A number of teachers have found that one way to interest and engage students in mathematical thinking is through literature. At the primary level, weaving together literature and mathematics may be a necessity, since so much classroom time at this level is needed to develop literacy. This section contains a short list of books that teachers have found connect well to topics in discrete mathematics. There are a number of publications that provide more complete lists of literature/mathematics connections, such as [4]; however we are not aware of any that highlight discrete math topics.
Dr. Seuss books
(pre-K-2) Iteration and Recursion
``Dr. Seuss''; Random House; $8-$15.
A number of Dr. Seuss books contain the seeds for thinking about iteration and recursion. The Cat in the Hat (1957) and Green Eggs and Ham (1960) are just two that come to mind. In these stories, events or activities are repeated over and over but in each repetition a new event is added. Another Dr. Seuss book, The Lorax (1971), is a variation on this pattern, with an environmental theme. As events occur in The Lorax they trigger other events, eventually throwing the environment out of balance.
One Hundred Hungry Ants (K-3)
Listing and Counting
Elinor Pinczes, Houghton-Mifflin, 1993; $15 (avail. from
Creative Pub.).
This is a simple story told in verse about one hundred hungry ants
heading towards a picnic. Different formations of 100 ants are tried
in order to speed their way to the food; illustrations
provide visual patterns for counting by twos, fives, and tens. In the
process the author
introduces the factors of 100 and the problem of counting factors.
Grandfather Tang's Story (K-3)
Visual Problem Solving
Ann Tompert; Crown, 1990; $15 (avail. from Cuisenaire or
Creative Pub.).
This is a Chinese folktale told with tangrams, a set of seven simple shapes cut from a square. Using tangrams, Grandfather Tang tells a story to his granddaughter: two shape-changing fox fairies try to best each other until a hunter brings danger to both of them. With tangrams students can be encouraged to investigate geometrical concepts and to use their visual imaginations to retell or invent their own stories.
The Tangram Magician (K-3)
Visual Problem Solving
Lisa Campbell Ernst and Lee Ernst,
Harry N. Abrams, NY, 1990; $20.
This is another good book for developing visual
imagination for geometric problem solving.
The story involves
a magician who can change shape, illustrated with
tangrams. The reader is asked to supply the end of the story
by creating the next shape that the magician will take on.
High school teacher Eric Simonian LP `94 reports on an interesting
classroom experience using this book involving students in
grades 2, 4, and 10, in [35].
A Three Hat Day (K-3)
Listing and Counting
Laura Geringer; Harper-Collins, 1987; $5 (paper).
This amusing tale about a hat collector and
his search for a perfect wife
provides an opportunity for teachers to ask
``How many different ways are there to ...?''
The story can be used
to introduce the concept of combinatorics, i.e., systematic
counting.
Sam Johnson and The Blue Ribbon Quilt (K-4)
Tessellations and Geometric Transformations
Lisa Campbell Ernst, Wm. Morrow and Co., 1983 (paper, 1992), $5
(paper).
Sam Johnson and the Blue Ribbon Quilt raises both mathematical
and social questions. While mending the awning over the pig pen, Sam
discovers that he enjoys sewing patches of cloth
together.
However, when he asks his wife if he can
join her quilting club, he meets at
first with scorn and ridicule.
The borders of the pages feature traditional
American quilt patterns which can be used to introduce mathematical
concepts such as symmetry, tessellations, and transformational
geometry.
A Cloak for the Dreamer (K-5)
Tessellations
A. Friedman, Scholastic, 1995; $15 (available from Creative Pub.).
A tailor asks each of his three sons to sew a colorful cloak that will keep out wind and rain. The first two sons sew watertight cloaks made of rectangles and triangles, but the third son, the dreamer, makes a cloak out of circles, which is full of holes. This book gives a good introduction to tessellations, and contains (for parents and teachers) a section on the underlying mathematical concepts.
Two of Everything
(1-4) Iteration; Exponential Growth
Lilly Toy Hong, Albert Whitman & Co., 1993;
$15 (available from Creative Pub.).
A Chinese folktale about a couple who find a magic pot that doubles everything that is put into it. The story is retold and illustrated by the author. This is a good starting point for thinking about iteration and exponential growth.
Anno's Mysterious Multiplying Jar (1-6)
Listing and Counting
Masaichiro and Mistumasa Anno; Putnam Publishing, 1983;
$17 (available from Creative Pub.).
Simple text and beautiful illustrations tell a tale about a porcelain jar with a sea inside. In the sea is one island, and on the island are two countries, and in each country are three mountains .... This book provides a rich introduction to the concept of counting by multiplication. One of our favorites!
Math Curse (4-8)
General Problem Solving
J. Scieszká and L. Smith;
Viking/Penguin Group, 1995; $11.
A popular new book. A young girl wakes up one
day afflicted with the ``math curse''--she sees math
in everything she does. The book has a wonderful crazy-quilt
graphical style, and is full of engaging
problems (mainly on algebra, geometry,
and numbers--but with a few discrete math problems).
Jurassic Park (6-up)
Fractals and Iteration
Michael Crichton; Random House, 1990; $6 (paper).
Jurassic Park, which connects mathematics, biotechnology, and prehistoric legend, has proved to be a ``student magnet'' in a number of mathematics classrooms and can serve as a stepping stone to the introduction of fractals. In the beginning of each chapter, the ``dragon-curve'' fractal is constructed to one more level, as a mathematical foreshadowing of the events to come. An 8th-grade teacher's students asked her to teach them more about fractals after reading the book, leading to some of the best learning she'd seen in her career--sparked by a real ``need to know.''