Connecting Research to Teaching: Guidelines for Teaching Plane Isometries in Secondary School

1995 ◽  
Vol 88 (7) ◽  
pp. 591-597
Author(s):  
Adela Jaime ◽  
Angel Gutiérrez
Keyword(s):  
Secondary School ◽  
School Mathematics ◽  
Multiple Perspectives ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Key Concepts ◽  
Points Of View

Two key concepts strongly supported by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) are (1) that geometry should be taught from multiple perspectives and (2) that it is necessary to make mathematical connections. Both concepts can be implemented by appropriately selecting topics that can be presented to students from several points of view in different environments and that can also link different branches of mathematics or mathematics and other sciences.

Implementing the Curriculum and Evaluation Standards: First-Year Algebra

1991 ◽  
Vol 84 (9) ◽  
pp. 715-722
Author(s):  
Judith Kysh
Keyword(s):  
Secondary School ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
First Year ◽  
Evaluation Standards ◽  
Secondary School Mathematics

Fans of Dr. Doolittle may recall his famous fictional beast, the Push-Me-Pull-You. It had heads at both ends but never knew which way to go. Many secondary school mathematics teachers feel as though they are trying to ride one of these creatures when they examine the NCTM's Curriculum and Evaluation Standards (1989) and then turn around to consider the institutional demands of their schools and local universities.

Implementing the Standards: Building key Concepts for Calculus in Grades 7–12

1990 ◽  
Vol 83 (7) ◽  
pp. 532-540
Author(s):  
Elizabeth A. Jockusch ◽  
Patrick J. Mcloughlin
Keyword(s):  
Conceptual Understanding ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Key Concepts ◽  
Natural Extensions

The NCTM'S Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) recommends that the mathematics curriculum should include informal explorations of calculus concepts. These concepts can be developed as natural extensions of topics that students have already encountered. The approach should focus on exploring concrete problems in a way designed to build conceptual understanding of key ideas and to offer an introduction to some interesting applications.

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.

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.

Mathematical Connections: Free Rides For Kids

1990 ◽  
Vol 38 (3) ◽  
pp. 10-14
Author(s):  
Harry Bohan
Keyword(s):  
School Mathematics ◽  
Evaluation Standards ◽  
Free Ride ◽  
Mathematical Connections ◽  
First Time

If one of your goals is to teach students to think mathematically for themselves (Curriculum and Evaluation Standards for School Mathematics, 1989; An Agenda for Action 1980), you may want to take them for some “free rides.” During a fourthgrade unit on fractions I incidentally used the term “free ride” for the first time in the introduction to a lesson on multiplication of mixed numbers. The class was told they were about to be taken on what could be called a free ride. A free ride was described as a situation in which they were studying a topic that was new, but one that could be attained by using what they know.

Exhibiting Connections between Algebra and Geometry

1991 ◽  
Vol 84 (9) ◽  
pp. 703-705
Author(s):  
David R. Laing ◽  
Arthur T. White
Keyword(s):  
Secondary School ◽  
Mathematics Classroom ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Secondary School Mathematics ◽  
Mathematical Ideas

NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 81) encourages the exploration of interconnections among mathematical ideas and the development of an appreciation of “the pervasive use and power of reasoning as a part of mathematics.” This article exhibits some connections between algebra and geometry and presents deductive arguments appropriate for the secondary school mathematics classroom.

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.

Illustrating Mathematical Connections: A Geometric Proof of Euler's Theorem

1996 ◽  
Vol 89 (1) ◽  
pp. 62-65
Author(s):  
Erin K. Frye ◽  
Peter L. Glidden
Keyword(s):  
Mathematical Reasoning ◽  
School Mathematics ◽  
Geometric Proof ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Euler’S Theorem ◽  
Problem Solvers

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) calls for teachers to emphasize mathematical connections, promote mathematical reasoning, and help students become better problem solvers. If teachers are to achieve these goals, they need compelling examples, problems, and theorems that address all these elements.

Discuss with Your Colleagues: Equiareal Polygons: A Mathematical Conversation about a New Concept

2001 ◽  
Vol 94 (3) ◽  
pp. 211-216
Author(s):  
Greisy Winicki-Landman
Keyword(s):  
Professional Development ◽  
Secondary School ◽  
Middle Grades ◽  
Development Program ◽  
Mathematical Discourse ◽  
Multiple Perspectives ◽  
Evaluation Standards ◽  
School Geometry ◽  
Specific Geometry ◽  
Mathematical Definitions

This article describes an activity that is connected with mathematical definitions and that illustrates the process of gradual refinement as a way to understand and construct knowledge. It presents a gradual construction of a specific geometry concept that was the result of the interaction among the participants in a mathematical discourse (Pimm 1987). This activity took place at the end of a professional development program for teachers of secondary school geometry. During this fourteen-week program, the participants were exposed to the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and to several activities adapted from two volumes in the Addenda Series: Geometry in the Middle Grades (Geddes 1992) and Geometry from Multiple Perspectives (Coxford 1991).

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.

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