

The Monte Carlo Method. Popular Lectures in Mathematics.

ERIC Educational Resources Information Center

Sobol', I. M.

The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…

Mighty Mathematicians: Using Problem Posing and Problem Solving to Develop Mathematical Power

ERIC Educational Resources Information Center

McGatha, Maggie B.; Sheffield, Linda J.

2006-01-01

This article describes a year-long professional development institute combined with a summer camp for students. Both were designed to help teachers and students develop their problem-solving and problem-posing abilities.

Interesting and Difficult Mathematical Problems: Changing Teachers' Views by Employing Multiple-Solution Tasks

ERIC Educational Resources Information Center

Guberman, Raisa; Leikin, Roza

2013-01-01

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

Student Teachers' Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools

ERIC Educational Resources Information Center

Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava

2014-01-01

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

Equity and Access: All Students Are Mathematical Problem Solvers

ERIC Educational Resources Information Center

Franz, Dana Pompkyl; Ivy, Jessica; McKissick, Bethany R.

2016-01-01

Often mathematical instruction for students with disabilities, especially those with learning disabilities, includes an overabundance of instruction on mathematical computation and does not include high-quality instruction on mathematical reasoning and problem solving. In fact, it is a common misconception that students with learning disabilities…

Analysing the Relationship between the Problem-Solving-Related Beliefs, Competence and Teaching of Three Cypriot Primary Teachers

ERIC Educational Resources Information Center

Andrews, Paul; Xenofontos, Constantinos

2015-01-01

In this article, we analyse the problem-solving-related beliefs, competence and classroom practice of three Cypriot upper-primary teachers. Data derived from semi-structured interviews focused on teachers' beliefs about the nature of mathematical problems, problem-solving, and their competence as both problem-solvers and teachers of…

A Problem-Solving Conceptual Framework and Its Implications in Designing Problem-Posing Tasks

ERIC Educational Resources Information Center

Singer, Florence Mihaela; Voica, Cristian

2013-01-01

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that…

Opportunities to Pose Problems Using Digital Technology in Problem Solving Environments

ERIC Educational Resources Information Center

Aguilar-Magallón, Daniel Aurelio; Fernández, Willliam Enrique Poveda

2017-01-01

This article reports and analyzes different types of problems that nine students in a Master's Program in Mathematics Education posed during a course on problem solving. What opportunities (affordances) can a dynamic geometry system (GeoGebra) offer to allow in-service and in-training teachers to formulate and solve problems, and what type of…

Individual differences in mathematical competence predict parietal brain activation during mental calculation.

PubMed

Grabner, Roland H; Ansari, Daniel; Reishofer, Gernot; Stern, Elsbeth; Ebner, Franz; Neuper, Christa

2007-11-01

Functional neuroimaging studies have revealed that parietal brain circuits subserve arithmetic problem solving and that their recruitment dynamically changes as a function of training and development. The present study investigated whether the brain activation during mental calculation is also modulated by individual differences in mathematical competence. Twenty-five adult students were selected from a larger pool based on their performance on standardized tests of intelligence and arithmetic and divided into groups of individuals with relatively lower and higher mathematical competence. These groups did not differ in their non-numerical intelligence or age. In an fMRI block-design, participants had to verify the correctness of single-digit and multi-digit multiplication problems. Analyses revealed that the individuals with higher mathematical competence displayed stronger activation of the left angular gyrus while solving both types of arithmetic problems. Additional correlational analyses corroborated the association between individual differences in mathematical competence and angular gyrus activation, even when variability in task performance was controlled for. These findings demonstrate that the recruitment of the left angular gyrus during arithmetic problem solving underlies individual differences in mathematical ability and suggests a stronger reliance on automatic, language-mediated processes in more competent individuals.

Learning biology through connecting mathematics to scientific mechanisms: Student outcomes and teacher supports

NASA Astrophysics Data System (ADS)

Schuchardt, Anita

Integrating mathematics into science classrooms has been part of the conversation in science education for a long time. However, studies on student learning after incorporating mathematics in to the science classroom have shown mixed results. Understanding the mixed effects of including mathematics in science has been hindered by a historical focus on characteristics of integration tangential to student learning (e.g., shared elements, extent of integration). A new framework is presented emphasizing the epistemic role of mathematics in science. An epistemic role of mathematics missing from the current literature is identified: use of mathematics to represent scientific mechanisms, Mechanism Connected Mathematics (MCM). Building on prior theoretical work, it is proposed that having students develop mathematical equations that represent scientific mechanisms could elevate their conceptual understanding and quantitative problem solving. Following design and implementation of an MCM unit in inheritance, a large-scale quantitative analysis of pre and post implementation test results showed MCM students, compared to traditionally instructed students) had significantly greater gains in conceptual understanding of mathematically modeled scientific mechanisms, and their ability to solve complex quantitative problems. To gain insight into the mechanism behind the gain in quantitative problem solving, a small-scale qualitative study was conducted of two contrasting groups: 1) within-MCM instruction: competent versus struggling problem solvers, and 2) within-competent problem solvers: MCM instructed versus traditionally instructed. Competent MCM students tended to connect their mathematical inscriptions to the scientific phenomenon and to switch between mathematical and scientifically productive approaches during problem solving in potentially productive ways. The other two groups did not. To address concerns about teacher capacity presenting barriers to scalability of MCM approaches, the types and amount of teacher support needed to achieve these types of student learning gains were investigated. In the context of providing teachers with access to educative materials, students achieved learning gains in both areas in the absence of face-to-face teacher professional development. However, maximal student learning gains required the investment of face-to-face professional development. This finding can govern distribution of scarce resources, but does not preclude implementation of MCM instruction even where resource availability does not allow for face-to-face professional development.

The Coffee-Milk Mixture Problem Revisited

ERIC Educational Resources Information Center

Marion, Charles F.

2015-01-01

This analysis of a problem that is frequently posed at professional development workshops, in print, and on the Web--the coffee-milk mixture riddle--illustrates the timeless advice of George Pólya's masterpiece on problem solving in mathematics, "How to Solve It." In his book, Pólya recommends that problems previously solved and put…

The social essentials of learning: an experimental investigation of collaborative problem solving and knowledge construction in mathematics classrooms in Australia and China

NASA Astrophysics Data System (ADS)

Chan, Man Ching Esther; Clarke, David; Cao, Yiming

2018-03-01

Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question "How do we optimise social interaction for the promotion of learning in a mathematics classroom?" Employing the logic of multi-theoretic research design, this project uses the newly built Science of Learning Research Classroom (ARC-SR120300015) at The University of Melbourne and equivalent facilities in China to investigate classroom learning and social interactions, focusing on collaborative small group problem solving as a way to make the social aspects of learning visible. In Australia and China, intact classes of local year 7 students with their usual teacher will be brought into the research classroom facilities with built-in video cameras and audio recording equipment to participate in purposefully designed activities in mathematics. The students will undertake a sequence of tasks in the social units of individual, pair, small group (typically four students) and whole class. The conditions for student collaborative problem solving and learning will be manipulated so that student and teacher contributions to that learning process can be distinguished. Parallel and comparative analyses will identify culture-specific interactive patterns and provide the basis for hypotheses about the learning characteristics underlying collaborative problem solving performance documented in the research classrooms in each country. The ultimate goals of the project are to generate, develop and test more sophisticated hypotheses for the optimisation of social interaction in the mathematics classroom in the interest of improving learning and, particularly, student collaborative problem solving.

Responsiveness to mathematical problem-solving instruction: comparing students at risk of mathematics disability with and without risk of reading disability.

PubMed

Fuchs, Lynn S; Fuchs, Douglas; Prentice, Karin

2004-01-01

This study assessed responsiveness to a 16-week mathematical problem-solving treatment as a function of students' risk for disability. Among 301 third graders, TerraNova scores were used to categorize students as at risk for both reading and mathematics disability (MDR/RDR; 20 control and 12 experimental), at risk for mathematics disability only (MDR-only; 5 and 8), at risk for reading disability only (RDR-only; 12 and 15), or not at risk (NDR; 60 and 69). Interactions among at-risk status, treatment, and time showed that as a function of treatment, MDR/RDR, MDR-only, and RDR-only students improved less than NDR students on computation and labeling, and MDR/RDR students improved less than all other groups on conceptual underpinnings. Exploratory regressions suggested that MDR/RDR students' math deficits or their underlying mechanisms explained a greater proportion of variance in responsiveness to problem-solving treatment than reading deficits or their underlying mechanisms.

The Association between Mathematical Word Problems and Reading Comprehension

ERIC Educational Resources Information Center

Vilenius-Tuohimaa, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik

2008-01-01

This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9-10 (Grade 4). The children's text comprehension and mathematical word problem-solving performance was tested. Technical reading skills were investigated in order to categorise participants as…

A Problem on Optimal Transportation

ERIC Educational Resources Information Center

Cechlarova, Katarina

2005-01-01

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

Are Mathematics Problems a Problem for Women and Girls?

ERIC Educational Resources Information Center

Schonberger, Ann K.

The primary questions investigated are: Is it true that males excel in mathematical problem solving and, if so, when does this superiority develop? An examination of recent research showed that sex-related differences did exist, although small, even after controlling for mathematics background. Differences appeared in early adolescence and were…

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

ERIC Educational Resources Information Center

Leikin, Roza; Waisman, Ilana; Leikin, Mark

2016-01-01

We asked: "What are the similarities and differences in mathematical processing associated with solving learning-based and insight-based problems?" To answer this question, the ERP research procedure was employed with 69 male adolescent subjects who solved specially designed insight-based and learning-based tests. Solutions of…

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

NASA Astrophysics Data System (ADS)

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.

From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

NASA Astrophysics Data System (ADS)

Jupri, Al

2017-04-01

In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

Problem Posing with Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Mahendra, R.; Slamet, I.; Budiyono

2017-09-01

One of the difficulties of students in the learning of geometry is on the subject of plane that requires students to understand the abstract matter. The aim of this research is to determine the effect of Problem Posing learning model with Realistic Mathematics Education Approach in geometry learning. This quasi experimental research was conducted in one of the junior high schools in Karanganyar, Indonesia. The sample was taken using stratified cluster random sampling technique. The results of this research indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students’ conceptual understanding significantly in geometry learning especially on plane topics. It is because students on the application of Problem Posing with Realistic Mathematics Education Approach are become to be active in constructing their knowledge, proposing, and problem solving in realistic, so it easier for students to understand concepts and solve the problems. Therefore, the model of Problem Posing learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on geometry material. Furthermore, the impact can improve student achievement.

Facilitating problem solving in high school chemistry

NASA Astrophysics Data System (ADS)

Gabel, Dorothy L.; Sherwood, Robert D.

The major purpose for conducting this study was to determine whether certain instructional strategies were superior to others in teaching high school chemistry students problem solving. The effectiveness of four instructional strategies for teaching problem solving to students of various proportional reasoning ability, verbal and visual preference, and mathematics anxiety were compared in this aptitude by treatment interaction study. The strategies used were the factor-label method, analogies, diagrams, and proportionality. Six hundred and nine high school students in eight schools were randomly assigned to one of four teaching strategies within each classroom. Students used programmed booklets to study the mole concept, the gas laws, stoichiometry, and molarity. Problem-solving ability was measured by a series of immediate posttests, delayed posttests and the ACS-NSTA Examination in High School Chemistry. Results showed that mathematics anxiety is negatively correlated with science achievement and that problem solving is dependent on students' proportional reasoning ability. The factor-label method was found to be the most desirable method and proportionality the least desirable method for teaching the mole concept. However, the proportionality method was best for teaching the gas laws. Several second-order interactions were found to be significant when mathematics anxiety was one of the aptitudes involved.

Investigating adaptive reasoning and strategic competence: Difference male and female

NASA Astrophysics Data System (ADS)

Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The series of adaptive reasoning and strategic competencies represent the five components of mathematical proficiency to describe the students' mathematics learning success. Gender contribute to the problem-solving process. This qualitative research approach investigated the adaptive reasoning and strategic competence aspects of a male student and a female student when they solved mathematical problem. They were in the eleventh grade of high school in Makassar. Both also had similar mathematics ability and were in the highest category. The researcher as the main instrument used secondary instrument to obtain the appropriate subject and to investigate the aspects of adaptive reasoning and strategic competence. Test of mathematical ability was used to locate the subjects with similar mathematical ability. The unstructured guideline interview was used to investigate aspects of adaptive reasoning and strategic competence when the subject completed the task of mathematical problem. The task of mathematical problem involves several concepts as the right solution, such as the circle concept, triangle concept, trigonometry concept, and Pythagoras concept. The results showed that male and female subjects differed in applying a strategy to understand, formulate and represent the problem situation. Furthermore, both also differed in explaining the strategy used and the relationship between concepts and problem situations.

Pre-Service Physics Teachers’ Problem-solving Skills in Projectile Motion Concept

NASA Astrophysics Data System (ADS)

Sutarno, S.; Setiawan, A.; Kaniawati, I.; Suhandi, A.

2017-09-01

This study is a preliminary research aiming at exploring pre-service physics teachers’ skills in applying the stage of problem-solving strategies. A total of 76 students of physics education study program at a college in Bengkulu Indonesia participated in the study. The skills on solving physics problems are being explored through exercises that demand the use of problem-solving strategies with several stages such as useful description, physics approach, specific application of physics, physics equation, mathematical procedures, and logical progression. Based on the results of data analysis, it is found that the pre-service physics teachers’ skills are in the moderate category for physics approach and mathematical procedural, and low category for the others. It was concluded that the pre-service physics teachers’ problem-solving skills are categorized low. It is caused by the learning of physics that has done less to practice problem-solving skills. The problems provided are only routine and poorly trained in the implementation of problem-solving strategies.The results of the research can be used as a reference for the importance of the development of physics learning based on higher order thinking skills.

Diagrams Benefit Symbolic Problem-Solving

ERIC Educational Resources Information Center

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

2017-01-01

Background: 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…

Problem Solving Software for Math Classes.

ERIC Educational Resources Information Center

Troutner, Joanne

1987-01-01

Described are 10 computer software programs for problem solving related to mathematics. Programs described are: (1) Box Solves Story Problems; (2) Safari Search; (3) Puzzle Tanks; (4) The King's Rule; (5) The Factory; (6) The Royal Rules; (7) The Enchanted Forest; (8) Gears; (9) The Super Factory; and (10) Creativity Unlimited. (RH)

Persona-Based Journaling: Striving for Authenticity in Representing the Problem-Solving Process

ERIC Educational Resources Information Center

Liljedahl, Peter

2007-01-01

Students' mathematical problem-solving experiences are fraught with failed attempts, wrong turns, and partial successes that move in fits and jerks, oscillating between periods of inactivity, stalled progress, rapid advancement, and epiphanies. Students' problem-solving journals, however, do not always reflect this rather organic process. Without…

Solving Optimization Problems with Spreadsheets

ERIC Educational Resources Information Center

Beigie, Darin

2017-01-01

Spreadsheets provide a rich setting for first-year algebra students to solve problems. Individual spreadsheet cells play the role of variables, and creating algebraic expressions for a spreadsheet to perform a task allows students to achieve a glimpse of how mathematics is used to program a computer and solve problems. Classic optimization…

Working Memory Components and Problem-Solving Accuracy: Are There Multiple Pathways?

ERIC Educational Resources Information Center

Swanson, H. Lee; Fung, Wenson

2016-01-01

This study determined the working memory (WM) components (executive, phonological short-term memory [STM], and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy in elementary schoolchildren (N = 392). The battery of tests administered to assess mediators between WM and problem-solving included measures of…

6 Essential Questions for Problem Solving

ERIC Educational Resources Information Center

Kress, Nancy Emerson

2017-01-01

One of the primary expectations that the author has for her students is for them to develop greater independence when solving complex and unique mathematical problems. The story of how the author supports her students as they gain confidence and independence with complex and unique problem-solving tasks, while honoring their expectations with…

Cognitive Strategy Instruction for Teaching Word Problems to Primary-Level Struggling Students

ERIC Educational Resources Information Center

Pfannenstiel, Kathleen Hughes; Bryant, Diane Pedrotty; Bryant, Brian R.; Porterfield, Jennifer A.

2015-01-01

Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word…

Student Errors in Dynamic Mathematical Environments

ERIC Educational Resources Information Center

Brown, Molly; Bossé, Michael J.; Chandler, Kayla

2016-01-01

This study investigates the nature of student errors in the context of problem solving and Dynamic Math Environments. This led to the development of the Problem Solving Action Identification Framework; this framework captures and defines all activities and errors associated with problem solving in a dynamic math environment. Found are three…

An Astronomical Problem in a Japanese Traditional Mathematical Text: The 49th Problem of the Kenki-sanpo of Takebe Katahiro

NASA Astrophysics Data System (ADS)

Ôhashi, Yukio

During the Edo period (Tokugawa-shogunate period) (1603-1867), there was a mathematical tradition now called "Wasan" which was primarily based on Chinese mathematics, but Japanese mathematicians also created new devices. It was quite popular, and common people could enjoy solving mathematical problems through Wasan regardless of their social status. Some astronomical problems were also treated there.

Les Representations Graphiques Dans La Resolution De Problemes: Une Experience D'Entrainement D'Etudiants Dans Un Club Mathematique (Graphic Representations in Problem Solving: A Training Program for Students in a Mathematical Club).

ERIC Educational Resources Information Center

Callejo, Maria Luz

1994-01-01

Reports, in French, an investigation on the use of graphic representations in problem-solving tasks of the type in Spanish Mathematical Olympiads. Analysis showed that the choice and interpretation of the first graphic representation played a decisive role in the discovery of the solution. (34 references) (Author/MKR)

Mathematics Skill of Fifteen Years Old Students in Yogyakarta in Solving Problems Like PISA

ERIC Educational Resources Information Center

Wulandari, Nidya Ferry; Jailani

2018-01-01

The aims of this research were to describe mathematics skill of 8th fifteen-year old students in Yogyakarta in solving problem of PISA. The sampling was combination of stratified and cluster random sampling. The sample consisting of 400 students was selected from fifteen schools. The data collection was by tests. The research finding revealed that…

Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

ERIC Educational Resources Information Center

Ben-Hur, Meir

2006-01-01

Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…

The Social Essentials of Learning: An Experimental Investigation of Collaborative Problem Solving and Knowledge Construction in Mathematics Classrooms in Australia and China

ERIC Educational Resources Information Center

Chan, Man Ching Esther; Clarke, David; Cao, Yiming

2018-01-01

Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question "How do we optimise social interaction for the promotion of learning in a mathematics classroom?" Employing the logic of multi-theoretic research design,…

One More Time: The Need for More Mathematical Problem Solving and What the Research Says about It

ERIC Educational Resources Information Center

Woodward, John

2013-01-01

This article reviews recent research in math problem solving for students with learning disabilities. Two recently published syntheses of research on mathematics by the Institute of Education Sciences (IES) are used as frameworks for interpreting this body of work. A significant amount of the work in special education over the last decade is…

Problem Solving and Immigrant Student Mathematics and Science Achievement: Multination Findings from the Programme for International Student Assessment (PISA)

ERIC Educational Resources Information Center

Martin, Andrew J.; Liem, Gregory A. D.; Mok, Magdalena M. C.; Xu, Jacob

2012-01-01

The present study investigates problem-solving skill alongside more widely recognized settlement and sociodemographic factors in first-generation (1G) and second-generation (2G) immigrant students' science and mathematics achievement. A total of 113,767 students (ages 15-16 years) from 17 countries were drawn from the 2003 Programme for…

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

ERIC Educational Resources Information Center

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…

Improving Mathematical Problem-Solving Ability and Self-Confidence of High School Students through Contextual Learning Model

ERIC Educational Resources Information Center

Surya, Edy; Putri, Feria Andriana; Mukhtar

2017-01-01

The purposes of this study are: (1) to know if students' mathematical problem-solving ability taught by contextual learning model is higher than students taught by expository learning, (2) to know if students' self-confidence taught by contextual learning model is higher than students taught by expository learning, (3) to know if there is…

Comparison of Types of Generalizations and Problem-Solving Schemas Used to Solve a Mathematical Problem

ERIC Educational Resources Information Center

Hodnik Cadež, Tatjana; Manfreda Kolar, Vida

2015-01-01

A cognitive schema is a mechanism which allows an individual to organize her/his experiences in such a way that a new similar experience can easily be recognised and dealt with successfully. Well-structured schemas provide for the knowledge base for subsequent mathematical activities. A new experience can be assimilated into a previously existing…

The Effects of Computer Programming on High School Students' Reasoning Skills and Mathematical Self-Efficacy and Problem Solving

ERIC Educational Resources Information Center

Psycharis, Sarantos; Kallia, Maria

2017-01-01

In this paper we investigate whether computer programming has an impact on high school student's reasoning skills, problem solving and self-efficacy in Mathematics. The quasi-experimental design was adopted to implement the study. The sample of the research comprised 66 high school students separated into two groups, the experimental and the…

Predicting Academic Success of Junior Secondary School Students in Mathematics through Cognitive Style and Problem Solving Technique

ERIC Educational Resources Information Center

Badru, Ademola K.

2015-01-01

This study examined the prediction of academic success of Junior secondary school mathematics students using their cognitive style and problem solving technique. A descriptive survey of correlation type was adopted for this study. A purposive sampling procedure was used to select five Public Junior secondary schools in Ijebu-Ode local government…

Approach to Mathematical Problem Solving and Students' Belief Systems: Two Case Studies

ERIC Educational Resources Information Center

Callejo, Maria Luz; Vila, Antoni

2009-01-01

The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study of 61 students 12-13 years old. In this study we identified different types of approaches to…

Problem Solving in Mathematics: Focus for the Future. 1987. Senior High School Monograph.

ERIC Educational Resources Information Center

Alberta Dept. of Education, Edmonton. Curriculum Branch.

This monograph was developed with the intention of addressing the concerns of high school mathematics teachers in Alberta (Canada) who want to base their programs on problem solving but have questions about effective and efficient ways to do so. Considered are the most basic philosophical questions, and a framework is provided to use in solving…

Exploring Effects of High School Students' Mathematical Processing Skills and Conceptual Understanding of Chemical Concepts on Algorithmic Problem Solving

ERIC Educational Resources Information Center

Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya

2013-01-01

The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…

A Specialist Professional Experience Learning Community for Primary Pre-Service Teachers Focussed on Mathematical Problem Solving

ERIC Educational Resources Information Center

Cavanagh, Michael; McMaster, Heather

2017-01-01

Problem solving has been identified as an important approach to learning and teaching mathematics, yet many primary pre-service teachers (PSTs) struggle to implement it during their professional experience. In this paper, we report the experiences of a group of four primary PSTs who, in an additional professional experience placement, formed a…

Revisiting Mathematical Problem Solving and Posing in the Digital Era: Toward Pedagogically Sound Uses of Modern Technology

ERIC Educational Resources Information Center

Abramovich, S.

2014-01-01

The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…

The Effects of Schema-Based Instruction on the Proportional Thinking of Students With Mathematics Difficulties With and Without Reading Difficulties.

PubMed

Jitendra, Asha K; Dupuis, Danielle N; Star, Jon R; Rodriguez, Michael C

2016-07-01

This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest (g = 0.40) and again 6 weeks later (g = 0.42). The interaction between treatment group and students' difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students' performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas. © Hammill Institute on Disabilities 2014.

An electromagnetism-like metaheuristic for open-shop problems with no buffer

NASA Astrophysics Data System (ADS)

Naderi, Bahman; Najafi, Esmaeil; Yazdani, Mehdi

2012-12-01

This paper considers open-shop scheduling with no intermediate buffer to minimize total tardiness. This problem occurs in many production settings, in the plastic molding, chemical, and food processing industries. The paper mathematically formulates the problem by a mixed integer linear program. The problem can be optimally solved by the model. The paper also develops a novel metaheuristic based on an electromagnetism algorithm to solve the large-sized problems. The paper conducts two computational experiments. The first includes small-sized instances by which the mathematical model and general performance of the proposed metaheuristic are evaluated. The second evaluates the metaheuristic for its performance to solve some large-sized instances. The results show that the model and algorithm are effective to deal with the problem.

Problem-Posing as a Didactic Resource in Formal Mathematics Courses to Train Future Secondary School Mathematics Teachers

ERIC Educational Resources Information Center

Solórzano, Lorena Salazar

2015-01-01

Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of…

The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge.

PubMed

Fuchs, Lynn S; Gilbert, Jennifer K; Powell, Sarah R; Cirino, Paul T; Fuchs, Douglas; Hamlett, Carol L; Seethaler, Pamela M; Tolar, Tammy D

2016-12-01

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Students' Mathematical Reasoning and Beliefs in Non-Routine Task Solving

ERIC Educational Resources Information Center

Jäder, Jonas; Sidenvall, Johan; Sumpter, Lovisa

2017-01-01

Beliefs and problem solving are connected and have been studied in different contexts. One of the common results of previous research is that students tend to prefer algorithmic approaches to mathematical tasks. This study explores Swedish upper secondary school students' beliefs and reasoning when solving non-routine tasks. The results regarding…

Math Ties: Problem Solving, Logic Teasers, and Math Puzzles All "Tied" to the Math Curriculum. Book A1.

ERIC Educational Resources Information Center

Santi, Terri

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

Process Inquiry: Analysis of Oral Problem-Solving Skills in Mathematics of Engineering Students

ERIC Educational Resources Information Center

Trance, Naci John C.

2013-01-01

This paper presents another effort in determining the difficulty of engineering students in terms of solving word problems. Students were presented with word problems in algebra. Then, they were asked to solve the word problems orally; that is, before they presented their written solutions, they were required to explain how they understood the…

From Poor Performance to Success under Stress: Working Memory, Strategy Selection, and Mathematical Problem Solving under Pressure

ERIC Educational Resources Information Center

Beilock, Sian L.; DeCaro, Marci S.

2007-01-01

Two experiments demonstrate how individual differences in working memory (WM) impact the strategies used to solve complex math problems and how consequential testing situations alter strategy use. In Experiment 1, individuals performed multistep math problems under low- or high-pressure conditions and reported their problem-solving strategies.…

Improving Primary Students' Mathematical Literacy through Problem Based Learning and Direct Instruction

ERIC Educational Resources Information Center

Firdaus, Fery Muhamad; Wahyudin; Herman, Tatang

2017-01-01

This research was done on primary school students who are able to understand mathematical concepts, but unable to apply them in solving real life problems. Therefore, this study aims to improve primary school students' mathematical literacy through problem-based learning and direct instruction. In addition, the research was conducted to determine…

Gender differences in algebraic thinking ability to solve mathematics problems

NASA Astrophysics Data System (ADS)

Kusumaningsih, W.; Darhim; Herman, T.; Turmudi

2018-05-01

This study aimed to conduct a gender study on students' algebraic thinking ability in solving a mathematics problem, polyhedron concept, for grade VIII. This research used a qualitative method. The data was collected using: test and interview methods. The subjects in this study were eight male and female students with different level of abilities. It was found that the algebraic thinking skills of male students reached high group of five categories. They were superior in terms of reasoning and quick understanding in solving problems. Algebraic thinking ability of high-achieving group of female students also met five categories of algebraic thinking indicators. They were more diligent, tenacious and thorough in solving problems. Algebraic thinking ability of male students in medium category only satisfied three categories of algebraic thinking indicators. They were sufficient in terms of reasoning and understanding in solving problems. Algebraic thinking ability group of female students in medium group also satisfied three categories of algebraic thinking indicators. They were fairly diligent, tenacious and meticulous on working on the problems.

Limitations to Teaching Children 2 + 2 = 4: Typical Arithmetic Problems Can Hinder Learning of Mathematical Equivalence

ERIC Educational Resources Information Center

McNeil, Nicole M.

2008-01-01

Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7-9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __),…

Visual Representations in Mathematics Teaching: An Experiment with Students

ERIC Educational Resources Information Center

Debrenti, Edith

2015-01-01

General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

Mission Mathematics: Linking Aerospace and the NCTM Standards, K-6.

ERIC Educational Resources Information Center

Hynes, Mary Ellen, Ed.

This book is designed to present mathematical problems and tasks that focus on the National Council of Teachers of Mathematics (NCTM) curriculum and evaluation standards in the context of aerospace activities. It aims at actively engaging students in NCTM's four process standards: (1) problem solving; (2) mathematical reasoning; (3) communicating…

Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

Projects, Puzzles and Other Pedagogies: Working with Kids to Solve Local Problems

ERIC Educational Resources Information Center

Marshman, Margaret

2012-01-01

Engaging and extending middle years students in mathematics is a continual challenge. One of the aims of the "Australian Curriculum: Mathematics" is to ensure that students are "confident, creative users and communicators of mathematics" (ACARA, 2011). Use of mathematical models and/or problems has been suggested as methods of…

Using Mathematics and Engineering to Solve Problems in Secondary Level Biology

ERIC Educational Resources Information Center

Cox, Charles; Reynolds, Birdy; Schunn, Christian; Schuchardt, Anita

2016-01-01

There are strong classroom ties between mathematics and the sciences of physics and chemistry, but those ties seem weaker between mathematics and biology. Practicing biologists realize both that there are interesting mathematics problems in biology, and that viewing classroom biology in the context of another discipline could support students'…

Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

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

ERIC Educational Resources Information Center

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…

Mathematics Teacher-Candidates' Performance in Solving Problems with Different Representation Styles: The Trigonometry Example

ERIC Educational Resources Information Center

Dündar, Sefa

2015-01-01

Using multiple representations of a problem can reveal the relationship between complex concepts by expressing the same mathematical condition differently and can contribute to the meaningful learning of mathematical concepts. The purpose of this study is to assess the performances of mathematics teacher-candidates on trigonometry problems…

What Are You Assuming?

ERIC Educational Resources Information Center

Kennedy, Nadia Stoyanova

2012-01-01

Students are often encouraged to work on problems "like mathematicians"--to be persistent, to investigate different approaches, and to evaluate solutions. This behavior, regarded as problem solving, is an essential component of mathematical practice. Some crucial aspects of problem solving include defining and interpreting problems, working with…

Effects of Cognitive Strategy Interventions on Word Problem Solving and Working Memory in Children with Math Disabilities

ERIC Educational Resources Information Center

Swanson, H. Lee; Lussier, Catherine; Orosco, Michael

2011-01-01

Although current categories of learning disabilities include as specific disabilities calculation and mathematical problem solving [see IDEA reauthorization, 2004, Sec. 300.8(c)(10)], the majority of research focuses on calculation disabilities. Previous studies have shown, however, that deficits in word problem solving difficulties are persistent…

Extricating Justification Scheme Theory in Middle School Mathematical Problem Solving

ERIC Educational Resources Information Center

Matteson, Shirley; Capraro, Mary Margaret; Capraro, Robert M.; Lincoln, Yvonna S.

2012-01-01

Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research…

Mathematical Geology.

ERIC Educational Resources Information Center

Jones, Thomas A.

1983-01-01

Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)

Students’ metacognitive activities in solving the combinatorics problem: the experience of students with holist-serialist cognitive style

NASA Astrophysics Data System (ADS)

Trisna, B. N.; Budayasa, I. K.; Siswono, T. Y. E.

2018-01-01

Metacognition is related to improving student learning outcomes. This study describes students’ metacognitive activities in solving the combinatorics problem. Two undergraduate students of mathematics education from STKIP PGRI Banjarmasin were selected as the participants of the study, one person has a holist cognitive style and the other a serialist. Data were collected by task-based interviews where the task contains a combinatorial problem. The interviews were conducted twice using equivalent problem at two different times. The study found that the participants showed metacognitive awareness (A), metacognitive evaluation (E), and metacognitive regulation (R) that operated as pathways from one function to another. Both, holist and serialist, have metacognitive activities in different pathway. The path of metacognitive activities of the holist is AERCAE-AAEER-ACRECCECC-AREERCE with the AERAE-AER-ARE-ARERE pattern, while the path of metacognitive activities of the serialist is AERCA-AAER-ACRERCERC-AREEEE with the AERA-AER-ARERER-ARE pattern. As an implication of these findings, teachers/lecturers need to pay attention to metacognitive awareness when they begin a stage in mathematical problem solving. Teachers/lecturers need to emphasize to students that in mathematical problem solving, processes and results are equally important.

Selective Spatial Working Memory Impairment in a Group of Children with Mathematics Learning Disabilities and Poor Problem-Solving Skills

ERIC Educational Resources Information Center

Passolunghi, Maria Chiara; Mammarella, Irene Cristina

2012-01-01

This study examines visual and spatial working memory skills in 35 third to fifth graders with both mathematics learning disabilities (MLD) and poor problem-solving skills and 35 of their peers with typical development (TD) on tasks involving both low and high attentional control. Results revealed that children with MLD, relative to TD children,…

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

ERIC Educational Resources Information Center

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…

Visual Reasoning Tools in Action: Double Number Lines, Area Models, and Other Diagrams Power Up Students' Ability to Solve and Make Sense of Various Problems

ERIC Educational Resources Information Center

Watanabe, Tad

2015-01-01

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Fostering Perseverance

ERIC Educational Resources Information Center

Lewis, Jennifer M.; Özgün-Koca, S. Asli

2016-01-01

Sustaining engagement with a mathematics task is not a novel suggestion for effective mathematics teaching. "Principles and Standards for School Mathematics" (2000) specified that "students need to know that a challenging problem will take some time and that perseverance is an important aspect of the problem-solving process and of…

Flowing toward Correct Contributions during Group Problem Solving: A Statistical Discourse Analysis

ERIC Educational Resources Information Center

Chiu, Ming Ming

2008-01-01

Groups that created more correct ideas (correct contributions or CCs) might be more likely to solve a problem, and students' recent actions (micro-time context) might aid CC creation. 80 high school students worked in groups of 4 on an algebra problem. Groups with higher mathematics grades or more CCs were more likely to solve the problem. Dynamic…

"I'm Not Very Good at Solving Problems": An Exploration of Students' Problem Solving Behaviours

ERIC Educational Resources Information Center

Muir, Tracey; Beswick, Kim; Williamson, John

2008-01-01

This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories…

Math Ties: Problem Solving, Logic Teasers, and Math Puzzles All "Tied" To the Math Curriculum. Book B1.

ERIC Educational Resources Information Center

Santi, Terri

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 6-8, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, exponents, fractions, pre-algebra, algebra, geometry, number theory, set theory, ratio, proportion, percent, probability,…

Solving the Sailors and the Coconuts Problem via Diagrammatic Approach

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2010-01-01

In this article, we discuss how to use a diagrammatic approach to solve the classic sailors and the coconuts problem. It provides us an insight on how to tackle this type of problem in a novel and intuitive way. This problem-solving approach will be found useful to mathematics teachers or lecturers involved in teaching elementary number theory,…

Symbolic and Verbal Representation Process of Student in Solving Mathematics Problem Based Polya's Stages

ERIC Educational Resources Information Center

Anwar, Rahmad Bustanul; Rahmawati, Dwi

2017-01-01

The purpose of this research was to reveal how the construction process of symbolic representation and verbal representation made by students in problem solving. The construction process in this study referred to the problem-solving stage by Polya covering; 1) understanding the problem, 2) devising a plan, 3) carrying out the plan, and 4) looking…

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

ERIC Educational Resources Information Center

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…

Teaching Mathematical Word Problem Solving: The Quality of Evidence for Strategy Instruction Priming the Problem Structure

ERIC Educational Resources Information Center

Jitendra, Asha K.; Petersen-Brown, Shawna; Lein, Amy E.; Zaslofsky, Anne F.; Kunkel, Amy K.; Jung, Pyung-Gang; Egan, Andrea M.

2015-01-01

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et…

Class and Home Problems: Optimization Problems

ERIC Educational Resources Information Center

Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard

2011-01-01

Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…

The Music of Mathematics: Toward a New Problem Typology

NASA Astrophysics Data System (ADS)

Quarfoot, David

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

Using What Matters to Students in Bilingual Mathematics Problems

ERIC Educational Resources Information Center

Dominguez, Higinio

2011-01-01

In this study, the author represented what matters to bilingual students in their everyday lives--namely bilingualism and everyday experiences--in school-based mathematical problems. Solving problems in pairs, students demonstrated different patterns of organizing and coordinating talk across problem contexts and across languages. Because these…

Mathematical problem solving ability of sport students in the statistical study

NASA Astrophysics Data System (ADS)

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.

Solving of Clock Problems Using An Algebraic Approach And Developing An Application For Automatic Conversion

NASA Astrophysics Data System (ADS)

Lakshmi Devaraj, Shanmuga

2018-04-01

The recent trend in learning Mathematics is through android apps like Byju’s. The clock problems asked in aptitude tests could be learnt using such computer applications. The Clock problems are of four categories namely: 1. What is the angle between the hands of a clock at a particular time 2. When the hands of a clock will meet after a particular time 3. When the hands of a clock will be at right angle after a particular time 4. When the hands of a clock will be in a straight line but not together after a particular time The aim of this article is to convert the clock problems which were solved using the traditional approach to algebraic equations and solve them. Shortcuts are arrived which help in solving the questions in just a few seconds. Any aptitude problem could be converted to an algebraic equation by tracing the way the problem proceeds by applying our analytical skills. Solving of equations would be the easiest part in coming up with the solution. Also a computer application could be developed by using the equations that were arrived at in the analysis part. The computer application aims at solving the four different problems in Clocks. The application helps the learners of aptitude for CAT and other competitive exams to know the approach of the problem. Learning Mathematics with a gaming tool like this would be interesting to the learners. This paper provides a path to creating gaming apps to learn Mathematics.

Cognitive Theory. Volume 2.

ERIC Educational Resources Information Center

Castellan, N. John, Jr., Ed.; And Others

The conference papers in this collection emphasize the theoretical significance of their authors' work in the areas of mathematical and cognitive psychology. Major topics considered include facilitation of problem solving; psychological differences among problem isomorphs; the process of understanding in problem solving; processing information for…

Language and Thought in Mathematics Staff Development: A Problem Probing Protocol

ERIC Educational Resources Information Center

Kabasakalian, Rita

2007-01-01

Background/Context: The theoretical framework of the paper comes from research on problem solving, considered by many to be the essence of mathematics; research on the importance of oral language in learning mathematics; and on the importance of the teacher as the primary instrument of learning mathematics for most students. As a nation, we are…

Etiological Distinction of Working Memory Components in Relation to Mathematics

PubMed Central

Lukowski, Sarah L.; Soden, Brooke; Hart, Sara A.; Thompson, Lee A.; Kovas, Yulia; Petrill, Stephen A.

2014-01-01

Working memory has been consistently associated with mathematics achievement, although the etiology of these relations remains poorly understood. The present study examined the genetic and environmental underpinnings of math story problem solving, timed calculation, and untimed calculation alongside working memory components in 12-year-old monozygotic (n = 105) and same-sex dizygotic (n = 143) twin pairs. Results indicated significant phenotypic correlation between each working memory component and all mathematics outcomes (r = 0.18 – 0.33). Additive genetic influences shared between the visuo-spatial sketchpad and mathematics achievement was significant, accounting for roughly 89% of the observed correlation. In addition, genetic covariance was found between the phonological loop and math story problem solving. In contrast, despite there being a significant observed relationship between phonological loop and timed and untimed calculation, there was no significant genetic or environmental covariance between the phonological loop and timed or untimed calculation skills. Further analyses indicated that genetic overlap between the visuo-spatial sketchpad and math story problem solving and math fluency was distinct from general genetic factors, whereas g, phonological loop, and mathematics shared generalist genes. Thus, although each working memory component was related to mathematics, the etiology of their relationships may be distinct. PMID:25477699

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

NASA Astrophysics Data System (ADS)

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.

Using Proportional Reasoning to Solve Geometric Problems

ERIC Educational Resources Information Center

Pandiscio, Eric A

2004-01-01

Students solve a geometric problem of measuring polygons with the help of proportional reasoning. Thus the importance of conceptual reasoning is emphasized as a highly efficient technique for teaching and strengthening mathematical content.

Noticing relevant problem features: activating prior knowledge affects problem solving by guiding encoding

PubMed Central

Crooks, Noelle M.; Alibali, Martha W.

2013-01-01

This study investigated whether activating elements of prior knowledge can influence how problem solvers encode and solve simple mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __). Past work has shown that such problems are difficult for elementary school students (McNeil and Alibali, 2000). One possible reason is that children's experiences in math classes may encourage them to think about equations in ways that are ultimately detrimental. Specifically, children learn a set of patterns that are potentially problematic (McNeil and Alibali, 2005a): the perceptual pattern that all equations follow an “operations = answer” format, the conceptual pattern that the equal sign means “calculate the total”, and the procedural pattern that the correct way to solve an equation is to perform all of the given operations on all of the given numbers. Upon viewing an equivalence problem, knowledge of these patterns may be reactivated, leading to incorrect problem solving. We hypothesized that these patterns may negatively affect problem solving by influencing what people encode about a problem. To test this hypothesis in children would require strengthening their misconceptions, and this could be detrimental to their mathematical development. Therefore, we tested this hypothesis in undergraduate participants. Participants completed either control tasks or tasks that activated their knowledge of the three patterns, and were then asked to reconstruct and solve a set of equivalence problems. Participants in the knowledge activation condition encoded the problems less well than control participants. They also made more errors in solving the problems, and their errors resembled the errors children make when solving equivalence problems. Moreover, encoding performance mediated the effect of knowledge activation on equivalence problem solving. Thus, one way in which experience may affect equivalence problem solving is by influencing what students encode about the equations. PMID:24324454

Relooking "Look Back": A Student's Attempt at Problem Solving Using Polya's Model

ERIC Educational Resources Information Center

Leong, Yew Hoong; Toh, Tin Lam; Tay, Eng Guan; Quek, Khiok Seng; Dindyal, Jaguthsing

2012-01-01

Against the backdrop of half a century of research in mathematics problem solving, Polya's last stage is especially conspicuous--by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, "Conditions for promoting reasoning in problem solving: Insights from a longitudinal…

Performance in Mathematical Problem Solving as a Function of Comprehension and Arithmetic Skills

ERIC Educational Resources Information Center

Voyer, Dominic

2011-01-01

Many factors influence a student's performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils' real-world knowledge, which support the construction of a…

Problem Solving at the Middle School Level: A Comparison of Different Strategies

ERIC Educational Resources Information Center

Baraké, Farah; El-Rouadi, Naim; Musharrafieh, Juhaina

2015-01-01

This article sheds light and reflects on how students in grades seven and eight read and understand implicit data when solving a story problem. Problem solving experiences help in adding up to the child's mathematical knowledge and promote a higher level of critical thinking abilities. Seventh and eighth grade students were selected from two…

Some Thoughts about Molecular-Level Representations in Conceptual Problem Solving.

ERIC Educational Resources Information Center

Nakhleh, Mary B.

One of the more interesting areas of problem solving in chemistry attempts to answer the question, "What do students understand about the molecular level of chemistry?" This question is also implicit in the more traditional area of mathematical problem solving but in this paper, more focus is placed on devising ways to help students develop a…

Conceptual Learning in a Principled Design Problem Solving Environment

ERIC Educational Resources Information Center

Prusak, Naomi; Hershkowitz, Rina; Schwarz, Baruch B.

2013-01-01

To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…

The Effects of Differentiating Instruction by Learning Styles on Problem Solving in Cooperative Groups

ERIC Educational Resources Information Center

Westbrook, Amy F.

2011-01-01

It can be difficult to find adequate strategies when teaching problem solving in a standard based mathematics classroom. The purpose of this study was to improve students' problem solving skills and attitudes through differentiated instruction when working on lengthy performance tasks in cooperative groups. This action research studied for 15 days…

Schema-Based Instruction with Concrete and Virtual Manipulatives to Teach Problem Solving to Students with Autism

ERIC Educational Resources Information Center

Root, Jenny R.; Browder, Diane M.; Saunders, Alicia F.; Lo, Ya-yu

2017-01-01

The current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In…

Analyses of Attribute Patterns of Creative Problem Solving Ability among Upper Elementary Students in Taiwan

ERIC Educational Resources Information Center

Lin, Chia-Yi

2010-01-01

The purpose of this research is to find the relationships among attributes of creative problem solving ability and their relationships with the Math Creative Problem Solving Ability. In addition, the attribute patterns of high, medium, and low mathematical creative groups were identified and compared. There were 409 fifth and sixth graders…

Collaborative Problem Solving Skills of 15-Year-Olds: Results from PISA 2015. Data Point. NCES 2017-249

ERIC Educational Resources Information Center

National Center for Education Statistics, 2017

2017-01-01

The Program for International Student Assessment (PISA) is a global education study of 15-year-old students' reading, mathematics, and science literacy and, in 2015, two optional components: financial literacy and collaborative problem solving. Fifty-one education systems administered the collaborative problem solving assessment, including 32 of…

A Problem-Solving Framework to Assist Students and Teachers in STEM Courses

ERIC Educational Resources Information Center

Phillips, Jeffrey A.; Clemmer, Katharine W.; McCallum, Jeremy E. B.; Zachariah, Thomas M.

2017-01-01

Well-developed, problem-solving skills are essential for any student enrolled in a science, technology, engineering, and mathematics (STEM) course as well as for graduates in the workforce. One of the most essential skills is the ability to monitor one's own progress and understanding while solving a problem. Successful monitoring during the…

The Benefits of Computer-Generated Feedback for Mathematics Problem Solving

ERIC Educational Resources Information Center

Fyfe, Emily R.; Rittle-Johnson, Bethany

2016-01-01

The goal of the current research was to better understand when and why feedback has positive effects on learning and to identify features of feedback that may improve its efficacy. In a randomized experiment, second-grade children (N = 75) received instruction on a correct problem-solving strategy and then solved a set of relevant problems.…

Using Technology To Enhance Problem Solving and Critical Thinking Skills.

ERIC Educational Resources Information Center

Mingus, Tabitha; Grassl, Richard

1997-01-01

Secondary mathematics teachers participated in a problem-solving course in which technology became a means to develop as teachers and as problem solvers. Findings indicate a delineation between technical competence and metatechnology--thinking about how and when to apply technology to particular problems. (PVD)

A Case Study in Mathematics--The Cone Problem

ERIC Educational Resources Information Center

Damaskos, Nickander J.

1969-01-01

A case study in mathematics designed to illustrate how the computer may be instructed to solve complicated problems. The problem is to find the volume of a right truncated cone given the altitude and a half angle or the base radius. (RP)

The Effect of Scratch- and Lego Mindstorms Ev3-Based Programming Activities on Academic Achievement, Problem-Solving Skills and Logical-Mathematical Thinking Skills of Students

ERIC Educational Resources Information Center

Korkmaz, Özgen

2016-01-01

The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…

Counting to 20: Online Implementation of a Face-to-Face, Elementary Mathematics Methods Problem-Solving Activity

ERIC Educational Resources Information Center

Schwartz, Catherine Stein

2012-01-01

This study describes implementation of the same problem-solving activity in both online and face-to-face environments. The activity, done in the first class period or first module of a K-2 mathematics methods course, was initially used in a face-to-face class and then adapted later for use in an online class. While the task was originally designed…

The Effects of a Modified Learning Strategy on the Multiple Step Mathematical Word Problem Solving Ability of Middle School Students with High-Functioning Autism or Asperger's Syndrome

ERIC Educational Resources Information Center

Schaefer Whitby, Peggy J.

2009-01-01

Children with HFA/AS are outperformed by their neuro-typical peers on mathematical problem solving skills even though they have average-to-above-average intelligence (Dickerson Mayes & Calhoun, 2003b); have average-to-above-average computation skills (Chiang & Lin, 2007); and, are educated in the general education setting (Twenty Eighth…

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

ERIC Educational Resources Information Center

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…

Guide to Mathematics Released Items: Understanding Scoring

ERIC Educational Resources Information Center

Partnership for Assessment of Readiness for College and Careers, 2017

2017-01-01

The Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics items measure critical thinking, mathematical reasoning, and the ability to apply skills and knowledge to real-world problems. Students are asked to solve problems involving the key knowledge and skills for their grade level as identified by the Common Core…

The Locker Problem: An Open and Shut Case

ERIC Educational Resources Information Center

Kimani, Patrick M.; Olanoff, Dana; Masingila, Joanna O.

2016-01-01

This article discusses how teaching via problem solving helps enact the Mathematics Teaching Practices and supports students' learning and development of the Standards for Mathematical Practice. This approach involves selecting and implementing mathematical tasks that serve as vehicles for meeting the learning goals for the lesson. For the lesson…

Modelling Mathematical Reasoning in Physics Education

ERIC Educational Resources Information Center

Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche

2012-01-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…

Scott Foresman-Addison Wesley Elementary Mathematics. What Works Clearinghouse Intervention Report. Updated

ERIC Educational Resources Information Center

What Works Clearinghouse, 2013

2013-01-01

"Scott Foresman-Addison Wesley Elementary Mathematics" is a core mathematics curriculum for students in prekindergarten through grade 6. The program aims to improve students' understanding of key math concepts through problem-solving instruction, hands-on activities, and math problems that involve reading and writing. The curriculum…

It's Not a Math Lesson--We're Learning to Draw! Teachers' Use of Visual Representations in Instructing Word Problem Solving in Sixth Grade of Elementary School

ERIC Educational Resources Information Center

Boonen, Anton J. H.; Reed, Helen C.; Schoonenboom, Judith; Jolles, Jelle

2016-01-01

Non-routine word problem solving is an essential feature of the mathematical development of elementary school students worldwide. Many students experience difficulties in solving these problems due to erroneous problem comprehension. These difficulties could be alleviated by instructing students how to use visual representations that clarify the…

The effects of using diagramming as a representational technique on high school students' achievement in solving math word problems

NASA Astrophysics Data System (ADS)

Banerjee, Banmali

Methods and procedures for successfully solving math word problems have been, and continue to be a mystery to many U.S. high school students. Previous studies suggest that the contextual and mathematical understanding of a word problem, along with the development of schemas and their related external representations, positively contribute to students' accomplishments when solving word problems. Some studies have examined the effects of diagramming on students' abilities to solve word problems that only involved basic arithmetic operations. Other studies have investigated how instructional models that used technology influenced students' problem solving achievements. Still other studies have used schema-based instruction involving students with learning disabilities. No study has evaluated regular high school students' achievements in solving standard math word problems using a diagramming technique without technological aid. This study evaluated students' achievement in solving math word problems using a diagramming technique. Using a quasi-experimental experimental pretest-posttest research design, quantitative data were collected from 172 grade 11 Hispanic English language learners (ELLS) and African American learners whose first language is English (EFLLs) in 18 classes at an inner city high school in Northern New Jersey. There were 88 control and 84 experimental students. The pretest and posttest of each participating student and samples of the experimental students' class assignments provided the qualitative data for the study. The data from this study exhibited that the diagramming method of solving math word problems significantly improved student achievement in the experimental group (p<.01) compared to the control group. The study demonstrated that urban, high school, ELLs benefited from instruction that placed emphasis on the mathematical vocabulary and symbols used in word problems and that both ELLs and EFLLs improved their problem solving success through careful attention to the creation and labeling of diagrams to represent the mathematics involved in standard word problems. Although Learnertype (ELL, EFLL), Classtype (Bilingual and Mixed), and Gender (Female, Male) were not significant indicators of student achievement, there was significant interaction between Treatment and Classtype at the level of the Bilingual students ( p<.01) and between Treatment and Learnertype at the level of the ELLs (p<.01).

On two mathematical problems of canonical quantization. IV

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1992-11-01

A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions.

Quantitative Reasoning in Problem Solving

ERIC Educational Resources Information Center

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.

Effects of Preventative Tutoring on the Mathematical Problem Solving of Third-Grade Students With Math and Reading Difficulties.

PubMed

Fuchs, Lynn S; Seethaler, Pamela M; Powell, Sarah R; Fuchs, Douglas; Hamlett, Carol L; Fletcher, Jack M

2008-01-01

This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits.

Effects of Preventative Tutoring on the Mathematical Problem Solving of Third-Grade Students With Math and Reading Difficulties

PubMed Central

Fuchs, Lynn S.; Seethaler, Pamela M.; Powell, Sarah R.; Fuchs, Douglas; Hamlett, Carol L.; Fletcher, Jack M.

2009-01-01

This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits. PMID:20209074

Ratio Analysis: Where Investments Meet Mathematics.

ERIC Educational Resources Information Center

Barton, Susan D.; Woodbury, Denise

2002-01-01

Discusses ratio analysis by which investments may be evaluated. Requires the use of fundamental mathematics, problem solving, and a comparison of the mathematical results within the framework of industry. (Author/NB)

Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

ERIC Educational Resources Information Center

Wang, Youjun

2009-01-01

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

How Readability Factors Are Differentially Associated with Performance for Students of Different Backgrounds When Solving Mathematics Word Problems

ERIC Educational Resources Information Center

Walkington, Candace; Clinton, Virginia; Shivraj, Pooja

2018-01-01

The link between reading and mathematics achievement is well known, and an important question is whether readability factors in mathematics problems are differentially impacting student groups. Using 20 years of data from the National Assessment of Educational Progress and the Trends in International Mathematics and Science Study, we examine how…

Mathematics Self-Efficacy and Flow in Developmental Mathematics Students

ERIC Educational Resources Information Center

Golnabi, Laura

2017-01-01

This study examined mathematics self-efficacy and the characteristics of flow in the context of performing mathematical tasks. In particular, it explored the subjective experiences of 113 undergraduate students enrolled in a developmental mathematics course while they were independently solving certain mathematical problems. This study…

Teaching the Mathematics of Radioactive Dating.

ERIC Educational Resources Information Center

Shea, James H.

2001-01-01

Describes a method used to teach the concept of radiometric dating using mathematical equations. Explores the lack of information in textbooks on how to solve radiometric dating problems using mathematical concepts. (SAH)

The Epistemological Perceptions of the Relationship between Physics and Mathematics and Its Effect on Problem-Solving among Pre-Service Teachers at Yarmouk University in Jordan

ERIC Educational Resources Information Center

Al-Omari, Wesal; Miqdadi, Ruba

2014-01-01

The purpose of this paper was to examine the perception pre-service teachers hold to the nature of the relationship between physics and mathematics. The study examined this relationship in reference to their performance in problem solving and strategies they used. The results of this empirical study suggested that most participants hold a naïve…

Development of the Metacognitive Skills of Prediction and Evaluation in Children With or Without Math Disability

PubMed Central

Garrett, Adia J.; Mazzocco, Michèle M. M.; Baker, Linda

2009-01-01

Metacognition refers to knowledge about one’s own cognition. The present study was designed to assess metacognitive skills that either precede or follow task engagement, rather than the processes that occur during a task. Specifically, we examined prediction and evaluation skills among children with (n = 17) or without (n = 179) mathematics learning disability (MLD), from grades 2 to 4. Children were asked to predict which of several math problems they could solve correctly; later, they were asked to solve those problems. They were asked to evaluate whether their solution to each of another set of problems was correct. Children’s ability to evaluate their answers to math problems improved from grade 2 to grade 3, whereas there was no change over time in the children’s ability to predict which problems they could solve correctly. Children with MLD were less accurate than children without MLD in evaluating both their correct and incorrect solutions, and they were less accurate at predicting which problems they could solve correctly. However, children with MLD were as accurate as their peers in correctly predicting that they could not solve specific math problems. The findings have implications for the usefulness of children’s self-review during mathematics problem solving. PMID:20084181

Effect of Causal Stories in Solving Mathematical Story Problems

ERIC Educational Resources Information Center

Smith, Glenn Gordon; Gerretson, Helen; Olkun, Sinan; Joutsenlahti, Jorma

2010-01-01

This study investigated whether infusing "causal" story elements into mathematical word problems improves student performance. In one experiment in the USA and a second in USA, Finland and Turkey, undergraduate elementary education majors worked word problems in three formats: 1) standard (minimal verbiage), 2) potential causation…