The Wonder and Creativity in “Looking Back” at Problem Solutions

1988 ◽  
Vol 81 (6) ◽  
pp. 429-434
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Position Paper ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Competence ◽  
Mathematics Educators ◽  
Looking Back

Mathematics educators have always viewed problem solving as a preferential objective of mathematics instruction. It was not, however, until the National Council of Teachers of Mathematics published its position paper An Agenda for Action: Recommendations for School Mathematics of the 1980s that problem solving truly came of age. As its very first recommendation, the Council (1980) directed that “problem solving be the focus of school mathematics in the 1980s” and proclaimed that “performance in problem solving will measure the effectiveness of our personal and national possession of mathematical competence.”

Integrating Manipulatives and Computers in Problem-Solving Experiences

1990 ◽  
Vol 38 (2) ◽  
pp. 8-10
Author(s):  
Sue Brown
Keyword(s):  
Problem Solving ◽  
Group Work ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Good Mathematics Instruction ◽  
K 12

In 1980, the National Council of Teachers of Mathematics stated that “problem solving must be the focus of school mathematics.” In 1989 the Council reaffirmed that belief with the Curriculum and Evaluation Standards for School Mathematics (Standards). Standard 1 for grades K–12 is “Mathematics as Problem Solving.” The Standards also asserts that “a computer should be available in every classroom for demonstration purposes, and every student should have access to a computer for individual and group work.” Also according to the Standards, “manipulative materials are necessary for good mathematics instruction.” In a typical classroom, problem solving may be taught, manipulative materials may be used, or students may be working at a computer. These functions, however, are usually completed as disjoint activities. Integrating these activities is possible, and this article illustrates how it can be done.

Guiding Young Children in Successful Problem Solving

1982 ◽  
Vol 29 (5) ◽  
pp. 15-17
Author(s):  
Kil S. Lee
Keyword(s):  
Problem Solving ◽  
Young Children ◽  
Conference Report ◽  
School Mathematics ◽  
National Council ◽  
Mathematical Skills ◽  
The Past ◽  
Mathematics Educators ◽  
Mathematics Curricula

In the past twenty years, problem solving has received much attention from mathematics educators. Inclusion of imaginative problems in school mathematics curricula was recommended in the 1963 Cambridge Conference report. Problem solving was the first of the ten basic mathematical skills identified by the National Council of Supervisors of Mathematics in 1976 and the position of the NCSM was endorsed by the National Council of Teachers of Mathematics in 1978. “That problem solving be the focus of school mathematics in the 1980s” is the first of eight recommendations expressed in An Agenda for Action: Recommendations for School Mathematics of the 1980s published by the NCTM.

Critiques: Seeking Meaning in Mathematics Instruction: A Response to Gagné

1983 ◽  
Vol 14 (3) ◽  
pp. 210-213
Author(s):  
Leslie P. Steffe ◽  
Rick N. Blake
Keyword(s):  
Problem Solving ◽  
Mathematics Instruction ◽  
Mathematics Learning ◽  
Mathematics Educators ◽  
Teaching Of Mathematics ◽  
Mental Operations

Mathematics educators have for some time been interested in psychological bases for the teaching of mathematics in the schools (Buswell, 1951). They have naturally turned to cognitive theorists in their quest to understand such terms as knowledge, meaning, concepts, mental operations, problem solving, and insight. Gagné's (1983) paper is bur one example of this historical collaboration. His purpose is to “relate what is known about learning, … from the kind of theory [he has] described, to the problem of improving mathematics learning” (p. 10).

1089: An Example of Generating Problems

1984 ◽  
Vol 77 (1) ◽  
pp. 14-19
Author(s):  
Rick N. Blake
Keyword(s):  
Problem Solving ◽  
Mathematics Teacher ◽  
Position Paper ◽  
National Council ◽  
Joint Position ◽  
Mathematical Skills ◽  
Principal Reason

Emphasis on problem solving in mathematics has gained considerable attention in the last few years. A joint position paper on basic mathematical skills by the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics, in the February 1978 Mathematics Teacher, stated that “learning to solve problems is the principal reason for studying mathematics.”

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.

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.

Exploring Patterns, Relations, and Functions

1992 ◽  
Vol 39 (9) ◽  
pp. 19-21
Author(s):  
Charles P. Geer
Keyword(s):  
Problem Solving ◽  
Cognitive Skills ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
First Century ◽  
Evaluation Standards ◽  
Learning Mathematics ◽  
New Knowledge ◽  
Paper And Pencil ◽  
Twenty First Century

As teachers use NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) to develop programs that will prepare students for the twenty-first century, some are discovering that mathematics instruction is going to be very different in the 1990s. Many previous programs placed a heavy emphasis on paper-and-pencil proficiency with computational skills and learning mathematics by memorizing rules. Because of advances in technology, new knowledge about how learning occurs, and the changing needs of business and industry, future programs will focus on mathematics with meaning, problem solving, and higher-level cognitive skills.

Investigating the Mathematical Process with Nonlinear Asymptotes

2008 ◽  
Vol 101 (8) ◽  
pp. 574-580
Author(s):  
Michael J. Bossé ◽  
Karen A. DeUrquidi ◽  
David L. Edwards ◽  
N. R. Nandakumar
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Multiple Representations ◽  
School Mathematics ◽  
School Students ◽  
Mathematical Ideas ◽  
Mathematics Educators ◽  
Algebraic Concept ◽  
Mathematical Process

Principles and Standards for School Mathematics (NCTM 2000) emphasizes having students experience mathematics as mathematicians do and demonstrates that the Process Standards—Problem Solving, Reasoning and Proof, Communication, Connections, and Representation—are not simply means through which mathematics is learned and taught; they are also the manner through which mathematics is done. This article presents an abbreviated version of the musings and methodologies experienced by mathematics educators through a genuine problemsolving investigation. This account will investigate dimensions of an algebraic concept known to many high school students and show how these lead to an intuitive understanding of the limit in calculus. Readers will experience and come to a deeper understanding of the Process Standards as well as experience the necessity of using multiple representations to make and solve mathematical conjectures. To accomplish these multidimensional goals, the authors describe a chronological development of mathematical ideas among themselves and invite readers to reason along with them in their actual investigations.

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?

Power On!: Learning Statistics with Technology

1994 ◽  
Vol 1 (2) ◽  
pp. 130-136
Author(s):  
Gary Kader ◽  
Mike Perry
Keyword(s):  
Problem Solving ◽  
Mathematics Curriculum ◽  
Real Data ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Problem Solving Process ◽  
K 12

In its Curriculum and Evaluation Standards for School Mathematics (1989), the National Council of Teachers of Mathematics recommends that the K-12 mathematics curriculum be broadened and designates statistics as an area deserving increased attention. The standards document promotes the concept that statistics be learned through the study of real problems with real data collected by the students. Rather than focus on developing formulas from which answers are simply computed, teachers should present statistics in a coherent fashion and develop the topic as a whole problem-solving process.

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