Practical Geometry Problems: The Case of the Ritzville Pyramids

1993 ◽  
Vol 86 (3) ◽  
pp. 198-200
Author(s):  
Donald Nowlin
Keyword(s):  
Real World ◽  
Washington State ◽  
Traditional Curriculum ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Geometry Problem ◽  
Eastern Washington ◽  
Practical Geometry ◽  
The Relationship ◽  
Real World Problems

The wheat-producing country of eastern Washington state furnishes a practical example of an applied geometry problem requiring only a knowledge of the relationship between the parts of a circle and the parts of a right triangle. The solution of this problem is related to several topics in the Curriculum and Evaluation Standards (NCTM 1989) that do not appear in a traditional curriculum. One of the main features of this example is that it shows that memorized formulas from textbooks must sometimes be modified to fit real-world problems. The solution of the problem requires the students to make some desirable connections among mathematical concepts that may otherwise be perceived as unrelated.

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).

Integrating Spreadsheets into the Mathematics Classroom

1988 ◽  
Vol 81 (8) ◽  
pp. 615-622
Author(s):  
Janet L. McDonald
Keyword(s):  
Real World ◽  
Computer Literacy ◽  
Mathematics Classroom ◽  
Mathematical Concepts ◽  
Business Courses ◽  
Real World Problems

Spreadsheets have become an integral part of computer literacy and business courses, allowing students to see the power of such utility software and use it to solve problems. But, the spreadsheet can also be an extremely effective tool in the mathematics classroom. There the spreadsheet can be used to help solve many real-world problems and, at the same time, promote students' understanding of important mathematical concepts and principles.

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.

Maximizing Area and Perimeter Problems

2021 ◽  
Vol 114 (1) ◽  
pp. 41-46
Author(s):  
Samuel L. Eskelson ◽  
Brian E. Townsend ◽  
Elizabeth K. Hughes
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Mathematical Concepts ◽  
Area And Perimeter ◽  
Technological Tool ◽  
Real World Problems

Use this context and technological tool to assist students in embracing the mathematical and pragmatic nuances of “real-world” problems so they become fertile opportunities to explore mathematical concepts, express reasoning, and engage in mathematical modeling.

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.

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.

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.

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.

Mathematical Explorations: A Fair Game? The Case of Rock, Paper, Scissors

2008 ◽  
Vol 14 (5) ◽  
pp. 311-319
Author(s):  
Cheryl Nelson ◽  
Nicole Williams
Keyword(s):  
Real World ◽  
Middle Grades ◽  
Theoretical Probability ◽  
Classroom Activities ◽  
Fair Game ◽  
The Relationship ◽  
Real World Problems

Rock, paper, scissors is a popular game. Middle-grades students often use it to choose the person who will go first in some activity or larger game. This game also provides a rich context to explore the relationship between experimental and theoretical probability through the concept of a fair game. Research finds that students learn best from classroom activities that connect to real-world problems (NCTM 2000; Sutton and Krueger 2002).

Prospective Elementary Teachers' Knowledge of Division

1993 ◽  
Vol 24 (3) ◽  
pp. 233-253 ◽  
Author(s):  
Martin A. Simon
Keyword(s):  
Elementary Teachers ◽  
Prospective Teachers ◽  
Real World ◽  
Conceptual Knowledge ◽  
Prospective Elementary Teachers ◽  
Research Results ◽  
Individual Interviews ◽  
The Relationship ◽  
Mathematical Preparation ◽  
Real World Problems

Prospective teachers' knowledge of division was investigated through an open-response written instrument and through individual interviews. Problems were designed to focus on two aspects of understanding division: connectedness within and between procedural and conceptual knowledge and knowledge of units. Results indicated that the prospective teachers' conceptual knowledge was weak in a number of areas including the conceptual underpinnings of familiar algorithms, the relationship between partitive and quotitive division, the relationship between symbolic division and real-world problems, and identification of the units of quantities encountered in division computations. The research also characterized aspects of individual conceptual differences. The research results suggest conceptual areas of emphasis for the mathematical preparation of elementary teachers.

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