Reading Texts & Writing Problems to Improve Problem Solving

Bolema: Boletim de Educação Matemática, 2021

In an age where we live surrounded by technology, it is increasingly important to develop capabilities that differentiate us from “machines”. The habit of solving problems can help us develop some of them, including the ability to solve problems, and stimulate critical thinking. It is, therefore, important to propose tasks of a diverse nature in the classroom, and to invest more in mathematical problem-solving by students. For students to solve those problems, it is essential that they know different strategies to use and it is necessary that the teacher can identify the difficulties experienced by students in solving mathematical problems, so the teacher can help students overcome them. This article aims to identify the strategies students use to solve a problem, acknowledge the difficulties students experience, and characterize students’ written communication in their answers. To achieve these objectives, the answers to a mathematical problem which was solved by students of three ...

Mathematical problem solving is notoriously difficult to teach. Many mainstream university mathematics courses predominantly teach algorithm based learning and leave problem solving to be implicitly acquired as a skill rather than being explicitly taught. In 2004 at the University of Cape Town an initiative was undertaken using writing of explanatory paragraphs as a tool to enhance problem solving ability in first year university mathematics students. Data took the form of interviews, students' assessment tasks and the students' writing. Analysis of the results found that the initiative aided understanding of the problems in question as well as mathematics more generally, The mechanism of increased understanding, sometimes in sharp contrast to the lack of deep understanding by students not taking part in the writing exercise, has been theorised according to a framework suggested by Beth and Piaget, and further discussed by Dubinsky and Lewin.

The mathematics word problem solving in EFL setting of Jordanian undergraduates were investigated through Polya's (1957) adopted test as accompanied by self-report open questions procedures. In this study, mathematical problems content is used to assess their language and learning strategies. The results indicated that participating undergraduates were identified either as low problem solvers as well as limited English language proficiency students.

European Journal of Education

This study aims to analyze the correlation of the student’s progress in solving a given problem with the logic of the teacher in the layout of the questions asked. The research was conducted in the government’s secondary schools and colleges in the district of Abidjan and involved 453 participants, including 423 student and 30 teachers. The data was collected based on a survey questionnaire and then annalysed based on a quantitative and qualitative point of view. The results of the study focused on the concordance of the student’s progress in solving a given problem with the teacher’s logic in the layout of the questions asked. The study shows that students’ performance in mathematics is not dependent on how often they follow the order of the question in the statement.

The Mathematics Enthusiast, 2020

In mathematical problem solving, students' written work mostly reveals their mathematical algorithm skills and has very little information about their reasoning skills of the problem solving process. This study extends the features of mathematical writing that integrate the language and mathematical thinking to increase students' mathematical problem solving skills. The main feature of this study is the use of mathematics writing workbook as a practical approach to guide the students in the problem solving process. Thirty Foundation students in Engineering participated in a six weeks of writing to solve mathematical problems. An exploratory case study analysis was used to examine the written contents of the participants' mathematical writing workbook, the performance of their formal test as well as their perceptions of mathematical writing. The trace of work in the workbooks showed that mathematical writing has somehow given some impact on these students to visualize, aware and recognize their problem solving behaviors in words.

CEPS Journal, 2022

Problem solving and problem posing are leading mathematical activities that stimulate mathematical thinking. From the theoretical point of view, these activities are very complex, partly due to the various issues that describe/define problem solving and problem posing and their role in the process of teaching and learning mathematics. Problem solving and problem posing are interrelated activities; we could say that they are in an interdependent relationship: we solve the problems we pose, we pose the problems in a way that we can solve them. However, the two processes are not equally present in every situation. Research into problem solving focuses mainly on the following areas: the basic characteristics of a mathematical problem; the nature (conceptual, procedural) and role of representation (interplay between internal and external) of a mathematical problem; mental schemas for problem solving; heuristics as principles, methods and (cognitive) tools for solving problems; types of generalisations and reasoning (abductive, narrative, naïve, arithmetic, algebraic); problem solving as a challenging activity for mathematically gifted students; and the role of the teacher in guiding problem solving as a way of implementing student problem solving in the classroom. Regarding problem posing, there are also some critical questions: How can the existing definitions of problem posing be categorised? How is problem posing conceived by the research community in relation to other mathematical constructs? What are the possible ways of implementing problem posing in research and teaching settings? Regarding problem solving, problem posing is formulated/used in research findings for generating (formulating, finding, creating) new problems; reformulating existing problems; creating and/or reformulating problems; raising questions and viewing old questions from a new angle; and an act of modelling. Research has demonstrated and frequently confirmed that (mathematical) problem posing and solving possess great potential for learners, but the reality in terms of teaching practice, external examinations, teaching material, and mathematics curricula seems out of alignment with the research findings. In this focus issue, we have considered two aspects of problem posing and problem solving: conceptualisation and implementation in the mathematics classroom. This issue contains five articles that address the issues of problem posing and problem-solving. The authors come from different backgrounds (Greece, Croatia, Hungary, Germany), which means that diverse perspectives and research

CEPS Journal : Center for Educational Policy Studies Journal, 2022

Problem solving and problem posing are leading mathematical activities that stimulate mathematical thinking. From the theoretical point of view, these activities are very complex, partly due to the various issues that describe/define problem solving and problem posing and their role in the process of teaching and learning mathematics. Problem solving and problem posing are interrelated activities; we could say that they are in an interdependent relationship: we solve the problems we pose, we pose the problems in a way that we can solve them. However, the two processes are not equally present in every situation. Research into problem solving focuses mainly on the following areas: the basic characteristics of a mathematical problem; the nature (conceptual, procedural) and role of representation (interplay between internal and external) of a mathematical problem; mental schemas for problem solving; heuristics as principles, methods and (cognitive) tools for solving problems; types of generalisations and reasoning (abductive, narrative, naïve, arithmetic, algebraic); problem solving as a challenging activity for mathematically gifted students; and the role of the teacher in guiding problem solving as a way of implementing student problem solving in the classroom. Regarding problem posing, there are also some critical questions: How can the existing definitions of problem posing be categorised? How is problem posing conceived by the research community in relation to other mathematical constructs? What are the possible ways of implementing problem posing in research and teaching settings? Regarding problem solving, problem posing is formulated/used in research findings for generating (formulating, finding, creating) new problems; reformulating existing problems; creating and/or reformulating problems; raising questions and viewing old questions from a new angle; and an act of modelling. Research has demonstrated and frequently confirmed that (mathematical) problem posing and solving possess great potential for learners, but the reality in terms of teaching practice, external examinations, teaching material, and mathematics curricula seems out of alignment with the research findings. In this focus issue, we have considered two aspects of problem posing and problem solving: conceptualisation and implementation in the mathematics classroom. This issue contains five articles that address the issues of problem posing and problem-solving. The authors come from different backgrounds (Greece, Croatia, Hungary, Germany), which means that diverse perspectives and research

2000

Internationally, educators are concerned about effective methods to empower students with skills to equip them to function in a technological, global world. This paper reviews literature that explores the relationship between mathematical problem solving and literacy, through mathematical modelling and top-level structuring of text. The mathematical modelling problem solving process offers students an opportunity for learning mathematical skills through what

Jurnal Ilmiah Peuradeun, 2016

This article describes the implementation of writing in Mathematics as an effort to improve students' problem solving skill. The research method was classroom action research which was conducted in three cycles. Research participants were 24 first-year students at PGSD FKIP Syiah Kuala University. Data was collected using a written test consisted of mathematical word problems presented to the students at the end of each cycle, and interview. Students' problem solving skill was analyzed based on the four steps of problem solving proposed by Polya: 1. the ability to understand the problem, 2. the ability to plan a strategy to solve the problem, 3. the ability to execute the plan, and 4. the ability to recheck. Result shows that writing in Mathematics improve students' problem solving skill. In cycle 1, the average score of students' problem solving skill was 51.7. In cycle 2, the average score was 75.6, and finally in cycle 3, the average score was 83.4. During interview, the students confessed that writing helped them organize their thinking so that they can solve a problem satisfactorily.

Encyclopedia of Mathematics Education, 2014

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