Teacher to Teacher: Building A Teenage Dance Club

1998 ◽  
Vol 4 (1) ◽  
pp. 26-30
Author(s):  
Mary Ann Christina
Keyword(s):  
Teaching And Learning ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Technological Society ◽  
Conscious Decision ◽  
Paper And Pencil

As the nctm's curriculum and evaluation Standards for School Mathematics (1989) became more well known and I attended more workshops. I made a conscious decision to make algebra more closely tied to the outside world and show it importance in today's technological society. I started using the graphing calculator to eliminate some obsolete paper-and-pencil kill and started using relevant project that became an integral part of my course. I became involved in, and committed to, the philosophy of “Opening the Gate,” which is a series of activities developed in Florida to supplement the curriculum and to reform the teaching and learning of algebra. The idea is to make algebra more accessible, more dynamic, and more relevant to today's and tomorrow's society.

Applications: Using Technology to Understand the Jury Decision-making Process

1994 ◽  
Vol 87 (2) ◽  
pp. 110-114
Author(s):  
Kenneth P. Goldberg
Keyword(s):  
Teaching And Learning ◽  
Potential Effect ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Decision Making Process ◽  
Jury Decision Making ◽  
Evaluation Standards ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Jury Decision

Two of the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) are to use technology to enhance teaching and learning mathematics and to relate school mathematics to the world in which the students Jive through developing and interpreting mathematical models. This article demonstrates how computer or graphing-calculator technology can be used to help students develop and interpret three increasingly realistic models of jwy behavior and explore the potential effect of such decisions as changing jury size. The only mathematics required is an understanding of simple binomial probabilities and the use of sigma, or summation, notation

Informing Learning Through the Clinical Interview

1991 ◽  
Vol 38 (6) ◽  
pp. 44-46
Author(s):  
Madeleine J. Long ◽  
Meir Ben-Hur
Keyword(s):  
Student Outcomes ◽  
Clinical Interview ◽  
School Mathematics ◽  
Assessment Tools ◽  
Teaching Mathematics ◽  
National Council ◽  
Evaluation Standards ◽  
Paper And Pencil ◽  
Primary Assessment

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Srandards for Teaching Mathematics (1989) endorse the view that assessment should be made an integral part of teaching. Although many of the student outcomes described in the Srandards cannot properly be assessed using paper-and-pencil tests, such tests remain the primary assessment tools in today's classroom.

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.

Technology Tips: Exploring Hill Ciphers with Graphing Calculators

1998 ◽  
Vol 91 (3) ◽  
pp. 240-244
Author(s):  
Dennis St. John
Keyword(s):  
Relative Frequency ◽  
English Language ◽  
Matrix Multiplication ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Modular Arithmetic ◽  
Evaluation Standards ◽  
Hill Cipher ◽  
The Matrix ◽  
Coded Messages

Throughout history, coded messages have been used for various reasons. Today's students are fascinated by the secretive nature of these codes, and this fascination can lead them to explore the mathematics of cryptography. The simplest codes are called substitution ciphers. In these codes, each letter is replaced by another number or letter in the alphabet. These codes are easy to crack, or decode, because of the relative frequency of letters in messages. For example, e is the most often used letter in the English language; therefore, the substituted value for e is relatively easy to determine. One way to make substitution codes more difficult to crack is to group letters and then encode the groups of letters. A particular application of this strategy, one that combines matrix multiplication and modular arithmetic, is known as the Hill cipher (Anton and Rorres 1987). This article explains coding and decoding messages using Hill ciphers. These ciphers are an interesting example of an application of matrices called for in NCTM's Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) for grades 9-12. A graphing calculator will facilitate the matrix and modular arithmetic used in the coding and decoding procedures.

Students Generating Test Items: A Teaching and Assessment Strategy

1998 ◽  
Vol 91 (3) ◽  
pp. 198-202
Author(s):  
Victor U. Odafe
Keyword(s):  
Learning Process ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Mathematics Reform ◽  
Evaluation Standards ◽  
Assessment Strategy ◽  
Test Items

The more students invest in their own learning process, the more they will learn. This widely documented view is supported by publications from the mathematics-reform community. For example, the National Research Council's (NRC) Moving beyond Myths (1991) and Everybody Counts (1989) and NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) have called for changes in the teaching and learning of mathematics.

Exploring Patterns, Relations, and Functions

1992 ◽  
Vol 39 (9) ◽  
pp. 19-21
Author(s):  
Charles P. Geer
Keyword(s):  
Problem Solving ◽  
Cognitive Skills ◽  
Mathematics Instruction ◽  
School Mathematics ◽  
First Century ◽  
Evaluation Standards ◽  
Learning Mathematics ◽  
New Knowledge ◽  
Paper And Pencil ◽  
Twenty First Century

As teachers use NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) to develop programs that will prepare students for the twenty-first century, some are discovering that mathematics instruction is going to be very different in the 1990s. Many previous programs placed a heavy emphasis on paper-and-pencil proficiency with computational skills and learning mathematics by memorizing rules. Because of advances in technology, new knowledge about how learning occurs, and the changing needs of business and industry, future programs will focus on mathematics with meaning, problem solving, and higher-level cognitive skills.

Solution Revolution

1993 ◽  
Vol 86 (1) ◽  
pp. 15-22
Author(s):  
Roger P. Day
Keyword(s):  
Teaching And Learning ◽  
School Mathematics ◽  
Graphical Solution ◽  
Evaluation Standards

In Consortium, the newsletter of the Consortium for Mathematics and its Applications, Froelich (1988) explored graphical strategies for solving the equation 2x = x10. He described his use of a function plotter as he sought a graphical solution for that equation. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) has proposed the increased use of function plotters and other technology to investigate and solve problems. Equations such as 2x = x10 can be used to illustrate the potential of that technology and to consider its implications for the teaching and learning of mathematics.

Promoting Number Sense in the Middle Grades

1994 ◽  
Vol 1 (2) ◽  
pp. 114-120
Author(s):  
Barbara J. Reys
Keyword(s):  
Common Sense ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Middle Grades ◽  
Number Sense ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Teaching And Learning ◽  
Way Of Thinking

Phrases such as “number sense,” “Operation sense,” and “intuitive understanding of number” are used throughout the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) to describe an intangible quality possessed by successful mathematics learners. Number sense refers to an intuitive feeling for numbers and their various uses and interpretations, an appreciation for various levels of accuracy when computing, the ability to detect arithmetical errors, and a common-sense approach to using numbers (Howden 1989; McIntosh, Reys, and Reys 1991). Number sense is not a finite entity that a student either has or does not have but rather a process that develops and matures with experience and knowledge. It does not develop by chance, nor does being skilled at manipulating numbers necessarily reflect this acquaintance and familiarity with numbers. Above all, number sense is characterized by a desire to make sense of numerical situations, including relating numbers to context and analyzing the effect of manipulations on numbers. It is a way of thinking that should permeate all aspects of mathematics teaching and learning.

Using The Geometer's Sketchpad to Visualize Maximum-Volume Problems

2000 ◽  
Vol 93 (3) ◽  
pp. 224-228 ◽  
Author(s):  
David C. Purdy
Keyword(s):  
High School ◽  
Graphing Calculator ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Maximum Volume ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Traditional Courses

An underlying tenet of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and other movements toward reform in school mathematics is breaking down content barriers between traditional mathematical topics, with the goal of teaching mathematics as a logically interconnected body of thought. As teachers move toward integrating the various areas of mathematics into traditional courses, problems that were once reserved for higher courses, for example, precalculus and calculus, now surface earlier as interesting explorations that can be tackled with such tools as the graphing calculator. One such problem is the well-known maximum-volume-box problem. Although this problem and related optimization questions have been common in advanced algebra, precalculus, and calculus textbooks, they have only recently found their way into high school geometry textbooks, including Discovering Geometry: An Inductive Approach (Serra 1997).

I Do and I Understand, I Reflect and I Improve

1994 ◽  
Vol 1 (4) ◽  
pp. 242-246
Author(s):  
Carolyn Schcibelhut
Keyword(s):  
Elementary Teachers ◽  
Teaching And Learning ◽  
School Mathematics ◽  
Methods Course ◽  
Methods Courses ◽  
Prospective Elementary Teachers ◽  
Evaluation Standards ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

“I hear and I forget. I see and I remember. I do and I understand.” In my college methods course on teaching and learning mathematics, my goal is to prepare prospective elementary teachers to meet the challenge of implementing the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). My colleagues agree that it is important for our students majoring in education to develop understanding by “doing,” so our students are given the opportunity to plan and teach lessons in a clinical classroom during live semester in which they take their methods courses.

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