The Role of Problem Solving

1985 ◽  
Vol 32 (6) ◽  
pp. 48-50
Author(s):  
Randall I. Charles
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Mathematical Thinking ◽  
Development Of Students

The importance of problem solving in mathematics has been attested to by many individuals and groups (e.g., Snowmass 1973; NCSM 1977; CBMS 1982). Furthermore, the belief seems to be common that the development of students' problem-solving abilities is one of the most important goals of mathematics education. In view of the importance of problem solving, it is templing to argue that problem solving and mathematical thinking are in fact different names tor the same activity. However, such an argument would provide too narrow an interpretation of mathematical thinking and too broad a view of problem solving. The purposes of this article are to describe one view of “mathematical thinking” and to describe the characteristics of a problem-solving program necessary to develop this kind of thinking.

Research on the Role of Structure in Thinking

1985 ◽  
Vol 32 (6) ◽  
pp. 58-60
Author(s):  
Thomas P. Carpenter
Keyword(s):  
Problem Solving ◽  
Empirical Research ◽  
Mathematical Thinking ◽  
Mathematics Students ◽  
Mathematical Thought ◽  
High Level ◽  
Mathematics Research

One of the most basic questions with regard to mathematical thinking is “What is mathematical thinking?” This question Is not the kind that is readily answered by empirical research. However, research can provide some perspective on the nature of mathematical thought if the question is rephrased: “What characterizes the thinking of individuals who have demonstrated a high level of ability in mathematics?” Research that compares the abilities of very capable mathematics students with those of less capable students or the problem-solving processes exhibited by experts and novices otfers some insights into this question.

Mathematical Symbols: Insight through Invention

1985 ◽  
Vol 32 (6) ◽  
pp. 20-22
Author(s):  
Daiyo Sawada
Keyword(s):  
Mathematics Education ◽  
Mathematical Thinking ◽  
The Other ◽  
Mathematical Symbols ◽  
Algorithmic Technique ◽  
The One ◽  
New Math ◽  
Basic Movement ◽  
Do So

Over the years, like a pendulum. the emphasis in mathematics education has swung from a focus on concepts and understanding (e.g., the new-math movement) on the one hand to skill with facts and algorithms (e.g., the back-to-basic movement) on the other. Currently. children can adequately perform algorithms, but they may do so with little understanding of the underlying concepts (Resnick 1982, 136–55). In part, the difficulty lies in students having lo t sight of the role of symbols in mathematical thinking. The development of approache. that help children integrate the insight of symbolic understanding with the power of algorithmic technique should be of value. Accordingly, the intent of this article is to suggest how children can be guided to see and personally feel the power and simplicity that thinking with and about mathematical symbols can bring to their algorithmic competence. Although, for the sake of concretene and pecificity, attention hall be confined to computation, stress shall be placed on an approach that the reader may find generalize to other areas.

The role of protagonists in implementing research on problem solving in school practice

2019 ◽  
pp. 213-214
Author(s):  
Lukas Baumanns ◽  
Sarina Scharnberg
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Problem Solving ◽  
Direct Impact ◽  
Research Results ◽  
School Practice ◽  
Dissemination Of Research ◽  
Research Findings ◽  
Discussion Question

Based on seminal works of Pólya (1945) and Schoenfeld (1985), problem solving has become a major focus of mathematics education research. Even though there exists a variety of recent research on problem solving in schools, the research results do not have a direct impact on problem solving in school practice. Instead, a dissemination of research results by integrating different protagonists is necessary. Within our working group, the roles of three different protagonists involved in implementing research on problem solving in school practice were discussed, namely researchers, pre-service, and in-service teachers, by examining the following discussion question: To what extent do the different protagonists enable implementation of research findings on problem solving in school practice?

scholarly journals DIGITAL TOOLS AND PAPER-AND-PENCIL IN SOLVING-AND-EXPRESSING: HOW TECHNOLOGY EXPANDS A STUDENT’S CONCEPTUAL MODEL OF A COVARIATION PROBLEM

2021 ◽  
Vol 12 (1) ◽  
pp. 113-132
Author(s):  
Hélia Jacinto ◽  
Susana Carreira
Keyword(s):  
Problem Solving ◽  
Conceptual Model ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Digital Tools ◽  
Data Collection And Analysis ◽  
Paper And Pencil ◽  
Multiple Sequences ◽  
Mathematical Justification

This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

scholarly journals A RELATIONSHIP BETWEEN PROBLEM SOLVING ABILITY AND STUDENTS’ MATHEMATICAL THINKING

2017 ◽  
Vol 6 (1) ◽  
pp. 21
Author(s):  
Nita Delima
Keyword(s):  
Information System ◽  
Information Systems ◽  
Mathematics Education ◽  
Problem Solving ◽  
Quantitative Method ◽  
Mathematical Thinking ◽  
Discrete Mathematics ◽  
Education Department ◽  
Mathematics Courses ◽  
Know How

This research have a purpose to know is there an influence of problem solving abilty to students mathematical thinking, and to know how strong problem solving ability affect students mathematical thinking. This research used descriptive quantitative method, which a population is all of students that taking discrete mathematics courses both in department of Information Systems and department of mathematics education. Based on the results of data analysis showed that there are an influence of problem solving ability  to students mathematical thinking either at department of mathematics education or at department of information systems. In this study, it was found that the influence of problem solving ability to students mathematical thinking which take place at mathematics education department is stonger than at information system department. This is because, at mathematics education department, problem-solving activities more often performed in courses than at department of information system. Almost 75% of existing courses in department of mathematics education involve problem solving to the objective of courses, meanwhile, in the department of information systems, there are only 10% of these courses. As a result, mathematics education department student’s are better trained in problem solving than information system department students. So, to improve students’ mathematical thinking, its would be better, at fisrtly enhance the problem solving ability.

scholarly journals A RELATIONSHIP BETWEEN PROBLEM SOLVING ABILITY AND STUDENTS’ MATHEMATICAL THINKING

2017 ◽  
Vol 6 (1) ◽  
pp. 21 ◽  
Author(s):  
Nita Delima
Keyword(s):  
Information System ◽  
Information Systems ◽  
Mathematics Education ◽  
Problem Solving ◽  
Quantitative Method ◽  
Mathematical Thinking ◽  
Discrete Mathematics ◽  
Education Department ◽  
Mathematics Courses ◽  
Know How

This research have a purpose to know is there an influence of problem solving abilty to students mathematical thinking, and to know how strong problem solving ability affect students mathematical thinking. This research used descriptive quantitative method, which a population is all of students that taking discrete mathematics courses both in department of Information Systems and department of mathematics education. Based on the results of data analysis showed that there are an influence of problem solving ability  to students mathematical thinking either at department of mathematics education or at department of information systems. In this study, it was found that the influence of problem solving ability to students mathematical thinking which take place at mathematics education department is stonger than at information system department. This is because, at mathematics education department, problem-solving activities more often performed in courses than at department of information system. Almost 75% of existing courses in department of mathematics education involve problem solving to the objective of courses, meanwhile, in the department of information systems, there are only 10% of these courses. As a result, mathematics education department student’s are better trained in problem solving than information system department students. So, to improve students’ mathematical thinking, its would be better, at fisrtly enhance the problem solving ability.

What's Going On…

1977 ◽  
Vol 24 (3) ◽  
pp. 199-200
Keyword(s):  
Twentieth Century ◽  
Mathematics Education ◽  
Problem Solving ◽  
Mathematics Curriculum ◽  
College Of Education ◽  
State University ◽  
Arizona State University ◽  
Education Curriculum ◽  
Home Computers

DO YOU HAVE ANY IDEAS on the mathematics education curriculum of the future?—any feelings about the role of the pocket calculators, problem solving, computers, television, home computers, microprocessors, basic skills, survival mathematics, metrication, and so on, in mathematics education? If so, will you share your thoughts with Gary Bitter, College of Education, Arizona State University, Tempe, AZ 85281. He is currently on sabbatical leave to do an assessment of the mathematics curriculum of the latter part of the Twentieth Century.

Instructional Computing

1985 ◽  
Vol 32 (6) ◽  
pp. 27-30
Author(s):  
Larry L. Hatfield
Keyword(s):  
Elementary School ◽  
Mathematics Education ◽  
Mathematical Thinking ◽  
School Teacher ◽  
Elementary School Teacher ◽  
Instructional Computing ◽  
Development Of Students

One of the most important goals of mathematics education is the development of students' abilities to think and reason in numerical and spatial situations. How might we use computers as tools for stimulating and guiding the construction of the child's mathematical thinking? The approaches taken by two elementary school teacher are briefly described. Although the uses of the computer by the teacher differ, both adopt a problematic approach to teaching to emphasize the child's mathematical thinking.

scholarly journals PROMOTING HIGH-LEVEL MATHEMATICAL THINKING THROUGH PROBLEM-SOLVING ACTIVITIES IN INDONESIAN PRIMARY SCHOOLS

2015 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Didi Suryadi
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Key Words ◽  
Primary Schools ◽  
Mathematical Thinking ◽  
High Level ◽  
High Level Thinking

Paper ini memuat sebagian kecil dari hasil penelitian yang dilakukan selama tiga tahun oleh Utari, Suryadi, Rukmana, Dasari, dan Suhendra (1998-2000) yang berfokus pada upaya pengembangan kemampuan berfikir matematik tingkat tinggi siswa sekolah dasar di Jawa Barat. Tujuan utama penelitian ini antara lain mencakup: (1) mengidentifikasi jenis kemampuan berfikir matematik tingkat tinggi yang bisa dikembangkan, (2) mengembangkan model bahan ajar yang sesuai, dan (3) mengembangkan alternatif model pembelajaran yang kondusif untuk pengembangan kemampuan berfikir matematik tingkat tinggi di sekolah dasar.  Key words:  high level thinking, problem-solving, mathematics education

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