Math Their Way (Book, K-3)
Mary Baretta-Lorton; Addison-Wesley, 1976; $39
(available from Creative Publications); blackline masters are included.
An old favorite. This book contains an activity-centered mathematics program which focuses on patterns. It can be used as a self-contained curriculum or for enrichment.
Wonderful Ideas (Newsletter, K-6)
Wonderful Ideas, 8/yr; $26/yr (individuals),
$38/yr (schools).
This newsletter provides interesting elementary-level activities, often developed around a single theme. Sample topics include the ``Monty Hall'' problem (probability) and making a pinwheel (geometry and origami).
The Elementary Mathematician (Newsletter, K-6)
COMAP, 4/yr; only available with $16/yr membership
(which includes other publications and discounts).
This is another good source of classroom activities, many of which integrate mathematics with science, health, history, and other areas. The pull-out section in each issue contains a complete classroom-ready lesson. Also available is The Elementary Mathematician Pull-out Book (Laurie Aragon, Ed.; $9), a collection of pull-out lessons from past newsletters.
INsides, OUTsides, LOOPS and LINES
(Book, K-8)
Herbert Kohl, W.H. Freeman, 1995; $13.
One of us (Kowalczyk) recently discovered this excellent
book, which introduces concepts from discrete mathematics and
topology.
If I had to recommend one resource book to elementary and middle grade teachers in discrete mathematics this would be it. ...[T]his book provides playful introductory activities [based on concepts in graph theory and topology]. The five chapter titles give you the best flavor for its contents: Lost in the Garden--simple closed curves; Map Coloring--figuring out the rules; Tracings--simple beginnings lead to complicated patterns; Stretching, Bending and Twisting--a new way to look at shapes; and Mobius Strips--some thoughts on doing mathematics with a twist. [21]
Math on the Wall (Looseleaf collection, 1-6)
Linda Holden;
Creative Publications, 1987;
three sets are available, for
grades 1-2, 3-4, and 5-6, $8.50/set.
This is a collection of problems and puzzles designed to decorate a classroom bulletin board. Blackline masters for cut-out designs are included. It has lots of combinatorial puzzles, posing such problems as ``How many different bouquets can you make with these flowers?'' (This includes pictures of flowers and vases to cut out and color).
Discrete Mathematics Across the Curriculum, K-12
(Collected Articles)
NCTM, 1991; see [19].
This edited collection is one of the NCTM Yearbook series, written to supplement the Discrete Mathematics Standard in the 1989 NCTM Standards [27]. Most of the articles focus on a single topic, such as graphs or recursion, illustrated with activities suggested for specific grade levels.
Teaching Children Mathematics (Journal, K-4)
Mathematics Teaching in the Middle School (Journal, 5-8)
Mathematics Teacher (Journal, 9-12)
National Council of Teachers of Mathematics, available with
membership (which includes other publications and discounts).
These journals often publish articles or include pullout sections with discrete mathematics activities. The newsletters of local mathematics teachers associations may also publish useful activities.
In Discrete Mathematics: Using Discrete Mathematics in the
Classroom (Newsletter, K-12)
DIMACS DM-Newsletter, 2/yr; for a subscription (no cost -- supported by
DIMACS), write to DIMACS-DM Newsletter (address in Appendix A).
This newsletter features articles by teachers (primarily participants in the Leadership Program in Discrete Mathematics) describing their experiences in creating and/or using discrete mathematics topics in the classroom. There are articles on special topics, such as elections or game theory, along with bibliographies for background reading, as well as resource recommendations. Puzzles and drawings by readers (or their students) also appear. The newsletter was previously edited by Joseph Rosenstein and Franzblau (and currently by Robert Hochberg); Kowalczyk edits a resource review column. Judy Brown (see Section 8) has introduced a new Internet resource column.
Discrete Mathematics in the Schools
(Book, K-12); see [33].
This edited collection of articles (which includes this
article on ``Recommended Resources'') is based on a conference which
took place in October 1992 at Rutgers University, under the
sponsorship of DIMACS, the NSF-funded Center for Discrete Mathematics
and Theoretical Computer Science. The articles present different
perspectives of discrete mathematics and how it can be reflected in
the school curricula. Many activities and topics are presented as
illustrations of the authors' perspectives.
A Comprehensive View of Discrete Mathematics: Chapter 14 of
the New Jersey Mathematics Curriculum Framework (Article,
K-12); in [33]
This chapter from the New Jersey Mathematics Curriculum
Framework presents a comprehensive discussion of discrete mathematics
topics and the grade levels at which they can be appropriately
presented. The grade-level overviews are illustrated by several
hundred activities appropriate for various grade levels.
HiMap and HistoMap Series (Topic modules, 4-12)
Various authors; COMAP; $9 - $12 (catalog available).
These are self-contained supplements on specific topics that can be used in a number of courses. They contain background reading, as well as blackline masters for student activity sheets and transparencies. A few of the modules are accompanied by special-purpose software, such as an implementation of the Moving Knife strategy to accompany a module on fair division. Suzanne Foley LP `95 (private communication.) mentioned that, ``One useful aspect of the HiMap books that I enjoy is the history behind the mathematics,'' and said that she appreciates the practical activities. There are many discrete topics in the large collection, including voting, fair division, graph problems, recurrence relations, and codes. (See also the specific modules recommended in Section 3.2.)
Consortium (Newsletter, 9-College)
COMAP, 4/yr; only available with $32/yr membership
(which includes other publications and discounts).
This newsletter is intended primarily for teachers of undergraduates, but continues to add more items of interest to high-school teachers. It focuses on applications of mathematics, and features pull-out modeling activities for the classroom. Lists of current and future HiMap module titles are given in each issue.
Problem Solving Strategies:
Crossing the River with Dogs
(Book, 9-College)
Ted Herr and Ken Johnson; Key Curriculum Press, 1993; $25
(teacher's resource book, $20).
This book, written to be used as a course text,
uses problem-solving to encourage reasoning skills
across the curriculum. Used mainly as a teacher resource,
the problems have been used with students ranging from
gifted fifth-graders to undergraduates.