Illustrating Mathematical Connections: Two Proofs That Only Five Regular Polyhedra Exist

1993 ◽  
Vol 86 (8) ◽  
pp. 657-661
Author(s):  
Peter L. Glidden ◽  
Erin K. Fry
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Mathematics Curriculum ◽  
Three Dimensional ◽  
Discrete Mathematics ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Regular Polyhedra ◽  
Real World Problems

The reforms proposed in the NCTM's Curriculum and Evaluation Standards (1989) call for specific changes in the grades 9-12 mathematics curriculum, as well as for general themes that should be emphasized throughout the curriculum. In particular, the standards document calls for including topics from discrete mathematics and three-dimensional geometry, and it calls for increased emphasis on paragraph-style proofs. Overall, these and other topics should be taught with the ultimate goals of illustrating mathematical connections and constructing mathematical models to solve real-world problems.

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.

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.

scholarly journals New Challenges Arising in Engineering Problems with Fractional and Integer Order

2021 ◽  
Vol 5 (2) ◽  
pp. 35
Author(s):  
Haci Mehmet Baskonus ◽  
Luis Manuel Sánchez Ruiz ◽  
Armando Ciancio
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Integer Order ◽  
Engineering Problems ◽  
New Challenges ◽  
Real World Problems

Mathematical models have been frequently studied in recent decades in order to obtain the deeper properties of real-world problems [...]

Using Logic Activities to Produce a Class Constitution

1992 ◽  
Vol 40 (3) ◽  
pp. 174-176
Author(s):  
Susan Strand Monchamp
Keyword(s):  
Real World ◽  
Evaluation Standards ◽  
The Real ◽  
Mathematical Connections ◽  
Relationship Of ◽  
The Relationship

One of my major goals in mathematics is to have my student understand the relationship of mathematics to the real world. To this end, we begin the year in my first-gradeclass by doing a series of logic activities that lead to the production of our class constitution. The activities reflect three of the NCTM' curriculum and evaluation standards—Mathematics a Communication, Mathematics as Reasoning, and Mathematical Connections (NCTM 1989).

Analyzing Data from the Olympic Games for Trends and Inferences

1996 ◽  
Vol 89 (5) ◽  
pp. 370-372
Author(s):  
Richard T. Edgerton
Keyword(s):  
Real World ◽  
Olympic Games ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Problem Situations ◽  
Real World Problems ◽  
The Olympic Games

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) emphasizes classroom mathematics that engages students in meaningful activities through which they construct their own understanding of important concepts. Students' investigations are derived from problem situations that arise from real-world contexts. The Olympic Games furnish ample data for students to connect meaningful mathematics with real-world problems.

Exploring Estimation through Children's Literature

1994 ◽  
Vol 41 (8) ◽  
pp. 436-441
Author(s):  
David J. Whitin
Keyword(s):  
Children's Literature ◽  
Real World ◽  
Mathematics Curriculum ◽  
Children’S Literature ◽  
Evaluation Standards ◽  
Mental Computation ◽  
Real World Applications

Estimation is a crucial mathematical strategy that can be woven throughout the entire mathematics curriculum. The strategy can certainly foster the development of many of the goals advocated by the NCTM's curriculum and evaluation standards (1989). Since approximately 80 percent of real-world applications of mathematics involve estimation or mental computation, the goal of becoming an “informed electorate” requires us to use and analyze various estimation strategies.

Sharing Teaching Ideas: A Mathematical Investigation of Quality Control

1995 ◽  
Vol 88 (3) ◽  
pp. 200-202
Author(s):  
Richard T. Edgerton
Keyword(s):  
Quality Control ◽  
Real World ◽  
School Mathematics ◽  
Curriculum Standards ◽  
Evaluation Standards ◽  
Mathematical Investigation ◽  
Teaching Ideas ◽  
Real World Problems

One way to apply the principles of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) is to use real-world problems. The curriculum standards are enacted as students develop “mathematical power” while they communicate, reason, and make connections within and outside mathematics.

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.

Our Diets May Be Killing Us

1995 ◽  
Vol 1 (5) ◽  
pp. 376-382
Author(s):  
Brenda K. J. Shannon
Keyword(s):  
Real World ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Knowledge And Skills ◽  
Everyday Lives ◽  
Grade Levels ◽  
Real World Applications ◽  
School Day ◽  
Class Period

A push seems to be on for more real-world applications in the mathematics curriculum at all grade levels. Recommendations from such sources as the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and the National Research Council's Everybody Counts (1989) advocate making mathematics more than just a subject taught one class period of each school day. The time has come to bring mathematics out of the classroom and show the students that the knowledge and skills from mathematics can be beneficial in their everyday lives. But how do we, as educators, actually accomplish this goal?

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