MED 607

Using Computers and Calculators in the Teaching of Mathematics

II. Reasons for Addition:

This course addresses the growing need for teachers with technical experience, particularly in the use of computers and calculators in mathematics classrooms. This course is intended to meet the recommendations from national organizations that mathematics teachers use technology appropriately and effectively as problem-solving tools.

III. Major Objectives of the Course:

A. To familiarize students with various types of technological aids available for use in the mathematics classroom, such as software and calculators.

B. To give students practice in evaluating software and other materials with respect to their use in the teaching and learning of mathematics.

C. To give students experience in developing curriculum units that employ technology.

D. To prepare students to expand and develop their own knowledge and expertise so that they can adopt new developments in equipment and software as they occur in the future.

IV. Topical Outline:

A. Experience with and evaluation of currently available technology.

1. Computer software.

a. Geometry — using tools for explorations, conjectures, constructions.

b. Algebra — using tools for multiple representations: graphs, equations, tables. Software includes graphing utilities, algebra systems, spreadsheets.

c. Probability and statistics — using tools for visualizing and analyzing data, running simulations to generate data.

d. Discrete mathematics — using software for recursively defined sequences, truth tables, graph theory, and Venn diagrams.

e. Calculus — using tools for visualizing derivatives, integration, and critical points.

f. Word-processing — using this tool for producing teaching materials.

2. Calculators.

a. Number sense — using fraction and four-function calculators to explore properties of numbers.

b. Algebra — using graphing calculators for visualizing, analyzing, exploring functions and relations.

c. Probability and statistics — using statistical calculators for analyzing data, using graphing calculators for visualizing and curve fitting.

3. Other types of technological materials that can be adapted for use in the mathematics classroom, such as laser discs and other media.
 
 

B. Development of teaching units.

1. Analysis of experience using the technology.

a. Attributes that can be exploited for enhancing the learning of mathematics.

b. Related problem-solving techniques.

c. Topics and new problems from the curriculum that could benefit from this treatment.

2. Students will develop new technology-enhanced teaching units.
 
 

V. Sample Bibliography:

A. Books and Articles:

Boyd, J.N. and Raychowdhury, P.N. "Largest Quadrilaterals" Mathematics Teacher, December 1992.

Bozeman, William. Computers and Computing in Education: An Introduction, Scottsdale, AZ: Gorsuch Scarisbrick Publishers, 1985.

Brown, Richard and Davis, Gretchen. "Ages of Oscar-winning Best Actors and Actresses" Mathematics Teacher, Feb. 1990.

Browne, Joseph. "Digits count: Significant digits and calculators." Mathematics Teacher, May 1991.

Burrill, Gail. "Statistics & Probability" Mathematics Teacher, Feb. 1990.

Burrill, John and Kepner, Henry Jr. "Relating graphs to their equations with a microcomputer." Mathematics Teacher, March 1986.

Chazan, Daniel. "Students’ Microcomputer-aided Exploration in Geometry." Mathematics Teacher, Nov. 1990.

Collis, Betty. Computers, Curriculum, and Whole-Class Instruction, Wadsworth Publishing, 1988.

Davis, Gretchen. "Using Data Analysis to Explore Class Enrollment" Mathematics Teacher, Feb. 1990.

Demana, Frank and Waits, Bert. "Pitfalls in Graphical Computation, or Why a Single Graph Isn’t Enough." The College Mathematics Journal, March 1988.

Demana, Frank and Waits, Bert. "Around the Sun in a Graphing Calculator." Mathematics Teacher, Oct. 1989.

Demana, Frank and Waits, Bert. "A Computer for All Students." Mathematics Teacher, Feb. 1992.

Ehrlich, Kate; Soloway, Elliot; and Abbott, Valerie. "Transfer effects from programming to algebra word problems: A preliminary study." Report on work supported by NSF Grant, 1982.

Erickson, Dianne. "Dancing Functions from a Graphing Calculator." Computing Teacher, May 1992.

Fey, James, editor. Computing and Mathematics: The Impact on Secondary School Curricula, Report of conference sponsored by NSF, 1984.

Goldberg, Kenneth. "Bringing Mathematics to the Social Studies Class: Spreadsheets & the Electoral Process." Computing Teacher, Aug./Sept. 1990.

Hirsch, Christian; Weinhold, Marcia; Nichols, Cameron. "Trigonometry Today." Mathematics Teacher, Feb. 1991.

Johnson, Jerry. "Motivate Your Students to Look Beyond the Answer." Computing Teacher, Feb. 1986.

Johnson, Jerry. "Derive: A Mathematical Assistant." Computing Teacher, May 1990.

Johnson, Jerry. "Are Paradigms Worth More Than a Pair of Dimes?" Computing Teacher, Oct. 1991.

Johnson, Luella. A Survey of the Use of Computers and Calculators in Mathematics Classrooms in Western New York Ph.D. dissertation, SUNY-Buffalo 1990.

Kenelly, John. "Using calculators in the standardized testing of mathematics." Mathematics Teacher, December 1990.

Lynch, Joan; Fischer, Peter; Green, Sarah. "Teaching in a Computer-Intensive Algebra Curriculum" Mathematics Teacher , Dec. 1989.

M.A.A. Computers and Mathematics: The Use of Computers in Undergraduate Instruction, M.A.A. Notes, Number 9, 1988.

Matras, Mary Ann. "Technology in the Classroom: Beginnings and Endings." Mathematics Teacher, Feb. 1991.

McDonald, Jacqueline. "Exploring Fibonacci Numbers with a Spreadsheet." Jl of Computers in Mathematics & Science Teaching, Winter 1989/90.

NCTM. Curriculum and Evaluation Standards for School Mathematics, 1989.

NCTM 1987 Yearbook: Learning and Teaching Geometry, K?12, Reston, VA: 1987.

NCTM 1988 Yearbook: The Ideas of Algebra, K?12. Reston, VA: 1988.

NCTM 1990 Yearbook: Teaching and Learning Mathematics in the 1990’s, Reston, VA: 1990.

NCTM 1991 Yearbook: Discrete Mathematics Across the Curriculum, K?12, Reston, VA: 1991.

NCTM 1992 Yearbook: Calculators in Mathematics Education, K?14, Reston, VA: 1992.

November, Alan. "Changing the grain." Update, March 1990.

Papert, Seymour. Mindstorms, New York: Basic Books, Inc., 1980.

Pinter-Lucke, Claudia. "Rootfinding with a Spreadsheet in Pre-Calculus." Jl of Computers in Mathematics & Science Teaching, Fall 1991.

Polin, Linda. "Research Windows: Subvert the Dominant Paradigm." Computing Teacher, May 1992.

Polya, George. Mathematical Discovery, New York: John Wiley & Sons, 1981.

Project ExCELS. Mathematics and Computers: Expanding Computer Education in the Learning of the Sciences, Indiana, PA: Indiana University of Pennsylvania, funded by an NSF grant, 1988.

Russell, John. "Probability Modeling with a Spreadsheet." Computing Teacher, Nov. 1987.

Scheaffer, Richard. "Why Data Analysis?" Mathematics Teacher, Feb. 1990.

Schoaff, Eileen Klimick. "A Study of a Use of Computers for a Problem Solving Approach to Learning School Mathematics." Ph.D. dissertation, SUNY-Buffalo 1988.

Schoaff, Eileen Klimick. "How to Develop a Mathematics Lesson Using Technology." Journal of Computers in Mathematics and Science Teaching, Volume 12, Number 1, pp. 19-27.

Schoaff, Eileen Klimick. "Calculus T/L: A Program for Doing, Teaching and Learning Calculus." The Mathematics Teacher, March 1991, Vol. 84, No. 3, pp. 234-235.

Schwartz, Judah and Yerushalmy, Michal. "The Geometric Supposer: An intellectual prosthesis for making conjectures." The College Math Journal, January 1987.

Szetela, Walter and Beattie, Ian. "Graphic methods for instruction in data analysis." Mathematics Teacher, April 1991.

Teppo, Anne. "Van Hiele levels of geometric thought revisited." Mathematics Teacher, March 1991.

Turner, Sandra and Land, Michael. Tools for Schools: Applications Software for the Classroom, Wadsworth Publishing, 1988.

Waits, Bert and Demana, Frank. "A Computer-Graphing-Based Approach to Solving Inequalities" Mathematics Teacher, May 1989.

White, Maurice. "Mathematics Exploration Toolkit" Computing Teacher, May 1990.

Willis, Jerry. Educational Computing: A guide to practical applications, Scottsdale, AZ: Gorsuch Scarisbrick Publishers, 1987.

Wilson, Beth, editor. Making Sense of the Future, Harvard, MA: Educational Technology Center, Harvard Graduate School of Education, 1988.

B. Periodicals

Academic Computing

Classroom Computer Learning

The College Mathematics Journal, a publication of the Mathematical Association of America

Computers in the Schools, the interdisciplinary journal of practice, theory, and applied research

The Computing Teacher, Journal of The International Council for Computers in Education

Educational Technology

Electronic Learning, published by Scholastic, Inc.

Journal of Computers in Mathematics and Science Teaching, publication of the Association for the Advancement of Computing in Education.

Journal of Computing in Teacher Education, a SIG publication of the International Society for Technology in Education.

Journal of Research on Computing in Education, published by the International Society for Technology in Education.

Journal of Technology and Teacher Education, published by the Society for Technology and Teacher Education, SIG of the Association for the Advancement of Computing in Education.

Mathematics and Computer Education

Mathematics Teacher and Arithmetic Teacher, published by the National Council of Teachers of Mathematics

D. Technological materials

Software tools, such as algebra systems, geometric construction tools, graphing utilities, simulations, spreadsheets, databases, and statistical packages.

Software developed for specific courses, such as discrete mathematics or calculus.

Software for developing lessons and presentations.

Equipment such as computers, projection devices, graphing calculators, statistics calculators, fraction calculators, overhead calculator units, VCR equipment.

VI. Presentation and Evaluation:

The class will be conducted as a seminar, where students gain experience with the use of a variety of materials and analyze their applications and impact on the teaching and learning of mathematics. (Class enrollment will be limited, depending on facilities.) Evaluation will be based on software evaluations and projects, where students develop lesson plans incorporating the technology.

VII. Prerequisites:

ISM 101 or MAT 141, or previous computer experience, and admission into the Masters program.

VIII. Credit

3 semester hours.

IX. Departmental Approval:

This course was examined with the recommended procedures and was approved by the graduate faculty of the Mathematics Department on May 13, 1993.
 
 

__________________________

Department Chair
 

X. Catalog Description:

MED 607 ? USING COMPUTERS AND CALCULATORS IN THE TEACHING OF MATHEMATICS

This course includes an introduction to the equipment and software available for use in the mathematics classroom. Class members will gain experience in using the technology from the perspective of the student, analyze their experiences, and then develop new activities and explorations for use in the classroom. Students will produce technology-enhanced lessons for use in the classroom.

A masters' degree in mathematics or mathematics education is the minimum formal education required. Beyond this, a person teaching this course should have experience in using computers, calculators, and other technology, and applying them effectively in the teaching of mathematics. Several members of the Mathematics Department meet this requirement. Some of the current faculty who could teach this course are Tom Giambrone (EdD, SUNY Buffalo 1983), Luella Johnson (PhD SUNY Buffalo 1990), Betty Krist (EdD SUNY Buffalo 1980), and Eileen Schoaff (PhD SUNY Buffalo 1988).

A. Under the jurisdiction of the department:

The department currently owns several pieces of software, computers, an LCD panel, and graphing and fraction calculators with overhead units to be used for the learning and teaching of mathematics. The department must make a commitment to add to this collection as funds and new materials develop.

B. Under the jurisdiction of another department or Academic Services:

Students in this course must have access to college computer lab facilities for both class meetings and outside assignments. Students should have experience with the various types of computers currently available in area schools. Currently this includes Apple II, IBM-compatible, and Macintosh. Classroom facilities should be appropriate for use the computers and calculators with overhead projection devices, such as in the Communication building.