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.

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.

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.

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.”

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.

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.

Mathematical Modeling and the Presidential Election

1992 ◽  
Vol 85 (7) ◽  
pp. 520-521
Author(s):  
Joseph C. Witkowski
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Secondary Schools ◽  
Presidential Election ◽  
Presidential Elections ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Modeling Problem ◽  
Mathematical Sciences ◽  
K 12

In recent years, interest in problem solving and mathematical modeling has increased. In 1975, the Conference Board of the Mathematical Sciences issued its Overview and Analysis of School Mathematics K-12, which recommended the incorporation of mathematical applications and modeling into secondary schools. More recently the Curriculum and Evaluation Standards for School Mathematics (1989) formulated by the NCTM stressed the importance of mathematical modeling as a facet of problem solving. The purpose of this article is to look at an interesting mathematical-modeling problem regarding presidential elections.

NCTM's Standards for School Mathematics, K – 12

1988 ◽  
Vol 81 (5) ◽  
pp. 348-351
Author(s):  
Charles S. Thompson ◽  
Edward C. Rathmell
Keyword(s):  
Mathematics Education ◽  
School Districts ◽  
Mathematics Learning ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
State And Local ◽  
K 12 ◽  
National Tests ◽  
Local Levels

The National Council of Teachers of Mathematics is in the process of generating a set of Curriculum and Evaluation Standards for School Mathematics (Standards) (Commission on Standards of the NCTM 1987). NCTM has committed considerable resources to this project, anticipating that the Standards will have a pervasive effect on mathematics education during the next five to ten years. The expectation is that the Standards will influence curriculum writing at the state and local levels and that the resulting curricular changes will influence the content of textbooks adopted by states and school districts. Furthermore, the newly written curricula, together with the new Standards for the evaluation of mathematics learning, should influence the content and emphasis of local, state, and national tests.

Soundoff: Are Teachers Prepared to Implement The Standards?

1990 ◽  
Vol 83 (4) ◽  
pp. 248-251
Author(s):  
Michael B. Fiske
Keyword(s):  
Mathematics Education ◽  
National Research Council ◽  
School Mathematics ◽  
National Commission ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Nation At Risk ◽  
Excellence In Education ◽  
Societal Expectations

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) presents a view of precollege mathematics t hat stresses the development of mathematical power. Framed within the context of students' needs, societal expectations, and engaging teaching, the Standards proposes to define the mathematical content of school mathematics. It responds to the crisis in mathematics education described in Everybody Counts: A Report to the Nation on the Future of Mathematics Education (National Research Council 1989), A Nation at Risk (National Commission on Excellence in Education 1983), and Educating Americans for the 21st Century (National Science Board Commission on Precollege Education in Mathematics, Science, and Technology 1983). Although representing a consensus of mathematics educators, the Standards does not present a research basis for its recommendations (NCTM 1988) and thus at times stands at odds with the descriptive accounts of current mathematics teaching practices found in The Underachieving Curriculum (McKnight et al. 1987) and The Mathematics Report Card (Dossey, Mullis, Lindquist, and Chambers 1988). This article examines implications for teaching of explicit and implicit assumptions in the Standards and compares them with other views in the literature.

Problem Solving: Dealing With Data in The Elementary School

1995 ◽  
Vol 1 (5) ◽  
pp. 256-260 ◽  
Author(s):  
Harry Bohan ◽  
Beverly Irby ◽  
Dolly Vogel
Keyword(s):  
Elementary School ◽  
Problem Solving ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards

Standard 11 of the K-4 recommendations of the National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics and Standard 10 of the grades 5-8 portion of this document suggest that students be given opportunities to—

Informing Learning Through the Clinical Interview

1991 ◽  
Vol 38 (6) ◽  
pp. 44-46
Author(s):  
Madeleine J. Long ◽  
Meir Ben-Hur
Keyword(s):  
Student Outcomes ◽  
Clinical Interview ◽  
School Mathematics ◽  
Assessment Tools ◽  
Teaching Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Paper And Pencil ◽  
Primary Assessment

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Srandards for Teaching Mathematics (1989) endorse the view that assessment should be made an integral part of teaching. Although many of the student outcomes described in the Srandards cannot properly be assessed using paper-and-pencil tests, such tests remain the primary assessment tools in today's classroom.

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