Problem Solving: Is More Than Solving Problems

1998 ◽  
Vol 4 (1) ◽  
pp. 20-25
Author(s):  
Michael G. Mikusa
Keyword(s):  
Problem Solving ◽  
Correct Answer ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Students First ◽  
Mathematics Class ◽  
General Goals ◽  
Problem Solvers

The curriculum and evaluation Standards for School Mathematics (NCTM 1989) states that one of its five general goals is for all students to become mathematical problem solvers. It recommends that “to develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve” (p. 6). Clearly the authors have not taught my students! When my students first encountered a mathematical problem, they believed that it could be solved simply because it was given to them in our mathematics class. They also “knew” that the technique or process for finding the solution to many problems was to apply a skill or procedure that had been recently taught in class. The goal for most of my students was simply to get an answer. If they ended up with the correct answer, great; if not, they knew that it was “my job” to show them the “proper” way to go about solving the problem.

Coordinate Geometry: A Powerful Tool for Solving Problems

1990 ◽  
Vol 83 (4) ◽  
pp. 264-268
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Standards ◽  
Problem Situations ◽  
Coordinate Geometry

In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.

Writing About the Problem Solving Process to Improve Problem Solving Performance

2003 ◽  
Vol 96 (3) ◽  
pp. 185-187 ◽  
Author(s):  
Kenneth M. Williams
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
National Council ◽  
Instructional Programs ◽  
Principles And Standards ◽  
Problem Solving Process ◽  
Problem Solvers

Problem solving is generally recognized as one of the most important components of mathematics. In Principles and Standards for School Mathematics, the National Council of Teachers of Mathematics emphasized that instructional programs should enable all students in all grades to “build new mathematical knowledge through problem solving, solve problems that arise in mathematics and in other contexts, apply and adapt a variety of appropriate strategies to solve problems, and monitor and reflect on the process of mathematical problem solving” (NCTM 2000, p. 52). But how do students become competent and confident mathematical problem solvers?

A Visual Approach to Solving Mixture Problems

1996 ◽  
Vol 89 (2) ◽  
pp. 108-111
Author(s):  
Albert B. Bennett ◽  
Eugene Maier
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Mathematical Problem ◽  
Multiple Representations ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Conceptual Understandings ◽  
Visual Approach

In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), the 9–12 standards call for a shift from a curriculum dominated by memorization of isolated facts and procedures to one that emphasizes conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving. One approach that affords opportunities for achieving these objectives is the use of diagrams and drawings. The familiar saying “A picture is worth a thousand words” could well be modified for mathematics to “A picture is worth a thousand numbers.” As an example of visual approaches in algebra, this article uses diagrams to solve mixture problems.

One Point of View: Using Manipulatives Successfully

1990 ◽  
Vol 38 (2) ◽  
pp. 6-7
Author(s):  
Jeane M. Joyner
Keyword(s):  
Mathematical Problem ◽  
Point Of View ◽  
School Mathematics ◽  
Major Difficulty ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Mathematical Connections ◽  
Learning To Reason ◽  
Problem Solvers

A curriculum with goals for students of valuing mathematics, being confident in their abilities, making mathematical connections, becoming mathematical problem solvers, and learning to reason and communicate mathematically is a call for classrooms in which students are actively involved in learning. It is a call for teachers to establish environments that encourage the use of manipulatives to assist students in attaining these goals proposed by the NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989). A major difficulty, however, is how to manage the materials efficiently.

Editorial: Welcome to Our Sampler: Emerging Programs for the First Two Years of High School

1995 ◽  
Vol 88 (8) ◽  
pp. 630
Author(s):  
Rheta N. Rubenstein
Keyword(s):  
Secondary School ◽  
Core Curriculum ◽  
School Administrators ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Content Standards ◽  
School Students ◽  
Specific Content ◽  
Evaluation Standards ◽  
Problem Solvers

In the late 1980s we challenged ourselves as a profession to meet the goals described in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). We envisioned programs that would “encourage and enable students to value mathematics, gain confidence in their own mathematical ability, become mathematical problem solvers, communicate mathematically, and reason mathematically” (NCTM 1989, 123). In particular, for secondary school students we sought to present a core curriculum consisting of a common body of mathematical ideas accessible to all students. These visions were further detailed in the specific content standards, in the Professional Standards for Teaching Mathematics (NCTM 1991), in an assortment of Addenda books, and, this past spring, in the Assessment Standards for School Mathematics (NCTM 1995). For many people, however, among them teachers, parents, students, and school administrators, these Standards documents were merely visions, perhaps even pipe dreams.

scholarly journals Mathematics teachers’ knowledge for teaching problem solving

2015 ◽  
Vol 3 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Olive Chapman
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Mathematical Problem ◽  
Research Literature ◽  
Mathematical Problem Solving ◽  
Knowledge For Teaching ◽  
General Ability ◽  
Mathematics Knowledge ◽  
Teaching Problem ◽  
Problem Solvers

In recent years, considerable attention has been given to the knowledge teachers ought to hold for teaching mathematics. Teachers need to hold knowledge of mathematical problem solving for themselves as problem solvers and to help students to become better problem solvers. Thus, a teacher’s knowledge of and for teaching problem solving must be broader than general ability in problem solving. In this article a category-based perspective is used to discuss the types of knowledge that should be included in mathematical problem-solving knowledge for teaching. In particular, what do teachers need to know to teach for problem-solving proficiency? This question is addressed based on a review of the research literature on problem solving in mathematics education. The article discusses the perspective of problem-solving proficiency that framed the review and the findings regarding six categories of knowledge that teachers ought to hold to support students’ development of problem-solving proficiency. It concludes that mathematics problem-solving knowledge for teaching is a complex network of interdependent knowledge. Understanding this interdependence is important to help teachers to hold mathematical problem-solving knowledge for teaching so that it is usable in a meaningful and effective way in supporting problem-solving proficiency in their teaching. The perspective of mathematical problem-solving knowledge for teaching presented in this article can be built on to provide a framework of key knowledge mathematics teachers ought to hold to inform practice-based investigation of it and the design and investigation of learning experiences to help teachers to understand and develop the mathematics knowledge they need to teach for problem-solving proficiency.

scholarly journals The Effect of Problem Solving Course on Pre-Service Teachers’ Beliefs about Problem Solving in School Mathematics and Themselves as Problem Solvers

2018 ◽  
Vol 12 (2) ◽  
pp. 141-159
Author(s):  
Ljerka Jukić Matić
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Teaching Practice ◽  
School Mathematics ◽  
Small Scale ◽  
Heuristic Strategies ◽  
Teachers Beliefs ◽  
Before And After ◽  
Problem Solvers ◽  
Positive Effect

Problem solving in schools begins with mathematics teachers. The degree to which mathematics teachers are prepared to teach for, about and through problem solving influences on their implementation of problem solving in school. We conducted a small scale study where we examined the effect of implementation of heuristic strategies and Polya’s steps in mathematics method course. We assessed pre-service teachers’ knowledge and attitudes about them as problem solvers before and after the course. Moreover we assessed their beliefs of problem solving in school mathematics. Those beliefs were assessed in two occasions: right after the course and after finished teaching practice. Although students’ knowledge on problem solving was improved, the results of students’ beliefs show that it is important that pre-service teachers, and consequently in-service teachers, are constantly reminded on the positive effect of constructivist and inquiry-based approach on teaching mathematics.

An Investigation of African American Students' Mathematical Problem Solving

1998 ◽  
Vol 29 (2) ◽  
pp. 143-163 ◽  
Author(s):  
Carol E. Malloy ◽  
M. Gail Jones
Keyword(s):  
African American ◽  
Problem Solving ◽  
Mathematical Problem ◽  
Strategy Selection ◽  
Mathematics Students ◽  
Learning Mathematics ◽  
8Th Grade ◽  
Highly Correlated ◽  
Problem Solvers ◽  
Analytic Reasoning

In this study we examined the problem-solving characteristics, strategy selection and use, and verification actions of 24 African American 8th-grade students. Students participated in individual, talk-aloud problem-solving sessions and were interviewed about their problem solutions and attitudes about learning mathematics. Students displayed approaches attributed to African American learners in the literature, regularly using holistic rather than analytic reasoning; their display of confidence and high self-esteem did not appear to be related to success. Students' problem-solving actions matched previously reported characteristics of good mathematical problem solvers: successful use of strategies, flexibility in approach, use of verification actions, and ability to deal with irrelevant detail. Success was highly correlated with strategy selection and use and moderately correlated with verification actions.

Implementing the Standards: Uses of Technology in Prealgebra and Beginning Algebra

1990 ◽  
Vol 83 (3) ◽  
pp. 194-198
Author(s):  
M. Kathleen Heid
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Classrooms ◽  
Beginning Algebra ◽  
Grade Levels ◽  
Mathematical Connections

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Stan dards) (1989) designates four standards that apply to all students at all grade levels: mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. These and NCTM's other standards are embedded in a vision of technologically rich school mathematics classrooms in which students and teachers have constant access to appropriate computing devices and in which students use computers and calculators as tools for the investigation and exploration of problems.

Problem Solving With Discrete Mathematics

1996 ◽  
Vol 2 (7) ◽  
pp. 426-431
Author(s):  
Louis M. friedler
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Discrete Mathematics ◽  
Evaluation Standards

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1981) calls for an emphasis on problem solving at all levels and recommends introducing discrete mathematics topics. In fact, the first standard for grades K-4 states that “the study of mathematics should emphasize problem solving …” (p. 23).

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