Piano Tuners and Problem Solving

1989 ◽  
Vol 82 (4) ◽  
pp. 248-249
Author(s):  
Randolph A. Philipp
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Central Focus

The draft of the NCTM Standards document states that problem solving should be the central focus of the mathematics curriculum (Commission on Standards for School Mathematics of the NCTM 1987). Now, more than ever, problem solving is being defined as a process. Akers (1984, 34) defined problem solving as “what you do when you don't know what to do,” and Schoenfeld (1988) wrote, “Indeed, ‘figuring it out’ is what mathematics is all about” (p. 8). Mathematics teachers, left with the task of determining how problemsolving skills should be taught, have the potential to play a key role in developing and sharing problems that interest students. I will share a certain type of problem that I think might be of some interest at the secondary and college levels.

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.

Problem Solving in the Singapore School Mathematics Curriculum

2019 ◽  
pp. 141-164 ◽  
Author(s):  
Tin Lam Toh ◽  
Chun Ming Eric Chan ◽  
Eng Guan Tay ◽  
Yew Hoong Leong ◽  
Khiok Seng Quek ◽  
...  
Keyword(s):  
Problem Solving ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
School Mathematics Curriculum

Investigating Problem-Solving Perseverance Using Lesson Study

2017 ◽  
Vol 111 (3) ◽  
pp. 207-212 ◽  
Author(s):  
Kristen N. Bieda ◽  
Craig Huhn
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Lesson Study ◽  
School Mathematics ◽  
High School Mathematics ◽  
High School Mathematics Teachers

Middle and high school mathematics teachers share what they learned about supporting students by conducting a series of three lesson studies.

One point of view: Stop the Bandwagon I Want Off

1981 ◽  
Vol 28 (8) ◽  
pp. 2
Author(s):  
Jeremy Kilpatrick
Keyword(s):  
Problem Solving ◽  
Mathematics Curriculum ◽  
Point Of View ◽  
School Mathematics

The 1980s, so we are told, are to be the decade of “problem solving.” Ready or not, we are apparently destined to have problem solving as the “focus” of school mathematics for the next ten years or so. Toward this goal, the NCTM's An Agenda for Action recommends the organization of the mathematics curriculum around problem solving. How can one argue with such a sensible agenda?

The fourth operation is not fundamental—fractional numbers and problem solving

1975 ◽  
Vol 22 (1) ◽  
pp. 28-32
Author(s):  
Marilyn J. Zweng
Keyword(s):  
Elementary School ◽  
Problem Solving ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Elementary School Mathematics ◽  
Fractional Numbers ◽  
School Mathematics Curriculum

Few topics in the elementary school mathematics curriculum are a greater waste of time than division of fractional numbers. It is seldom used to solve problems, and those problems which children are taught to solve by division of fractional numbers are dealt with just as adequately by resorting to multiplication.

Exploring Nonroutine Functions Algebraically and Graphically

2011 ◽  
Vol 104 (7) ◽  
pp. 508-513
Author(s):  
Christine P. Trinter ◽  
Joe Garofalo
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Multiple Representations ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Tasks ◽  
Preservice Mathematics Teachers

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. In our classes of precalculus students and preservice mathematics teachers, we have found that nonroutine tasks encourage our students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions.

Activities: Extending Problem-Solving Skills

1985 ◽  
Vol 78 (1) ◽  
pp. 36-44
Author(s):  
Robert A. Laing
Keyword(s):  
Problem Solving ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Problem Solving Skills ◽  
Technological Society ◽  
K 12

Introduction: Recognizing that the mathematics curriculum in grades K-12 must include more than the concepts and skills of mathematics to prepare students to be productive and contributing members of a rapidly changing technological society, the Agenda for Action (NCTM 1980, 3, 4) recommends that problem solving be the focus of school mathematics in the 1980s.

An Interesting Probability Problem

1982 ◽  
Vol 75 (9) ◽  
pp. 765-768
Author(s):  
Ernest Woodward ◽  
Jim R. Ridenhour
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
Mathematics Textbook ◽  
Probability Problem

In An Agenda for Action: Recommendations for School Mathematics of the 1980s, NCTM (1980) recommends that “problem solving be the focus of school mathematics in the 1980s." Unfortunately, present day mathematics textbook problems can often be classified and categorized, and so they are not really problems at all but actually computational exercises. As a result, mathematics teachers need to be continually searching for interesting, challenging problems. Recently we found such a problem (Gardner 1961).

Soundoff: Nctm's Standards, Curriculum Reform, And High School Mathematics Teachers

1990 ◽  
Vol 83 (7) ◽  
pp. 510-512
Author(s):  
William S. Hadley
Keyword(s):  
High School ◽  
Curriculum Reform ◽  
Mathematics Teachers ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Major Obstacle ◽  
Classroom Teachers ◽  
High School Mathematics ◽  
K 12 ◽  
High School Mathematics Teachers

With the release of NCTM's curriculum standards in the spring of 1989, emphasis on mathematics-curriculum reform at all levels K-12 has been renewed. Reform is obviously long overdue, but one major obstacle stands in the way of its achievement: the classroom teachers. Given t he proper opportunities, however, teachers can become the key to success.

Welcome to Our Focus Issue on Problem Solving

2003 ◽  
Vol 96 (8) ◽  
pp. 529
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Word Problems ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
National Council ◽  
Seminal Work ◽  
Strong Case ◽  
School Mathematics Curriculum

THE CALL FOR THIS FOCUS ISSUE BEGAN BY reminding readers that in 1980, the National Council of Teachers of Mathematics made a strong case for including problem solving in the mathematics curriculum. Problem solving was not a new topic at that time—after all, George Pólya published his seminal work, How to Solve It, in 1945. However, the 1980 Agenda for Action publication marked the beginning of a period in mathematics education when the processes of problem solving received specific attention in the school mathematics curriculum. Problem solving became much more than solving word problems.

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