Teaching Mathematics with Technology: Exploring Geometry with The Geometer's Sketchpad

1992 ◽  
Vol 40 (3) ◽  
pp. 187-191
Keyword(s):  
Middle School ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Curriculum Standards ◽  
Older Students ◽  
Evaluation Standards ◽  
Geometric Objects ◽  
Elementary And Middle School

Have you ever thought of exploring geometric relationships on the computer? The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) challenges us to pay increased attention to “developing an understanding of geometric objects and relationships” and “using geometry in solving problems” (p.70). The document also advises placing decreased emphasis on memorizing geometric vocabulary, facts, and relationships. This article describes several geometric investigations that were developed in the spirit of the curriculum standards and are appropriate for use at advanced elementary and middle school levels, as well as with older students. They encourage exploration, creativity, and discovery.

The Pond: Doing Research Together

1996 ◽  
Vol 1 (9) ◽  
pp. 696-704
Author(s):  
Kevin Kinneavy
Keyword(s):  
Middle School ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Approaches To Teaching ◽  
Interdisciplinary Instruction ◽  
Evaluation Standards ◽  
Interdisciplinary Approaches ◽  
Middle School Concept ◽  
School Concept

Interdisciplinary approaches to teaching all subjects are central to the middle school concept. Such approaches can be especially useful for teaching mathematics, a subject that has traditionally been the bane of many students' existence. The NCTM recognizes the importance of interdisciplinary instruction in its Curriculum and Evaluation Standards for School Mathematics (1989, 84).

Implementing the Professional Standards for Teaching Mathematics: Sharing, Supporting, Risk Taking: First Steps to Instructional Reform

1992 ◽  
Vol 85 (6) ◽  
pp. 466-470
Author(s):  
Steven J. Leinwand
Keyword(s):  
Risk Taking ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Curriculum Standards ◽  
Instructional Reform ◽  
Evaluation Standards ◽  
Teaching Standards

For many of us, the Professional Standards for Teaching Mathematics (NCTM 1991) represents a much scarier and much more intimidating vision of school mathematics than its predecessor, the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). Accordingly, implementing the teaching standards will require different strategies from those being used or proposed to implement the curriculum standards.

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).

Teaching Mathematics with Technology: Activities to Introduce Your Class to Logo

1991 ◽  
Vol 39 (3) ◽  
pp. 52-54
Author(s):  
Lyn Taylor
Keyword(s):  
Middle School ◽  
Teaching Mathematics ◽  
Older Students ◽  
Guided Discovery ◽  
Evaluation Standards

Papert (1980) developed Logo to encourage exploration, creativity, and discovery. The following classroom-tested, guided-discovery activities exemplify this spirit and further the goals of the NCTM's Curriculum and Evaluation Standards (1989). These activities are appropriate for use at the primary, intermediate, and middle school levels, as well as with older students.

Exploring Geometry with Technology

1998 ◽  
Vol 3 (6) ◽  
pp. 436-442
Author(s):  
Azita Manouchehri ◽  
Mary C. Enderson ◽  
Lyle A. Pugnucco
Keyword(s):  
Middle School ◽  
Mathematical Thinking ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
Evaluation Standards ◽  
Learning And Teaching ◽  
School Population ◽  
Teaching Geometry ◽  
Geometric Concepts ◽  
Fashion Students

The study of geometry in grades 5-8 should incorporate opportunities for students to engage in exploring and analyzing geometric shapes to conjecture about geometric relationships through data collection and model construction, according to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). In this fashion, students will develop an intuitive understanding of geometric concepts and learn to reason formally and informally. Moreover, it is hoped that through such processes, students will formulate relevant definitions and theorems. The Standards document also encourages the use of computer technologies in middle school mathematics instruction. This suggestion was based on the assumption that interactive environments provided by appropriate geometry software have the potential to foster students' movement from concrete expetiences with mathematics to more formal levels of abstractions, nurture students' conjectuting spirit, and improve their mathematical thinking. Although the NCTM's visions for the geometry curriculum and for methods of teaching geometry in the middle levels are certainly attractive, many teachers are concerned about what software is useful for the middle school population, how such software can be used in instruction. what issues are associated with their use, and what the consequences are of learning and teaching mathematics within such environments.

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.

TEACHING MATHEMATICS WITH TECHNOLOGY: Computation and Estimation

1992 ◽  
Vol 40 (1) ◽  
pp. 48-51
Author(s):  
Janet Parker ◽  
Connie Carroll Widmer
Keyword(s):  
School Mathematics ◽  
Teaching Mathematics ◽  
Evaluation Standards ◽  
Mental Mathematics

As we prepare for the day envisioned by the Curriculum ond Evaluation Standards for School Mathematics (NCTM 1989), when every student will have a calculator and every class will have at least one computer available at all times, we need to reexamine the roles of computation, estimation, and mental mathematics in the teaching and practice of mathematics. It is true that calculators and computers can perform virtually all computations, relieving us and our students of much drudgery; however, this is not their only role. Calculators and computers also make it easy for us to solve problems in a new mode, T-E-M-T-T: trial, error, and modified trial through technology.

IDEAS

1993 ◽  
Vol 40 (6) ◽  
pp. 325-337
Author(s):  
Rebecca B. Corwin ◽  
William R. Speer
Keyword(s):  
Middle School ◽  
Mathematics Teachers ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
Place Value ◽  
Elementary And Middle School

Many elementary and middle school mathematics teachers use a particular approach when planning mathematics units. We tend to match a mathematics concept that we want to teach with an activity or material that will convey the needed idea. When we teach fractions. we think of planning a pizza party or partitioning a geoboard. When we teach place value, we think of base-ten blocks or trading games. As we increase our teaching and planning repertoires over the year by adding more and more activities and materials, we make better matches among what we think of as basic curriculum elements: the students' needs. the mathematics topic, and choices of activities and materials. These elements, mixed differently year to year, facilitate many good mathematic lessons. But they may also give us a limited view of curriculum possibilities.

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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