Fostering Mathematical Thinking through Multiple Solutions

2000 ◽  
Vol 5 (8) ◽  
pp. 534-539
Author(s):  
Jinfa Cai ◽  
Patricia Ann Kenney
Keyword(s):  
Problem Solving ◽  
Multiple Solutions ◽  
Mathematical Thinking ◽  
School Mathematics ◽  
Reform Movement ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Teachers And Students

The reform movement in school mathematics advocates communication as a necessary component for learning, doing, and understanding mathematics (Elliott and Kenney 1996). Communication in mathematics means that one is able not only to use its vocabulary, notation, and structure to express ideas and relationships but also to think and reason mathematically. In fact, communication is considered the means by which teachers and students can share the processes of learning, doing, and understanding mathematics. Students should express their thinking and problem-solving processes in both written and oral formats. The clarity and completeness of students' communication can indicate how well they understand the related mathematical concepts.

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

Problem solving with the Sneetches

2016 ◽  
Vol 23 (5) ◽  
pp. 282-283
Author(s):  
James Russo ◽  
Toby Russo
Keyword(s):  
Problem Solving ◽  
Multiple Solutions ◽  
Mathematical Concepts ◽  
Mathematical Problems

Math by the Month features collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes four activities each for grade bands K–2, 3–4, and 5–6. In this issue, teachers read the classic Dr. Seuss book The Sneetches and other stories with their class and get students to engage with these associated mathematical problems. The problems, many of which are open-ended or contain multiple solutions or solution pathways, cover a range of mathematical concepts.

scholarly journals TYPICAL CLASS METHODS FOR SOLVING EQUATIONS AND INEQUALITIES WITH DIFFERENT STRUCTURES

2021 ◽  
Vol 58 (3) ◽  
pp. 53-62
Author(s):  
A.K. Alpysov ◽  
◽  
A.K. Seytkhanova ◽  
I.Sh. Abishova ◽  
◽  
...  
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematical Concept ◽  
Thinking Skills ◽  
Practical Application ◽  
Mathematical Concepts ◽  
Theoretical Substantiation ◽  
New Methods ◽  
General Article ◽  
Solving Equations

The article discusses the ways of developing skills and abilities to effectively solve problems when describing methods for solving equations and inequalities, clarifying theoretical knowledge, the basics of forming skills for practical application. The formation of mathematical concepts through solving problems in teaching mathematics opens the way to the development of mathematical thinking, the application of knowledge in practice, and the development of search skills. To master a mathematical concept, along with its definition, it is necessary to know its features and properties. This can be achieved primarily through problem solving and exercise. Problem solving is based on the development of new methods, the creation of algorithms, ways of developing practical skills in the methods and techniques mastered with the help of tasks.In addition, transforming equations and inequalities through the development of thinking skills helps to identify common or special properties in order to draw correct conclusions. Solving various problems, it shows what operations should be used to determine the situation in which a solution was found, and what features of the solution allow choosing the most effective methods. Thanks to the theoretical substantiation of the general article, it is possible to master convenient methods for solving equations and inequalities of various structures.

scholarly journals Piloting a problem solving module for undergraduate mathematics students

2019 ◽  
Vol 17 (2) ◽  
pp. 46
Author(s):  
David McConnell
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Thinking Skills ◽  
Mathematical Work ◽  
Assessment Practices ◽  
Traditional Teaching ◽  
Mathematics Students ◽  
Undergraduate Mathematics ◽  
Students First ◽  
Academic Year

We report on a new problem solving module for second-year undergraduate mathematics students first piloted during the 2016-17 academic year at Cardiff University.  This module was introduced in response to the concern that for many students, traditional teaching and assessment practices do not offer sufficient opportunities for developing problem-solving and mathematical thinking skills, and more generally, to address the recognised need to incorporate transferrable skills into our undergraduate programmes.  We discuss the pedagogic and practical considerations involved in the design and delivery of this module, and in particular, the question of how to construct open-ended problems and assessment activities that promote mathematical thinking, and reward genuinely original and independent mathematical work.  

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.

Principles for Principals: Facilitating Change

1989 ◽  
Vol 36 (6) ◽  
pp. 60-61
Author(s):  
Miriam A. Leiva
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Instructional Leaders ◽  
Mathematics Students

Changes are taking place in the teaching and learning of mathematics—students are actively involved in doing mathematics with manipulatives and models; they are discussing problems among themelves with their teacher's guidance; they are exploring alternate ways to solve problems; and they are posing questions and examining solu tions (Dossey et al. 1988). This student-oriented, problem-solving approach is advocated by NCTM's Curriculum and Evaluw ion Standards for School Mathematics (Commission on Standards for School Mathematics of the NCTM 1987) and supported by the finding of the 1986 National As essment of Educa tional Progress. Principals, the instructional leaders in the schools. can be facilitator of change, and their support of innovative programs and activitie is crucial to reforming school mathematics.

scholarly journals UNDERSTANDING OF BASIC CONCEPTS FOR MASTERING COMPETENCES OF SCHOOL MATHEMATICS

2016 ◽  
Vol 2 ◽  
pp. 330
Author(s):  
Anita Sondore ◽  
Elfrīda Krastiņa ◽  
Pēteris Daugulis ◽  
Elga Drelinga
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Life Quality ◽  
School Failure ◽  
School Mathematics ◽  
Mathematical Concepts ◽  
Mathematics Courses ◽  
Mathematical Competence ◽  
Basic Concepts ◽  
University Level

Mathematical competence as a universal and fundamental competence is essential for everyone as a problem solving and life quality improving tool. It is also essential for future teachers who will implement competence based teaching processes starting from elementary schools and preschools. The goal of this research is to discuss typical errors about certain basic mathematical concepts which are taught in school. Failure to grasp these concepts cause problems for learning subsequent mathematics courses and dealing with practical problems. This research will help to improve studies at university level. Experience analysis of university educators related to oral and written answers of students in tests is used in this research. Observations show that many errors get repeated year by year.

Implementing The Standards: Students' Microcomputer-Aided Exploration in Geometry

1990 ◽  
Vol 83 (8) ◽  
pp. 628-635
Author(s):  
Daniel Chazan
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematical Structure ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Mathematical Connections ◽  
Teachers And Students ◽  
K 12

Four important themes presented in the K–12 Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989) are mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. The high school component also stresses mathematical structure. Furthermore, the Standards calls for new roles for teachers and students and suggests that microcomputer technology can help support teachers and students in taking on these new roles.

Writing Samples to Understand Mathematical Thinking

2002 ◽  
Vol 7 (9) ◽  
pp. 517-520
Author(s):  
Dianne S. Goldsby ◽  
Barbara Cozza
Keyword(s):  
Mathematical Thinking ◽  
School Mathematics ◽  
Mathematics Students ◽  
Principles And Standards

NCTM's Principles and Standards for School Mathematics emphasizes the need for all students to organize and consolidate their mathematical thinking through communication and to communicate their mathematical thinking coherently to others (NCTM 2000). Writing helps students focus on their own understandings of mathematics: “Students gain insights into their thinking when they present their methods for solving problems, when they justify their reasoning to a classmate or teacher, or when they formulate a question about something that is puzzling them” (NCTM 2000, pp. 60–61).

Fostering Mathematical Thinking and Problem Solving: The Teacher's Role

2007 ◽  
Vol 13 (6) ◽  
pp. 308-314
Author(s):  
Nicole R. Rigelman
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Teacher’S Role ◽  
Teachers And Students ◽  
Teacher's Role ◽  
Teacher Actions

Describes the teacher's role in promoting mathematical thinking and problem solving in the classroom—identifying critical teacher actions and decisions; considering how beliefs influence the teacher's actions and decisions; and suggesting implications for teachers and students.

Sign in / Sign up

Export Citation Format

Share Document