The Cevian Problem

1998 ◽  
Vol 91 (5) ◽  
pp. 388-392
Author(s):  
Duane W. DeTemple ◽  
Marjorie Ann Fitting
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Multiple Representations ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The Real

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) challenges the teacher to shift away from memorization and set procedures. Instead, teachers should emphasize developing flexible strategies of problem solving, finding multiple representations, and making connections to other areas of mathematics and to the real world. The cevian problem presented here illustrates how to implement this shift of emphasis.

What Is in the Daily News? Problem-Solving Opportunities!

1999 ◽  
Vol 5 (7) ◽  
pp. 390-394
Author(s):  
Robyn Silbey
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Daily News ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
The Everyday ◽  
Everyday World ◽  
Real World Problems

In An Agenda for Action, the NCTM asserted that problem solving must be at the heart of school mathematics (1980). Almost ten years later, the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) stated that the development of each student's ability to solve problems is essential if he or she is to be a productive citizen. The Standards assumed that the mathematics curriculum would emphasize applications of mathematics. If mathematics is to be viewed as a practical, useful subject, students must understand that it can be applied to various real-world problems, since most mathematical ideas arise from the everyday world. Furthermore, the mathematics curriculum should include a broad range of content and an interrelation of that content.

Projects: Developing Modelers and Modeling Opportunities: The Stepping Stones Project

1997 ◽  
Vol 90 (8) ◽  
pp. 686-688
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Education ◽  
Real World ◽  
Mathematical Knowledge ◽  
School Mathematics ◽  
Stepping Stones ◽  
Evaluation Standards ◽  
The Real ◽  
World Modeling

Mathematical modeling is an emerging theme in mathematics education. In addition to giving students a knowledge of the applications of mathematics and a process for applying mathematics in the “real” world, modeling offers teachers an excellent vehicle for introducing and developing students' mathematical knowledge. For these reasons, modeling occupies a prominent place in the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

A Popcorn Project for All Students

1997 ◽  
Vol 90 (3) ◽  
pp. 194-200
Author(s):  
Lydotta M. Taylor ◽  
Joann L. King
Keyword(s):  
Problem Solving ◽  
Cooperative Learning ◽  
Real World ◽  
Data Gathering ◽  
School Mathematics ◽  
Combine Data ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Reasoning Problem

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) encourages teachers to include activities that help students “construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations” (p. 167) and “express mathematical ideas orally and in writing” (p. 140). The following activities combine data gathering and analysis with cooperative learning, mathematical connections, reasoning, problem solving, and communication.

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.

News from the Net: Aunty Math's Challenges for Kids

1999 ◽  
Vol 5 (7) ◽  
pp. 420
Author(s):  
Beth Lazerick
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Web Site ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The Real ◽  
Problem Solving Strategies ◽  
The Web

Aunty Math, for students and their teachers, is a terrific site that emphasizes problem-solving strategies listed in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The site is designed for children; the layout is easy to use, and the graphics are inviting. Aunty Math's problems, called “challenges,” are set in stories about Aunty Math's nephews and niece. The real Aunty Math behind the Web site is an experienced, awardwinning teacher who is very involved in mathematics education.

The Patchwork Quilt: A Context for Problem Solving

1992 ◽  
Vol 40 (4) ◽  
pp. 199-203
Author(s):  
Deborah A. Carey
Keyword(s):  
Children's Literature ◽  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
Children’S Literature ◽  
School Mathematics ◽  
Evaluation Standards ◽  
New Concepts ◽  
Patchwork Quilt

A mathematics curriculum that focuses on problem solving needs relevant, challenging problems for students to solve. The most engaging problems initially emerge from real-world contexts and offer opportunities for extensions that are limited only by the problem-solving abilities of the students. As suggested by the NCfM's Curriculum and Evaluation Standards for School Mathematics (1989), students learn new concepts and skills through problem-solving experiences. Therefore, selecting appropriate contexts that offer opportunities for problem solving and from which students can generate problems is critical. This article discusses how one piece of children's Literature be used to develop appropriate problem solving tasks.

The Football Coach's Dilemma: “Should We Go for 1 or 2 Points First?”

1995 ◽  
Vol 88 (9) ◽  
pp. 731-733
Author(s):  
Vincent P. Schielack
Keyword(s):  
Problem Solving ◽  
Mathematical Models ◽  
Real World ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Real World Problem ◽  
Mathematics Educators ◽  
Mathematical Techniques

Situations arise in many everyday endeavors that can be analyzed using various mathematical techniques. These situations give mathematics educators many opportunities to connect real-world problem-solving situations with appropriate mathematical models, as recommended in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The mathematics topic here involves applying elementary concepts of probability to a hotly debated question arising in football. h will be assumed throughout that a team values a win significantly more than a tie and also values a tie considerably more than a loss.

Links to Literature: May 2001

2001 ◽  
Vol 7 (9) ◽  
pp. 538-541
Author(s):  
Jorie Borden ◽  
Elsa Geskus
Keyword(s):  
Children's Literature ◽  
Problem Solving ◽  
Real World ◽  
Children’S Literature ◽  
School Mathematics ◽  
Teaching Skills ◽  
The Real ◽  
New Knowledge ◽  
Principles And Standards

The phenomenal resurgence of children's literature in the marketplace has allowed teachers to help their students construct new knowledge by fostering the love of literature while teaching skills and knowledge. Principles and Standards for School Mathematics (NCTM 2000) recommends connecting mathematics with the real-world experiences of children. The authors chose Cook-a-Doodle-Doo! (Stevens and Crummel 1999) to provide students with opportunities for problem solving, estimating, predictive reading, and enjoyable eating.

Building Mathematical Models of Simple Harmonic and Damped Motion

1995 ◽  
Vol 88 (1) ◽  
pp. 18-22
Author(s):  
Thomas Edwards
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Real World ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The Real ◽  
Mathematical Representations ◽  
Real World Problems

Given the recent public mania over bungee jumping, stimulating students' interest in a model of that situation should be an easy “leap.” Students should investigate the connections among various mathematical representations and their relationships to applications in the real world, asserts the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Mathematical modeling of real-world problems can make such connections more natural for students, the standards document further indicates. Moreover, explorations of periodic real-world phenomena by all students, as well as the modeling of such phenomena by college-intending students, is called for by Standard 9: Trigonometry.

Implementing the Curriculum and Evaluation Standards: What Will Implementation Take?

1991 ◽  
Vol 84 (6) ◽  
pp. 442-478
Author(s):  
Ruth E. Parker
Keyword(s):  
Real World ◽  
School Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
The Real ◽  
Short Answer ◽  
Mathematics Educators ◽  
Mathematics Student ◽  
History Of ◽  
Culture Of School

A long history of traditions has grown up around what is meant by a good mathematics teacher and a good mathematics student. As many educators recognize, however, those traditions have little in common with mathematics in the world of the 1990s. Mathematics as it is used in the real world is not about the memorization of theorems or rote procedures for getting right answers. It is not about performing well on multiplechoice or short-answer tests under time constraints. “At the heart of mathematics is the search for sense and meaning, order and predictability. Mathematics is the study of patterns and relationships” (Richardson and Salkeld, in press). The challenge for mathematics educators is to align the culture of school mathematics with the culture of mathematics in the real world. With its publication of the Curriculum and Evaluation S tandards for School Mathematics (1989), the National Council of Teachers of Mathematics (NCTM) established the direction for such mathematics reform.

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