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.

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.

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.

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.

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.

Spotlight on the Principles/Standards: Building Mathematically Powerful Students through Connections

2002 ◽  
Vol 7 (9) ◽  
pp. 484-488
Author(s):  
Christine Thomas ◽  
Carmelita Santiago
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematical Tasks ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Natural Inclination ◽  
Points Of View ◽  
Principles And Standards

Connections in mathematics can be implemented in ways that create excitement in the classroom, develop in students a love for doing mathematics, and foster students' natural inclination for pursuing mathematical tasks. According to the Curriculum and Evaluation Standards for School Mathematics, “If students are to become mathematically powerful, they must be flexible enough to approach situations in a variety of ways and recognize the relationships among different points of view” (NCTM 1989, p. 84). Principles and Standards for School Mathematics (NCTM 2000) further asserts that students develop a deeper and more lasting understanding of mathematics when they are able to connect mathematical ideas. The 1989 and 2000 Standards clearly delineate the power and importance of connections in the mathematics curriculum. This article examines and compares curricular recommendations for connections in the two documents.

Implementing the Standards: Developing Communication Skills in Mathematics for Students with Limited English Proficiency

1991 ◽  
Vol 84 (3) ◽  
pp. 186-189
Author(s):  
Gilbert J. Cuevas
Keyword(s):  
Problem Solving ◽  
Communication Skills ◽  
Limited English Proficiency ◽  
English Proficiency ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Listening And Speaking

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) emphasizes the need to address communication skills. These skills, including reading, writing, listening, and speaking, enhance mathematical understanding and problem-solving ability. Moreover, to communicate effectively, one must be able to interpret and analyze mathematical ideas. The curriculum and evaluation standards recommend that opportunities be afforded students to “use language to communicate their mathematical ideas” (NCTM 1989, 78). Although these recommendations are valuable, teachers may find them difficult to implement with students who are not proficient in English.

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.

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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