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.

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.

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.

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.

One Point of View: Using Manipulatives Successfully

1990 ◽  
Vol 38 (2) ◽  
pp. 6-7
Author(s):  
Jeane M. Joyner
Keyword(s):  
Mathematical Problem ◽  
Point Of View ◽  
School Mathematics ◽  
Major Difficulty ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Mathematical Connections ◽  
Learning To Reason ◽  
Problem Solvers

A curriculum with goals for students of valuing mathematics, being confident in their abilities, making mathematical connections, becoming mathematical problem solvers, and learning to reason and communicate mathematically is a call for classrooms in which students are actively involved in learning. It is a call for teachers to establish environments that encourage the use of manipulatives to assist students in attaining these goals proposed by the NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989). A major difficulty, however, is how to manage the materials efficiently.

Mathematical Connections: Making it Happen in Your Classroom

1993 ◽  
Vol 40 (8) ◽  
pp. 479-481
Author(s):  
Ray T. Robicheaux
Keyword(s):  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Connections

Some years ago I heard past NCTM president Shirley M. Frye admonish her audience not to be “two-by-four teachers—stuck between two covers of the book and the four walls of the classroom.” This statement seems to lie at the very heart of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), for it eems that teachers' efforts are basically aimed at changing school mathematics to more closely approximate realworld mathematics.

Connections: A Lottery, a Computer, and the Number e

1993 ◽  
Vol 86 (8) ◽  
pp. 652-655
Author(s):  
Alfinio Flores
Keyword(s):  
Mathematics Curriculum ◽  
School Mathematics ◽  
Mathematics Students ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Constant E ◽  
K 12 ◽  
Compound Interest ◽  
Probabilistic Context ◽  
Mathematical Constants

I mportant mathematical constants, like π and e. which are encountered first in specific contexts, appear throughout different branches of mathematics. Students are surprised to find rr, which they know as the ratio of the circumference to the diameter of a circle, in such a probabilistic context as Buffon's needle problem (Hirsch 1981). This article links Euler's constant e-the base of natural logarithms, which students usuaUy encounter in relation to compound-interest problems-with an experiment simulating a drawing. Establishing mathematical connections among different mathematical fields is one of the standards stressed throughout the K-12 mathematics curriculum in NCTM's Curriculum and Evaluation Standards for School Mathematics (1989).

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.

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.

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