ERIC Identifier: ED380310
Publication Date: 1995-00-00
Author: Reed, Michelle K.
Source: ERIC Clearinghouse for
Science Mathematics and Environmental Education Columbus OH.
Making Mathematical Connections in High School. ERIC Digest.
Of all of the reform recommendations being made by the National Council of
Teachers of Mathematics, making mathematical connections is among the more
difficult to achieve, especially at the high school level, where so much
emphasis is placed on distinct content courses. Mathematical connections can
relate mathematical topics to students' daily lives and to other mathematical
topics but are probably most important in relating mathematics to other
curriculum areas. These connections help students understand mathematics better
and see it as a useful and interesting subject to study.
This digest gives samples of activities appropriate for use in high school
classes to connect mathematics to other subjects. Resources are listed by
subject area and are drawn from a longer annotated bibliography of mathematical
connections available from ERIC/CSMEE (see end note).
"Fostering Collaborative Reading and Writing
Experiences in Mathematics" offers several collaborative strategies for
integrating reading and writing with mathematics instruction. Sample lessons
demonstrate the applicability of these strategies across grade levels and across
topics in mathematics.
Wood, K. D. (1992, October). Fostering collaborative reading and writing
experiences in mathematics. Journal of Reading, 36(2), 96-103.
"No Time for Writing in Your Class?" Writing activities do not have to steal
precious time from mathematics. Here are ideas for implementing four forms of
writing appropriate for the mathematics class: (1) logbooks, (2) journals, (3)
expository writing, and (4) creative writing. Specific examples and suggestions
for classroom activities for each form of writing are given.
McIntosh, M. (1991, September). No time for writing in your class?
Mathematics Teacher, 84(6), 423-433.
"Student-Authored Manuals as Semester Projects" describes a learning activity
that requires students to write a manual to explain how to apply procedures and
algorithms used in mathematics. A list of possible precalculus and calculus
topics that can be used in this activity is included.
Hurwitz, M. (1990, December). Student-authored manuals as semester projects.
Mathematics Teacher, 83(9), 701-703.
"Word Roots in Geometry" offers suggestions for a unit on word study in
geometry that includes defining, recognizing, producing, and appreciating the
concepts of geometry. Includes lists of terms and their Greek and Latin word
McIntosh, M. E. (1994, October). Word roots in geometry. Mathematics Teacher,
Mechanical devices offer an alternative to
computers for exploring mathematical concepts in various curricular areas. "The
Dynamic Discograph" describes a series of pulleys and wheels that can be used to
teach mathematical principles in pattern drawing, locus, rotation in geared
systems, gearing, rotational symmetry, regular plane figures, decimals, and
Bell, G. (1991, July). The dynamic discograph. Australian Mathematics
Teacher, 47(2), 4-8.
"How to Make a 'Bucky Ball'" describes how to construct polyhedra to
represent molecular structures. Each face forms regular polygons made up of
balls. Step-by-step directions are provided to perform the constructions.
Stephenson, P. (1992, September). How to make a "bucky ball." Mathematics in
School, 21(4), 14-16.
"Implementing the 'Curriculum and Evaluation Standards'" describes two
activities to analyze unit-cell structures from a geometric viewpoint and
invites students to apply their mathematical understanding to scientific
phenomena. Students form models of the simple cube, a building block of
crystalline structures, and a methane molecule.
Pacyga, R. (1994, January). Implementing the "Curriculum and Evaluation
Standards." Mathematics Teacher, 87(1), 43-47.
Recommendations for reform in mathematics and science education advocate the
integration of science and mathematics teaching and learning as a means of
improving achievement and attitudes within both disciplines. "Integrating
Science and Mathematics in Teaching and Learning: A Bibliography" is a
collaborative effort of the ERIC Clearinghouse for Science, Mathematics, and
Environmental Education; the National Center for Science Teaching and Learning;
the National Science Foundation; and the School Science and Mathematics
Association to suggest resources for classroom teachers, teacher educators,
curriculum developers, and educational researchers interested in the integration
of science and mathematics teaching and learning. The bibliography of 555
citations is divided into five sections: (1) Curriculum, (2) Instruction, (3)
Research, (4) Curriculum-Instruction, and (5) Curriculum-Evaluation.
Berlin, D. F. (1991, August). Integrating science and mathematics in teaching
and learning: A bibliography. Columbus, OH: ERIC Clearinghouse for Science,
Mathematics, and Environmental Education. (ED 348 233)
"Sharing Teaching Ideas" describes three activities designed to increase
student participation in the classroom. The first uses reports of earthquake
intensity on the Richter scale to study logarithms. The second discusses
student-generated examples to introduce probability. The third activity uses
prepared handouts and study groups to promote student interaction and
involvement in calculus classes.
Tometsko, N. R. (1991, October). Sharing teaching ideas. Mathematics Teacher,
"Civic Mathematics: A Real-Life General
Mathematics Course" presents a civic mathematics curriculum that considers
issues of race and gender, poverty and wealth, the environment, and teen issues.
Includes lists of mathematical skills reflected in the issues and a sample
lesson on water resources. Quarterly projects are suggested as an alternative to
Vatter, T. (1994, September). Civic mathematics: A real-life general
mathematics course. Mathematics Teacher, 87(6), 396-401.
"The Power of Numbers: A Teacher's Guide to Mathematics in a Social Studies
Context: An Interdisciplinary Curriculum" provides mathematical experiences in
real-world contexts that help students interpret, experiment, communicate, and
look for multiple solutions to complex problems. The curriculum uses mathematics
to help students develop higher-order thinking and communication skills.
Real-world contexts give students a reason to learn and remember mathematical
skills and concepts and shows them how these ideas are applied in actual
practice. Thematic contexts include polling, studying trends in census data, and
designing a public rail transportation system for Los Angeles. Through these
activities, students participate in discussions, interpret and analyze data,
make decisions, and present their ideas. Topical chapters begin with an overview
and include a list of mathematical concepts, skills, vocabulary, and materials
involved in the activities. Handouts are provided at the end of each chapter.
Gross, F. E. (1993). The power of numbers: A teacher's guide to mathematics
in a social studies context: An interdisciplinary curriculum. Cambridge, MA:
Educators for Social Responsibility (23 Garden Street, Cambridge, MA 02138). (ED
"Bringing Knowledge of Women Mathematicians Into the Mathematics Classroom"
describes an activity to attract and retain more female students in mathematics.
Visits from women who do mathematics and information about noteworthy women
mathematicians are brought into the mathematics classroom. A list of women
mathematicians is included.
Friedman, B. (1990, Fall). Bringing knowledge of women mathematicians into
the mathematics classroom. Mathematics and Computer Education, 24(3), 250-253.
"Historical Digressions in Greek Geometry Lessons" attempts to combine the
history of mathematics in ancient Greece with a course on theoretical geometry
taught in Greek secondary schools. Three sections present the history of ancient
Greek geometry, geometrical constructions using straightedge and compass, and an
application of Ptolemy's theorem in solving ancient astronomy problems.
Thomaidis, Y. (1991, June). Historical digressions in Greek geometry lessons.
For the Learning of Mathematics, 11(2), 37-43.
"The Artist's View of Points and Lines" promotes the
idea that art can be used to present early concepts of geometry, including the
notion of infinity. Discussed is the symbiosis that exists between the artistic
and mathematical views of points, lines, and planes. Geometric models in art and
using art in the classroom are also discussed.
Millman, R. S., & Speranza, R. R. (1991, February). The artist's view of
points and lines. Mathematics Teacher, 84(2), 133-138.
"From the Ground Up: Modeling, Measuring, and Constructing Houses" is part of
the Seeing and Thinking Mathematically in the Middle Grades series. In this unit
students use mathematics to design and construct a model home from the ground
up. Through the process of designing floor plans, constructing walls and roofs,
and making cost estimates, students explore key concepts in geometry and
measurement and engage in problem solving, communication, reasoning, and making
connections. Appendices include reproducible blackline masters in both English
and Spanish and sample student projects.
Education Development Center. (1993). From the ground up: Modeling,
measuring, and constructing houses. Portsmouth, NH: Heinemann. (ED 378 047)
The harmonic mean, neglected in favor of the arithmetic and geometric means
in modern mathematics, is defined and its historical relationship to music, as
presented by Pythagoras, is described in "Mathematics--A Search for Harmony."
Two geometric constructions present a picture of harmony, and an application in
calculating the square root of a number is given.
Arnold, S. (1991, December). Mathematics--A search for harmony. Australian
Mathematics Teacher, 47(4), 14-16.
"Rates and Taxes" proposes lessons for algebra
students using the context of tax calculations to learn about the concepts of
slope, split functions, averages, rates, marginal rates, and percents. Students
explore ramifications of possible tax revisions.
Esty, W. W. (1992, May). Rates and taxes. Mathematics Teacher, 85(5),
"Sharing Teaching Ideas: Career Posters" presents an activity in which
students create posters by interviewing someone who uses mathematics in his or
her job, describing an actual problem that person might have to solve, and
writing a paragraph explaining the problem. The posters created by the students
are then used in future mathematics lessons.
Tibbs, P., & Jordan, J. (1994, September). Sharing teaching ideas: Career
posters. Mathematics Teacher, 87(6), 410-411.