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.

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.

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.

Technology Tips: A Mathematical Look at a Free Throw Using Technology

1996 ◽  
Vol 89 (9) ◽  
pp. 774-779
Author(s):  
Charles Vonder Embse ◽  
Arne Engebretsen
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Free Throw ◽  
Problem Situations ◽  
Real World Problem

Technology can be used to promote students' understanding of mathematical concepts and problem-solving techniques. Its use also permits students' mathematical explorations prior to their formal development in the mathematics curriculum and in ways that can capture students' curiosity, imagination, and interest. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends that “[i]n grades 9–12, the mathematics curriculum should include the refinement and extension of methods of mathematical problem solving so that all students can … apply the process of mathematical modeling to real-world problem situations” (p. 137). Students empowered with technology have the opportunity to model real-world phenomena and visualize relationships found in the model while gaining ownership in the learning process.

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 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.

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.

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