The Importance of Informal Language in Representing Mathematical Ideas

1995 ◽  
Vol 1 (6) ◽  
pp. 332-335
Author(s):  
Kothleen Cramer ◽  
Lee Karnowski
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematical Connections

Mathematics as Problem Solving, Mathematics as Communication. Mathematics as Reasoning, and Mathematical Connections—these four Standards, which open the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), can be considered the pedagogical standards.

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.

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.

Implementing the Standards: Uses of Technology in Prealgebra and Beginning Algebra

1990 ◽  
Vol 83 (3) ◽  
pp. 194-198
Author(s):  
M. Kathleen Heid
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Classrooms ◽  
Beginning Algebra ◽  
Grade Levels ◽  
Mathematical Connections

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Stan dards) (1989) designates four standards that apply to all students at all grade levels: mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. These and NCTM's other standards are embedded in a vision of technologically rich school mathematics classrooms in which students and teachers have constant access to appropriate computing devices and in which students use computers and calculators as tools for the investigation and exploration of 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.

Implementing The Standards: Students' Microcomputer-Aided Exploration in Geometry

1990 ◽  
Vol 83 (8) ◽  
pp. 628-635
Author(s):  
Daniel Chazan
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematical Structure ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Mathematical Connections ◽  
Teachers And Students ◽  
K 12

Four important themes presented in the K–12 Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989) are mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. The high school component also stresses mathematical structure. Furthermore, the Standards calls for new roles for teachers and students and suggests that microcomputer technology can help support teachers and students in taking on these new roles.

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.

Pixy Stix Segments and the Midpoint Connection

1993 ◽  
Vol 86 (8) ◽  
pp. 668-675
Author(s):  
Ruth McClintock
Keyword(s):  
High School ◽  
Problem Solving ◽  
Cooperative Learning ◽  
Communication Skills ◽  
School Mathematics ◽  
Peter Pan ◽  
Evaluation Standards ◽  
High School Geometry ◽  
Mathematical Connections ◽  
School Geometry

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) offers a vision of mathematically empowered students embarking on exciting flights of discovery. This vision challenges teachers to look for ways to incorporate problem solving, cooperative learning, mathematical connections, reasoning, communication skills, and proofs into lesson plans. The Pixy Stix activities described in this article are not quite as magical as Peter Pan and Tinkerbell's prescription of sprinkling pixie dust over children who want to fly, but they do embody all the attributes mentioned above and may enable your high school geometry students to take off in some surprising directions.

Beyond the Golden Ratio: A Calculator-Based Investigation

2001 ◽  
Vol 94 (2) ◽  
pp. 138-144
Author(s):  
Peter L. Glidden
Keyword(s):  
Problem Solving ◽  
Mathematical Reasoning ◽  
Golden Ratio ◽  
School Mathematics ◽  
Opportunities To Learn ◽  
Mathematical Communication ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Principles And Standards ◽  
Classroom Use

NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) calls for increased emphasis on problem solving, mathematical reasoning, mathematical communication, and mathematical connections. This call is reaffirmed in Principles and Standards for School Mathematics (NCTM 2000). A preferred way of achieving these goals is by having students perform mathematical investigations in which they explore mathematics, search for patterns, and use technology when appropriate. In short, students should be given opportunities to learn mathematics by doing mathematics. Of course, if students are to learn mathematics through investigations, teachers must have a ready supply of such investigations available for classroom use.

Photographs and Committees: Activities That Help Students Discover Permutations and Combinations

2000 ◽  
Vol 93 (2) ◽  
pp. 93-96
Author(s):  
Jennifer Earles Szydlik
Keyword(s):  
Mathematics Curriculum ◽  
Mathematical Reasoning ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Problem Situations ◽  
Guiding Principles ◽  
Support Students

The vision of Mathematics Curriculum promoted by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) is based on two guiding principles: “First, activities should grow out of problem situations; and second, learning occurs through active as well as passive involvement with mathematics” (1989, 9). In particular, curriculum should be designed to support students in constructing their own mathematical ideas and connections. Students should solve problems, communicate ideas both orally and in writing, engage in mathematical reasoning, and search for mathematical connections.

Connecting Process Problem Solving to Children's Litcrature

1997 ◽  
Vol 3 (7) ◽  
pp. 398-406
Author(s):  
Annette Ricks Leitze
Keyword(s):  
Children's Literature ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Children’S Literature ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Connections

Since the publication of the Curriculum and evaluation Standards for School Mathematics (NCTM 1989), many mathematics teachers and educators have become especially interested in making mathematical connections, such as that found between mathematics and children's literature.

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