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Using Literature to Promote Mathematical Understanding
Introduction
One of the challenges teachers face in implementation of the new Georgia
Performance Standards (GPS) in mathematics is the incorporation of reading in the
mathematics classroom. The new GPS in mathematics includes a reading standard for
every grade level. Students are expected to read a minimum of 25 books per year from a
variety of disciplines, and read and discuss “both informational and fictional texts in a
variety of genres and modes of discourse.” The reading standard also states that students
should “relate messages and themes from one subject area to messages and themes in
another area” and “explore life experiences related to a subject area content.”
Content-area literacy, such as that described in the new GPA, is key to students’
learning in every subject (Literacy Across the Curriculum, p. 20). However, research has
shown that the English teacher is often seen as solely responsible for literacy instruction
and development (Romine, McKenna & Robinson,1996). There are a number of reasons
why teachers resist teaching content-area literacy. According to studies conducted by
Daisey & Shroyer (1993) and O’Brien, Stewart, & Moje (1995) teachers: (a) do not see
content-area strategies as meaningful in communicating content-area knowledge; (b) see
literacy strategies as violating their primary obligation to teach content; (c) view use of
literacy strategies as outside their job expectations; and (d) find that teaching content-area
literacy strategies violates unstated school expectations and norms for instruction. On the
other hand, it has been shown that student achievement improves when students are
adequately engaged with the written language of their content area (O’Brien, Stewart, &
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Moje, 1995). Teachers should be provided with opportunities to learn strategies that will
enable them to effectively link literature and mathematics.
Unfortunately, in a 2002 survey of middle-grades and high school teachers across
the country, only 28% of middle grades teachers and 32% of high school teachers
expected students to read three or more books annually (Literacy Across the Curriculum,
p. 53). At this rate students will fall short of the 25-book goal of the GPS. Although there
is no hard rule about how the reading is to be distributed from course to course, the goals
could be reached by reading eight to ten books in English and two or three books in each
of the student’s other classes such as mathematics (Literacy Across the Curriculum, p.
52)
This proposal seeks to provide teachers from middle school and high school with
an opportunity to explore grade-level appropriate literature that includes mathematical
themes. The teachers will help develop and test lesson plans that enable them to use
literature in the classroom and link the literature to specific Georgia Performance
Standards in mathematics. In the process of exploring the literature, teachers will also
deepen their own knowledge of mathematics and experience the thrill of reading material
that stirs the mathematical imagination and engenders interesting discussions of broad
concepts in mathematics.
Theoretical and Practical Considerations
As we consider the integration of mathematics and the study of reading literature,
Louise Rosenblatt’s (1978) work provides a theoretical stance from which to consider the
reading of text. She points out that in the reading process, the text and the reader come
together, and in that moment of intersection, meaning is made. Each reader brings
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something different to the reading process, and in the discussion of the text, each reader’s
response adds significance to the interpretation of the text. This is not to say that any
interpretation is correct, rather the discussion that ensues, based on shared and varied
reader perspectives, extends the making of meaning to so that multiple possibilities are
created. Finding the right answer to a multiple choice question, then, is not the purpose of
reading; instead, critical thinking, in the form of substantiating the reader’s perspective
through examination of the text, becomes the purpose of reading. Part of the study of
mathematics, like part of the study of literature, is the mental play involved in learning
about concepts and seeing those concepts applied in various reading experiences.
The integration of mathematics and reading also requires consideration of the
theory and practice of truly interdisciplinary activities, activities in which two disciplines
come together in a way that produces new insights and understandings. In
Interdisciplinary Curriculum: Challenges to Implementation (Wineburg & Grossman,
2000), the authors describe the theory and practice of interdisciplinary curricula in the K12 school setting. They describe the promise of interdisciplinary endeavors and the
practical impediments. We intend to use this work in our effort to model an
interdisciplinary pedagogy.
In designing this project, understanding what works and what doesn’t work in the
professional development of teachers is important. According to Loucks-Horsley,
Hewson, Love, and Stiles (1998) effective workshops can successfully alter a teacher’s
practice and understandings. Our design of the workshop is consistent with the
recommendations of this resource. We plan to actively engage the teachers in reading,
discussions, activities, and allow them a chance to complete and present a group project
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of their choosing. We will remain connected with the teachers throughout the school year
via a web site and a series of day-long workshops.
Project Goals and Objectives
We propose two series of workshops – one for middle-grades teachers and one for
secondary teachers. At the end of the series of workshops, the teachers will have (1) a
deeper understanding of certain broad concepts in mathematics, as well as an
understanding of the issue of reader response in reading; (2) an understanding of how to
best integrate mathematics and literature such that students are encouraged to ask new
questions and explore the mathematical and literary universe; (3) an understanding of
how to evaluate the quality of student responses to reading questions; and (4) a collection
of lesson plans that they helped to develop to use their new understandings and resources
effectively in their own classrooms. The lesson plans will also be made available to the
Georgia Department of Education to disseminate to other teachers as they implement the
new Georgia Performance Standards in mathematics.
Proposed Activities
Stage 1: Planning and Recruiting Teachers. The project faculty members will
begin recruiting teachers as soon as possible in the spring semester. Target schools will
be Cass Middle School, AND??? We will seek teams of mathematics teachers from the
same high school or middle school and accommodate teachers on a first-come, firstserved basis. We’ll meet weekly in May, June and July of 2007 in preparation for the
initial week-long workshops to be held in July of 2007. We’ll develop a series of lesson
plans to use as models in the workshops. A sample of such a lesson plan for a middle-
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grades classroom is shown on the next three pages. We’ll also refine a bibliography of
texts for use in the middle grades and secondary classroom.
Sample Lesson Plan
Grade Level: 6th, 7th, 8th
Enduring Understandings:
Mathematics is the study of patterns, and patterns can be expressed concisely in different
ways through the language of numbers and algebra.
Essential Questions:
What number patterns are described in the story Anno’s Magic Seeds?
How can I describe those patterns algebraically, graphically, through a table?
Georgia Performance Standards (Content, Reading and Process Standards):
M6A2. Students will consider relationships between varying quantities.
a. Analyze and describe patterns arising from mathematical rules, tables, and
graphs.
b. Use manipulatives or draw pictures to solve problems involving proportional
relationships.
M7A1. Students will represent and evaluate quantities using algebraic expressions.
M8A1. Students will use algebra to represent, analyze, and solve problems.
a. Represent a given situation using algebraic expressions or equations in one
variable.
b. Simplify and evaluate algebraic expressions.
MRC. Students will enhance reading in all curriculum areas by:
(a) Reading in all curriculum areas.
 Read both informational and fictional texts in a variety of genres and modes of
discourse.
(b) Discussing books
 Discuss messages and themes from books in all subject areas.
(c) Building vocabulary knowledge
 Demonstrate an understanding of contextual vocabulary in various subjects.
 Use content vocabulary in writing and speaking.
 Explore understanding of new words found in subject area texts.
MP3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
Learning Outcomes:
Students will be able to:
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

Analyze and describe in different ways (graphically, in tabular form, in words, in
pictures, in algebraic form) a pattern of numbers.
Write equations to match the pattern given and explain how they arrived at the
equations.
Materials:
Anno's Magic Seeds by Mitsumasa Anno
Counters or small pebbles (optional); scratch paper, pencil
Lesson Procedure:
Introduce and read the Japanese tale Anno's Magic Seeds, by Mitsumasa Anno. You may
wish to enlarge a few of the pages and project them as you introduce the story.
A wizard gives Jack two golden seeds with the instructions to eat one and bury the other.
The promise is that he will have two more magic seeds in the fall. Jack follows that
direction for several years, getting the promised seeds each time. At last inspiration
comes and Jack plants both seeds getting four seeds this time. He plants more and more
seeds, eating some and planting some with the yield increasing each time. Jack's life
expands as well. He marries and has children. A flood washes out the crop, but they have
seeds enough to plant again. The reader is asked questions: "How many seeds grew that
year?" "How many seeds did they bury?" The reader is encouraged to predict Jack's
progress based on the concept of algebraic patterns.

Several questions are posed throughout the reading. When a question is posed,
pause to allow students time to solve it.
 Have students work in pairs or small groups to solve each of the questions as it is
presented.
 Provide manipulatives (counters, pebbles, etc.) to assist students and help them to
"see" the pattern.
 Encourage students to show all work and explain their solutions! Encourage
different ways of visualizing the growth of seeds (table, graph, tree graph). Have
each group of students share their results with the class.
 Encourage students to write an equation/expression that will calculate the number
of seeds produced. Ask the students: How will this equation change when Jack's
wife is included? And the wedding party souvenir seeds? And the baby? What if
three seeds grew for every one planted?
 Depending on the level of the students, they may be encouraged to discuss and
compare different forms of the expression that calculates the number of seeds
produced. For example, how many seeds are produced after 1 year of planting n
seeds? How many seeds are produced after n years beginning with 1 seed? How
are the expressions different?
The discussion surrounding this text can vary greatly depending on the mathematical
sophistication of the group. The deep underlying concept is the idea of mathematics as
the science of patterns and representations of those patterns. The lesson could even be
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used in a high school classroom in a discussion of sequences and functions in recursive or
closed forms.
Closure
Ask the students to describe in their own words the answers to the essential questions of
the lesson: What number patterns are described in the story Anno’s Magic Seeds?
How can I describe those patterns algebraically, graphically, through a table? Which
representation is most effective? What different features of the number pattern are
brought out by the different representations?
Extensions
Given a number pattern or algebraic formula for a number pattern (either provided by the
teacher or by the students), write a story such as Anno’s Magic Seeds in which that
number pattern is used. (Note that different kinds of stories could fit with different
number patterns – linear, exponential, quadratic, logarithmic!)
Stage 2: Workshops. Readings and discussions will revolve around short stories and
specific excerpts from plays and texts that provide a view – either current or historical –
of a concept or concepts in mathematics. We propose to focus on Number and
Operations, Algebra, and Geometry for the middle school teachers, and on Algebra and
Geometry for the secondary teachers. Materials will be chosen according to how
effectively they open the window to further investigation of the mathematical universe,
and how they convey the idea that mathematics is not just the execution of algorithms,
but a world of ideas to be explored. Whitin (2002, 2004) provides a guide to choosing
literature in the lower grades and we intend to use this guide in choosing our literature.
For example, the concept of number can be explored through consideration of a book
entitled The Number Devil: A Mathematical Adventure (Enzenberger, 1998), a higherlevel text such as The Extraordinary Hotel or The Thousand and First Journey of Ion the
Quiet (Lem, 1999), to an even higher level text such as the short story by Argentinian
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author Jorge Luis Borges “The Library of Babel” (Borges, 1962) or a short story by
mathematician Alex Kaman about irrational numbers entitled “The Center of the
Universe” (Kasman, 2005). We will choose texts that appeal to a broad audience, provide
a variety of perspectives, engender different levels of discussion, and will, most of all, stir
the mathematical imagination and open the window to further investigation of the
mathematical universe. Sources of such material include Mathematical Magpie
(Fadiman, 1997), Mathenauts: Tales of Mathematical Wonder (Rudy Rucker, 1997),
Fantasia Mathematica (Fadiman, 1997), Ficciones (Borges, 1962), Imaginary Numbers:
An Anthology of Marvelous Mathematics Stories, Diversions, Poems and Musings
(Frucht, 1999), Flatland (Abbot, 1992). Participants will be grouped with teachers from
the same schools and will be required to complete and present a lesson plan for use of a
specific piece of literature or excerpt from a piece of literature. They will be expected to
consider how to guide their students to the higher-level thinking that draws
mathematicians and literary artists into thinking about concepts and possibilities rather
than just correct answers. They’ll be able to choose from a variety of materials that we’ll
make available, so that they can choose a text that will be particularly suitable for the
subject area they’ll be teaching in the fall.
Stage 3: Implementation of Lesson Plans and Follow-up Workshops. A one-day
workshop will be held for each group of teachers in the fall and the spring of 2007-2008.
The goal of these workshops will be to discuss ways to improve and revise the lesson
plans, discuss issues that arose in implementing the lesson plans, and examine and
discuss student reactions and student work.
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Description of Participants
Each workshop will include 20 teachers from Cobb County and Marietta City
schools, specifically including Marietta High School and Cass Middle School.
Evaluation
Evaluation of the project will be accomplished both informally and formally.
Informally, the project directors will each maintain a journal during the workshops,
describing and reflecting upon the activities of each day. At the end of the workshop, the
directors will exchange journals and discuss the workshop with the goal of identifying
and publishing an account of the successes and failures.
Formal evaluation procedures for the project will be designed to identify changes
with regard to specific workshop objectives. The objectives of the workshop are that the
teachers will have (1) a deeper understanding of certain broad concepts in mathematics,
as well as an understanding of the issue of reader response in reading; (2) an
understanding of how to best integrate mathematics and literature such that students are
encouraged to ask new questions and explore the mathematical and literary universe; (3)
an understanding of how to evaluate the quality of student responses to reading questions;
and (4) a collection of lesson plans that they helped to develop to use their new
understandings and resources effectively in their own classrooms. The teachers will be
asked to respond to a series of open-ended questions before and after the workshops to
evaluate each of the objectives. The questions will be modeled after those used in the
evaluation of the Dartmouth College Mathematics Across the Curriculum project, a
project that successfully integrated literature and mathematics in the college classroom.
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In addition, the project directors will design a form to be used to assess the lesson plans
presented by each team of participants on the last day of the summer workshops.
During the school year, the teachers will try the lesson plans developed by the
project directors and the teachers themselves, and suggest revisions. We will encourage
the teachers to videotape and share their experiences with literature and mathematics in
their classrooms.
Project Staff and Faculty
The four project directors are members of the College of Science and
Mathematics and the College of Humanities and Social Sciences at Kennesaw State
University. Three of the project directors are also members of the Professional Teacher
Education Unit at Kennesaw State University and have had experience in the training and
supervision of pre-service and in-service middle grades and secondary mathematics and
English teachers. The areas of expertise include mathematics, mathematics education,
English, and English education. Several of the faculty members have participated in
interdisciplinary seminars at KSU or have designed and taught innovative courses at KSU
that blend mathematics and literature. More specific information is included in Appendix.
Institutional, Industrial or Private, and School Contributions
As the facilitating institution, KSU will provide meeting rooms, food service
availability, secretarial support, financial services, administrative services, miscellaneous
supplies, and computer facilities necessary for the administration and delivery of the
workshops and follow-up activities.
References
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Bottoms, G., Ash, G., Buehl, D., Dick, E., Hodges, J., Lewis, et. al. (2006). Literacy
Across the Curriculum: Why students should read and what schools can do about
it. Atlanta, GA: Southern Regional Education Board.
Daisey, P. & Shroyer, M. (1993). Perceptions and attitudes of content and methods
instructors toward a required reading course. Journal of Reading, 36(8), 624-629.
O’Brien, D., Stewart, R., & Moje, E. (1995). Why content literacy is difficult to infuse
into the secondary school: Complexities of curriculum, pedagogy, and school
culture. Reading Research Quarterly, 20, 646-648.
Romine, B., McKenna, M., & Robinson, R. (1996). Reading coursework requirements for
Middle and high school content-area teachers: A U.S. survey. Journal of
Adolescent and Adult Literacy, 40(3), 194-198.
(ADD OTHER REFERENCES)