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.

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.

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.

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.

Developing Sense About Numbers

1993 ◽  
Vol 40 (5) ◽  
pp. 279-284 ◽  
Author(s):  
Carole Greenes ◽  
Linda Schulman ◽  
Rika Spungin
Keyword(s):  
Problem Solving ◽  
Number Sense ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Grade Levels ◽  
Mathematics Curricula

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) identifies number sense as one of the major standards of the K–4 curriculum and recommends that mathematics curricula at these grade levels develop students' number-sense skills. For grades 5 to 8, the standards document states that students' abilities to identify numerical relationships are central to their understanding of numeration concepts and to their judgment of the reasonableness of answers in problem-solving situations. But what is number sense? And how can it be developed?

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.

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.

IDEAS

1992 ◽  
Vol 40 (4) ◽  
pp. 215-225
Author(s):  
Barbara E. Moses ◽  
Linda Proudfit ◽  
William R. Speer
Keyword(s):  
Problem Solving ◽  
Evaluation Standards ◽  
Classroom Activities ◽  
Grade Levels ◽  
Parents And Children ◽  
The Creation ◽  
And Mathematics

The “IDEAS” section for this month focuses on connections between mathematics and music. including both the interpretation of music and the creation of music and musical tones. Music is very special. As a child listens to music, he or she may feel happy and want to smile or may feel a beat and want to clap or dance or may feel contemplative and want to think or write down some thoughts. The activities offer a variety of classroom happenings that tie together a student's perception of music and some important strands of mathematics. The visions of the Curriculum and Evaluation Standards (NCTM 1989), including mathematics as communication, mathematics as reasoning, and mathematics as problem solving, are an integral part of these activities. Other emphasized standards are those on estimation, measurement. statistics, fractions, and patterns. The reproducible sheets for the “IDEAS” section are designed to be used by multiple grade levels. Included are four classroom activities and an activity sheet that involves parents and children in listening together to the radio.

IDEAS

1992 ◽  
Vol 39 (6) ◽  
pp. 32-39
Author(s):  
Lisa M. Passarello ◽  
Francis (Skip) Fennell
Keyword(s):  
Problem Solving ◽  
Number Sense ◽  
Mathematics Learning ◽  
School Mathematics ◽  
Grade Levels ◽  
Or Groups ◽  
And Mathematics ◽  
Parent Child ◽  
At Home ◽  
A Performance

This month's IDEAS emphasizes connections between science and mathematics by using a performance-, or authentic-, asessment format. The month of February is close to the heart of many students and teachers. The activity sheets and the extensions offer a different approach to the valentine month. Students have the opportunity to explore applications involving their own personal valentine—the heart. The activities involve number sense, problem solving, measurement, and statistics. Additionally, this month's IDEAS involves a variety of important mathematics concepts and ideas in a performance-based setting. The activity sheets are designed to be used in multiple grade levels. The activity sheets can be completed by individual students or groups of students. The at-home-activity sheet is designed to connect school-mathematics learning with the home. Encourage students to complete this activity sheet as a parent-child experiment.

Animating Geometry with Flexigons

1994 ◽  
Vol 87 (8) ◽  
pp. 602-606
Author(s):  
Ruth McClintock
Keyword(s):  
Language Skills ◽  
School Mathematics ◽  
Professional Standards ◽  
Physical Models ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Grade Levels ◽  
Conversation Piece

Viewing mathematics as communication is the second standard listed for all grade levels in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This emphasis underscores the need for nurturing language skills that enable children to translate nonverbal awareness into words. One way to initiate discussion about mathematical concepts is to use physical models and manipulatives. Standard 4 of the Professional Standards for Teaching Mathematics (NCTM 1991) addresses the need for tools to enhance discourse. The flexigon is a simple and inexpensive conversation piece that helps students make geometric discoveries and find language to share their ideas.

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