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.

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.

Understanding Students' Problem-Solving Knowledge through Their Writing

2007 ◽  
Vol 13 (2) ◽  
pp. 102-109
Author(s):  
Diana F. Steele
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Writing In Mathematics ◽  
Principles And Standards

The Curriculum and Evaluation Standards for School Mathematics, published in 1989 by NCTM, placed an emphasis on the importance of communication for learning and doing mathematics. Writing is one way to achieve this valuable communication in the classroom. In 2000, Principles and Standards for School Mathematics emphasized writing as being an important aspect of communication: “Writing in mathematics can also help students consolidate their thinking because it requires them to reflect on their work and clarify their thoughts about the ideas developed in the lesson' (NCTM 2000, p. 61). Several studies have also shown ways that writing can be an effective tool for improving students' learning of mathematics (Bell and Bell 1985; Pugalee 2001; Steele 2005). Pugalee (2001) found in his work with students that writing could potentially help students increase their problemsolving ability in mathematics.

Principles and Standards: Developing Computational Fluency with Whole Numbers

2000 ◽  
Vol 7 (3) ◽  
pp. 154-158 ◽  
Author(s):  
Susan Jo Russell
Keyword(s):  
Mathematical Reasoning ◽  
Number System ◽  
Basic Number ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Computational Fluency ◽  
Mathematics Program ◽  
Principles And Standards ◽  
Learning To Reason ◽  
Fact Learning

Principles and Standards for School Mathematics (NCTM 2000) emphasizes the goal of computational fluency for all students. It articulates expectations regarding fluency with basic number combinations and the importance of computational facility grounded in understanding (see a summary of key messages regarding computation in Principles and Standards in the sidebar on page 156). Building on the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and benefiting from a decade of research and practice, Principles and Standards articulates the need for students to develop procedural competence within a school mathematics program that emphasizes mathematical reasoning and problem solving. In fact, learning about whole-number computation is a key context for learning to reason about the baseten number system and the operations of addition, subtraction, multiplication, and division.

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.

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.

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