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.

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).

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.

Teaching Geometry with Tangrams

1982 ◽  
Vol 30 (2) ◽  
pp. 34-38
Author(s):  
Dorothy S. Russell ◽  
Elaine M. Bologna
Keyword(s):  
High School ◽  
Elementary School ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Formal Structure ◽  
Elementary School Mathematics ◽  
Teaching Geometry ◽  
Geometric Concepts ◽  
School Mathematics Curriculum

What is the most neglected area of the elementary school mathematics curriculum? The answer, probably, is geometry. Too many people think of geometry as a formal structure, like the course they had in high school. As a result. they do not see its relevance to the elementary school mathematics curriculum. Activities that introduce children to geometric concepts provide experiences that help children develop and reinforce spatial perceptions.

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.

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.

Professional Development: Teachers' Communication and Collaboration Keys to Student Achievement

1995 ◽  
Vol 1 (6) ◽  
pp. 454-458
Author(s):  
Helene J. Sherman ◽  
Thomas Jaeger
Keyword(s):  
Professional Development ◽  
Student Achievement ◽  
Educational Reform ◽  
Mathematics Teaching ◽  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Professional Satisfaction ◽  
Evaluation Standards ◽  
Instructional Changes

The curriculum and evaluation standards for School Mathematics (NCTM 1989) and the Professional Standards for Teaching Mathematics (NCTM 1991) have served as both stimuli for, and responses to, numerous formal and informal programs, conferences, and conversations calling for educational reform and improvement in mathematics teaching. After all the plans are drawn and all the objectives are written, however, reform is most likely to occur and make a lasting difference when teachers are aware of the need for improvement, have a voice in planning it, and derive a real sense of professional satisfaction from implementing the instructional changes.

Teaching Sensible Mathematics in Sense-Making Ways with the CPMP

1995 ◽  
Vol 88 (8) ◽  
pp. 694-700 ◽  
Author(s):  
Christian R. Hirsch ◽  
Arthur F. Coxford ◽  
James T. Fey ◽  
Harold L. Schoen
Keyword(s):  
School Districts ◽  
School Mathematics ◽  
Sense Making ◽  
Teaching Mathematics ◽  
Assessment Practices ◽  
Classroom Teachers ◽  
Current Policy ◽  
Evaluation Standards ◽  
American Schools ◽  
Assessment Standards

Current policy reports addressing mathematics education in American schools, such as Everybody Counts (NRC 1989), Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), Professional Standards for Teaching Mathematics (NCTM 1991), and Assessment Standards for School Mathematics (NCTM 1995), call for sweeping reform in curricular, instructional, and assessment practices. Implementing the proposed reforms poses new opportunities and challenges for school districts, mathematics departments, and classroom teachers.

Learning Geometry and a New Language

2000 ◽  
Vol 7 (4) ◽  
pp. 246-250
Author(s):  
Donna Norton Swindal
Keyword(s):  
Conceptual Understanding ◽  
School Mathematics ◽  
Two Dimensional ◽  
Evaluation Standards ◽  
Spatial Sense ◽  
Television Shows ◽  
Geometric Concepts ◽  
The World

The world of geometry has a language of its own. Although most of our students learn the label names for several two-dimensional shapes from childrens' television shows, they still need to understand geometric concepts, recognize opportunities for applying these concepts, and be able to communicate using the concepts in authentic situations. NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) jolted many teachers into realizing the need for deeper exploration of geometry. Students need the time and opportunity to develop spatial sense and investigate two- and threedimensional figures in a setting that encourages inquiry and immerses students in the experience, language, and conceptual understanding of geometry.

Promising Research: The World's Largest Math Event: Promoting Mathematical Thinking

1999 ◽  
Vol 5 (7) ◽  
pp. 430-432
Author(s):  
Daniel J. Brahier ◽  
Melfried Olson
Keyword(s):  
United States ◽  
Real World ◽  
Mathematical Thinking ◽  
The United States ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The World

The Great Sphinx in Egypt is about 73.2 m (240 ft.) long, including the paws, which are each 15.3 m (50 ft.) long. Would one of its paws fit in a typical classroom? Would it fit in the school hallway? If the 90 800 kg (200 000 lbs.) of copper sheeting that make up the Statue of Liberty were melted down into pennies, how many pennies could be produced? How high would the pennies stand if they were stacked on one another? In which city and state would you find the world's largest ball of twine? Where would you find the world's largest catsup bottle? Such questions were the focus of the World's Largest Math Event 4— Landmarks: Seeing the World by Numbers— in April 1998. All over the United States and throughout the world, tens of thousands of students, from kindergarten through college, participated in the event. With the emphasis that the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) places on having students use real-world phenomena as a context for the study of mathematics, the World's Largest Math Event is a popular program.

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