Honors Thesis

Bridging the Gap: Integrating Literature into
Mathematics Education
Scott Davis
Thesis Advisor: Dr. Ann Ciasullo

1
The word technology comes from the Greek term “techne,” which at the time had a
nearly equivalent meaning to the Latin word “ars;” the root from which the word “art” stems. As
can be inferred from the modern words constructed from these roots, the Greek and Latin origins
encompassed many more activities than most people would have initially thought. Carpentry,
medicine, sculpture, even rhetoric was included in these two phrases. The ancient and medieval
societies made no distinction between what we would most likely consider sciences and the fine
arts.1
Only with the Enlightenment, and the evolution of scientific thinking, did the world see a
true breaking between the “sciences,” and the “arts.”
As time passed, and the gap between “scientific” and “creative” ways of thinking
continued to widen, people too began to prefer one method to the other.2
This distinction,
unfortunately, has become incredibly commonplace in the modern United States where people
tend to align themselves with either the arts or the sciences, with few pursuing a combination of
the two. Everyone has heard of the left-brain/right-brain distinction, and though the scientific
validity of this difference is not entirely accurate, people still often distinguish or identify
themselves as one or the other. What this means, then, is before even given the task of solving a
math problem or interpreting a short poem, many people will already have assumed a
predisposition that they will either enjoy and succeed with the “task,” or instead will struggle
through it and feel no joy when they are done. This assumed mindset can alter people’s
experience with the subject matter before they even interact with it.
Research has shown, in fact, that perhaps the distinction between left-brain and right-
brain could be the wrong division completely. In a 2009 study, psychologists Lee Thompson,
Sara Hart, and Stephen Petrill found that there is actually a genetic overlap between math
1
Schatzberg, Eric. 2012. “From Art to Applied Science.” Isis 103 (3) (September): 555-60.
2
Ibid

2
problem-solving skills and reading decoding, while “math fluency,” a measure of timed
calculation, and reading fluency also share genetic overlap.3
The skills within each of these
separate areas (reading and math) were completely independent of one another though. This
means that while our brains don’t really distinguish between the actual subject matter, they do
manage to detect the different types of thinking required by a certain aspect of each subject;
problem solving vs. calculating, for example.
Yet, the original left-brain, right-brain distinction remains popular within society, and
with very different connotations. In the United States, nearly all people would look down on
someone who is illiterate; it would be nearly impossible to find a job, or even someone who
sympathized whole-heartedly with that struggle. We take the ability to read for granted.
Mathematics, on the other hand, is more often viewed as a benefit; a skill that advantageous to
possess, but not wholly necessary. Unfortunately, our culture has widely accepted this belief.
While lacking the ability to read could harm one’s societal status, we are all too tolerant of
someone who “just can’t do numbers.”4
This cultural acceptance of the divide not only highlights
its presence, but continually widens the gap.
Signs of this attitude have permeated nearly all elements of our culture. In books and
movies, an understanding of mathematics is a surefire way to depict a character with extensive
intelligence.5
From Good Will Hunting to The Girl with the Dragon Tattoo, the brilliant
characters are assumed to be genius because they are portrayed interacting with higher level
mathematics. And this is by no means a new rhetorical technique. Take, for example, this
description from a popular 19th century novel: “He is a man of good birth and excellent
3
Hart, Sara A., Stephen A. Petrill, Lee A. Thompson, and Robert Plomin. 2009. “TheABCs of Math:A Genetic Analysis of
Mathematics and Its Links with Reading Ability and General Cognitive Ability.” Journal of Educational Psychology 101 (2):
388-402.
4
Rochman, Bonnie. 2013. Beyond counting sheep. Time 181 (7) (02/25): 52.
5
Fowler, David. 2010. “Mathematics in Science Fiction: Mathematics as Science Fiction.” World Literature Today 84 (3) (May):
48-52

3
education, endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one
he wrote a treatise upon the binomial theorem, which has had a European vogue.”6
This
description of Dr. Moriarty, taken from one of Arthur Conan Doyle’s Sherlock Holmes stories,
illustrates this point perfectly.
The success of this association between brilliance and math competency relies on the fact
that society unanimously agrees that mathematics, plain and simple, is just a hard subject to
learn. We separate our ability to perform even basic math from our ability to read and
comprehend a text, no matter how difficult. Odds are, most “right-brained” people would prefer
to read Moby Dick over spending an equivalent amount of time solving basic arithmetic
problems. This preference is a direct result of the cultural belief that math is inherently difficult.
Even Barbie herself, at one time, used to say, “math class is tough.”7
This societal mindset and
view of mathematics does absolutely nothing to help improve mathematical skills in our youth.
In fact, it does the opposite by fostering an abundance of math anxiety in students, very often
leading to an avoidance of math. Even in the data filled, technological world we live in, our
education system seems to continually be unsuccessful in teaching students numeracy, the math
equivalent to literacy.8
Some people might argue that students’ math-avoidance is due to a lack of intelligence;
that maybe math anxiety is merely regular anxiety for “unintelligent” individuals attempting to
perform mathematical tasks. This belief holds no ground, however, as studies have indicated that
math anxiety has almost no correlation with scores on an IQ test. In fact, there have even been
instances of improving scores on math tests after individuals went through math anxiety
6
Fowler “Math in Science Fiction,” 48-52
7
Ashcraft, Mark H. 2002. “Math Anxiety:Personal, Educational, and Cognitive Consequences.” Current Directions in
Psychological Science 11 (5) (Oct.):181-5.
8
Ibid

4
treatment which involved no mathematical instruction whatsoever.9
This means that it is possible
to help students with math anxiety perform better in test environments, letting their true
mathematical competency show through.
A more probable reason for math-avoidance, paired with math anxiety, comes from the
fact that many students in our modern world cannot see the benefit of obtaining a math
education. But who can blame them? We have calculators, and other online resources, that
essentially do the math for us. Why, then, should we spend time learning the material, if we will
never need to perform these operations for ourselves? This precious time could instead be spent
learning other valuable skills, such as reading, which most people perform every day.
Unfortunately, kids with this belief are unable to see the greater depth that the subject has to
offer. There are far more important problem-solving skills learned through the study of
mathematics that go way beyond addition and subtraction. Without any exposure to these skills,
however, students will begin spending more time on other subjects, leading to a snowball effect
with math anxiety; students who avoid math tend to become more math anxious, leading to more
avoidance, and more anxiety.10
While there have been successful means of treating math anxiety, as previously
mentioned, it would certainly be more beneficial to avoid it altogether. A major source of this
anxiety, and one explanation for the cultural views of math, originates from the manner in which
the subject is taught. Math classes too often spend a majority of the time emphasizing aptitude
and answers, as opposed to processes and effort. This unnecessary pressure to be “correct” all the
time tends to push students with math anxiety away from math-based majors in college, and then
9
Ibid
10
Ashcraft, “Math Anxiety,”181-5.

5
careers later in life.11
The moment students begin aligning themselves with the arts rather than the
sciences, many of them already write themselves off as not being math-oriented people, affecting
their eventual life choices for the wrong reasons.12
Another, more obscure explanation for
student’s disinterest, coming from Ellen and Bob Kaplan, the founders of the Math Circle in
Boston, comes from the belief that math is a subject which can be taught at all.13
The Kaplans
believe that mathematics is best learned through self-discovery and a construction the students
help to form, as opposed to information merely being handed to them. If more teachers began
taking this approach, the Kaplans claim students would begin to experience the aspects of math
that most instruction leaves out: “creativity, playfulness, wonder, and boundless curiosity.”14
While these are by no means the only possibilities, in either case, when instructors
demand perfection and place an importance on obtaining correct answers rather than giving
support for errors and mistakes, there tends to be a much higher rate of math avoidance in the
students after the course.15
Similarly, the rigid structure of most math courses limits the exposure
students have to the field. Greg Tang, an author of children’s math stories including “The Grapes
of Math,” has noted that in his experience nearly all younger students claim to enjoy math, but
this love begins to dwindle as they get older.16
One possible reason for this is because, unlike
reading, most students first encounter math in a classroom environment, meaning that the subject
immediately becomes compulsory as opposed to an activity for fun.17
As students’ interest in
school begins to decrease, so too will their interest in math. Another possibility, proposed by
Tang, again places the blame on the means of instruction. He believes most schools remove the
11
Ibid
12
13
Kennedy, Steve. 2003. “TheMath Circle.” Math Horizons 10 (4) (April): 9-10
14
Ibid
15
16
Tang, Greg. 2002. “Taking the WORRY Out of MATH.” Book Links 12 (2) (Oct):44-45.
17
Rochman, Bonnie. 2013. “Beyond Counting Sheep.” Time 181 (7) (02/25): 52-54

6
problem-solving aspect of math and instead present the material as lists of computations and
formulas. As he puts it, “math quickly becomes a jumble of rote methods and mechanical
procedures with little understanding or intuition.”18
Even the American award-winning novelist
David Foster Wallace agreed with this sentiment. In a review of two “math-melodramas” (to be
discussed later), he pointed out the problem with math education is that students barely skim the
surface of the subject, judging the whole field of mathematics on the introductory material,
“which is roughly analogous to halting one’s study of poetry at the level of grammar and
syntax.”19
Exposure to the more abstract and pure aspects of mathematics requires deeper
thinking, and much more problem solving creativity than calculator math necessitates.
Moreover, research has shown that most of society doesn’t even know what
mathematicians actually do; the general public’s understanding of the profession greatly differs
from the reality of professional mathematicians. This misconception holds especially true in
younger students, and does not occur solely in the United States. In a study of 12-13 year olds’
perceptions of mathematicians, across five countries, researchers found that the connection
between the student’s understandings and the actual work that mathematicians perform is nearly
invisible.20
The blame, as Tang, Rochman and Wallace see it, should be placed on the means of
instruction. Since students’ exposure to mathematics is primarily dependent on their interaction
with it in school, when instructors present the material in a cut-and-dry manner, students cannot
imagine the subject in a more interesting light. They begin viewing mathematicians in the
stereotypical manner, because they have nothing else to base their opinion on.
18
Tang, “WORRY Out of MATH,”44-45.
19
Wallace, David Foster. 2000. “Rhetoricand theMath Melodrama.” Science 290 (5500) (Dec. 22): 2263
20
Picker, Susan H., and John S. Berry. 2000. “Investigating Pupils' Images of Mathematicians.” Educational Studies in
Mathematics 43 (1): 65-70.

7
This constructed image, according to the study, includes many negative elements such as
nerdy glasses and antisocial behavior. Similarly, these 12-13 year olds think that
mathematicians’ job involves nothing more than long tedious calculations – essentially an
extension/complication of the type of problems that they encounter in their own classrooms.21
These intermediate mathematical skills, though necessary to study many advanced math
concepts, actually make up very little of a mathematician’s time, but with the customary
presentation of the material, students’ struggle to picture this. Unfortunately, if this cultural view
permeates too far and too strongly into younger students, it is unlikely that very many will opt to
pursue such a negatively viewed profession, once again leading to an avoidance of the subject. If,
however, instructors can present the material in creative and original ways, students will begin to
better understand what mathematicians do, and gain a better appreciation for math in general.
In fact, in the past few decades, there have been many successful programs which have
helped students gain an appreciation of mathematics. Laura Overdeck, a Princeton-trained
astrophysicist, began her “Bedtime Math” program whose mission it is to change the way
students go to bed.22
Although most parents already read to their children before putting them to
sleep, Overdeck argues that by if parents included solving just a single math problem in this
routine, that problem-solving in mathematics becomes much more enjoyable. And better yet, it
can also spur kids’ interest in math before they even begin school. By using a calendar of fun
events, such as Cookie Monster’s birthday, Overdeck’s program has been so influential than one
customer has begun to use math as a threat; “If you don’t brush your teeth, no math problem
tonight.”23
There are now more than 20,000 subscribers to Overdeck’s e-mail list for nightly
problems. Although there have not been any studies confirming the benefits of this routine, the
21
Picker, “Images of Mathematicians,” 66-70.
22
Rochman, “Counting Sheep,” 52-54
23
Ibid

8
anecdotal evidence indicates the success of the program. Similarly, though not a formal study,
“Snacktime Math” a program implemented at a summer camp in New Jersey reported data that
over 70% of primarily low-income students attending the camp improved their math skills in just
six weeks when they solved “Bedtime Math” problems on a daily basis.24
Another example, the Math Circle, which has now spread to many cities across the
country, has created enough appeal for students to wake up early on Sunday mornings to do math
rather than sleep in. The program, founded by Ellen and Bob Kaplan, has a simple formula for
piquing student interest: bring together a group of students, introduce some exciting problems,
and step back.25
Using the Moore method of teaching, a constructivist approach in which the
students make all the discoveries after the instructor merely introduces the topic (and gives an
occasional push in the right direction), the students get the full math experience. Twenty years
after being founded, the Math Circle still brings in enough students to fill sessions four days a
week every semester.26
The success of these two programs demonstrates the ability to stimulate student
fascination in a subject that is widely considered boring, difficult, and unpopular. No matter
where the dislike originated, there is the potential to make the subject more interesting and more
understandable to students, or rather people, of all ages. While there are many possible methods
to eliminate this math aversion, addressing the subject divide head-on should prove to be
effective at increasing student’s math abilities. By combining mathematics with literature and
reading, students will not only learn the material, but also gain a better appreciation of the
subject. The elimination of solely relying on rote mechanics in math classes, and increasing
24
Rochman, “Counting Sheep,” 52-54
25
Kennedy, “Math Circle.” 9-10
26
Kennedy, “Math Circle.” 27-28

9
exposure to (relatively) real-world problem-solving explorations will demonstrate the potential
necessity and beauty that the subject of mathematics can have.
With regards to math education, there are essentially three basic stages into which we can
divide the subject: elementary mathematics, basic mathematic topics, and advanced math
concepts. Elementary mathematics, as its name suggests, revolves around introducing young
children to the various areas of mathematics. Aside from counting and arithmetic, most topics at
this stage are open and conceptual. The overlap between math and literature is much larger at
this level, as many children’s books deal with introductory concepts such as counting, size, or
shapes. The next level, basic mathematic topics, include the common areas each of us studies in
our typical K-12 educational process: algebra, geometry, trigonometry, statistics, all the way up
through calculus. This area, which spans most of our educational math encounters, tends to be
incredibly problematic, as many students lose interest due to the inflexibility of the rules and
formulas in each respective area. There is very little overlap between math and English at this
stage, and the gap between the arts and sciences widens immensely. Finally, the last stage,
advanced math concepts, addresses ideas that few people outside of math majors and
professionals see. Topics at this stage include number theory, topology, numerical analysis,
differential equations, non-euclidean geometry, and more. Once again this stage allows for a
better overlap with the rising popularity of “math melodramas” novels, though there still remains
a lot of room for improved integration into classrooms. While these topics are not typically a part
of K-12 education, there is no specific time or age at which these subjects are (or can be) taught
to students. This means that although it may not be standard practice, it would be perfectly valid
(and even possibly beneficial) for students without a working knowledge of calculus to begin
learning about some of the topics covered in this section.

10
In addition to the three levels of mathematics education, there are two primary ways in
which a bridge between math and literature can be formed, though one could certainly argue for
more. The first, and more obvious, connection is through the incorporation of literature already
dealing with math concepts into the classroom. These types of readings can range from
children’s books, to sections of a grad student’s dissertation, all the way up to full-blown
fictional novels about number theory. The second way to combine the two subjects is through a
collaboration between math and English. To do this, ideas and math concepts would be drawn
from literary works and applied to a mathematics classroom. For example, teachers could take an
age-appropriate book, such as The Hunger Games, and create math activities revolving around
the relevant mathematical concepts, like algebra or geometry, based on the text. This example,
along with many others, will be explained in greater detail later. I propose that if all three levels
of math education can improve the relationship between mathematics and literature in the
classroom, students should gain a stronger, more sincere interest in math, helping even the most
math-averted people to acquire an appreciation of the subject.
~~~~~~
Before delving into the possible benefits for literature-infused mathematics, it would first
be beneficial to explore the ways in which reading and mathematics are already intertwined, and
the consequences of this relationship. When we perform or research mathematics, as with any
subject, we require the ability to recognize words and symbols and assign an appropriate
meaning to them; a skill better known as reading. The ability to read is, in a sense, a prerequisite
to perform mathematics. While it is possible to count and learn some basic arithmetic, short of a
genius with unparalleled mental math capabilities, it becomes necessary to write steps down to
present and solve problems which, even at the most basic level, requires reading. Similarly, most

11
of mathematics is learned, or at the very least printed, in textbook form; a medium through which
a lot of learning can take place. Even if a student rarely references it, their teacher most likely
relies on some form of hard copy to monitor class progress and ensure appropriate and extensive
coverage of the material. Having a written (and published) reference, such as a textbook, can
help teachers with course design. For example, when learning algebra, an instructor would not
start teaching exponential equations until all necessary pre-requisite topics, such as basic 𝑦 = 𝑥
equations, linear functions, polynomials, etcetera, have all been covered.
What we can take from this relationship is that whether we would instinctively notice it
or not, learning math necessitates the ability to read, making it appropriate to understand the
mental processes involved with reading comprehension. When we read a text, our brains create a
mental representation of the information.27
The most basic, trivial model of this mental
representation is a network of associations, like a tree diagram, with connections between all
related ideas and concepts, the width of the connecting lines representing the strength of the
association. The stronger, and more widely accepted model divides the associations into three
different levels: the surface component, the text-base, and the situation model.28
The surface
component, just as it sounds, is composed of the words and phrases which are encoded in the
brain, but free from their actual meaning. This specification means a representation with a strong
surface component may include exact wording or phrasing, but without any sort of understanding
of the text. The next level, the textbase, contains the meaning of the text as understood by the
reader. This distinction means that the information we take away from the text, whether it be
accurate or full of reading errors, is included at this level. Finally, the situation model is made up
of all the appropriate prior knowledge that helps to connect ideas in the mental representation.
27
Österholm, Magnus. 2006. “Characterizing Reading Comprehension of Mathematical Texts.” Educational Studies in
Mathematics 63 (3) (Nov.): 325-46.
28
Ibid

12
The situation model essentially integrates a reader’s relevant knowledge with the information
that becomes stored in the textbase.29
This model of reading comprehension, which has been verified by many studies, should
hold true for reading mathematical texts, as well as literature. In fact, a study has shown that the
content of the material makes less difference on reading comprehension than the use of symbols
in a text.30
This difference will be discussed in further detail later on. However, since we can
confidently assume that the reading comprehension of mathematical texts can be similarly
associated with literary texts, it would logically follow that connections can be made not only
with mathematical ideas, but literary ones as well. For example, should a student encounter a
problem in math class similar to one they have come across while reading, when they have
developed appropriate comprehension skills, strong connections and associations should already
exist, helping him or her overcome the distraction of math anxiety and better problem-solve how
to come up with a solution. The benefits of mixing these two disciplines are strong enough that
the National Council of Teachers of Mathematics (NCTM), and the International Reading
Association (IRA), as well as many state standards, often encourage, or even require, reading
across the curriculum.31
They even place a special emphasis on the use and understanding of
specific mathematical language, which can be found in a multitude of age-appropriate books.
When students are exposed to these mathematical terms outside of the classroom, and see them
being used in the real world, it becomes easier to see the applications of the material; an
important step in spurring student excitement about mathematics.
29
Ibid
30
Österholm, “Reading Comprehension,” 325-46.
31
Wallace, Faith H., Mary AnnaEvans, and Megan Stein. 2011. “Geometry Sleuthing in Literature.” Mathematics Teaching in
the Middle School 17 (3) (October): 154-9.

13
Aside from being a necessary skill to actually perform mathematics, reading can similarly
function in many other ways that can boost student learning, especially in an “inquiry-based”
classroom environment. As more and more teachers begin to utilize constructivist teaching
methods, the added skill of reading can greatly enhance a student’s experience with the material.
Constructivism is a learning theory that believes humans learn primarily through exploration,
experience, and reflection. Research performed at Cornell University’s Department of Human
Development agrees with this belief; their studies show that most people begin learning in this
manner as young as infancy.32
Cornell’s Tamar Kushnir says that babies formulate questions and
theories, then test these theories and draw conclusions from their findings. They learn by
exploring the world around them through experience. These results align perfectly with the
constructivist theory. Since humans already appear to be learning in a constructivist manner from
birth, it seems appropriate to continue this manner of learning throughout a student’s time in
school, and the math classroom should be no different.
Though it may be difficult to continuously implement, given the amount of information
necessary to learn in courses such as algebra and calculus, when lessons are planned in a
constructivist manner, the type of learning becomes deeper and more enrooted, giving the
students a better understanding than they would receive through mere repetition. Inquiry-based
learning resonates perfectly with the rise in popularity of this learning theory. Inquiry is defined
by Charles Saunders Peirce and John Dewey, two early 20th century mathematicians who helped
reform math education, as “the process of settling doubt and fixing belief within a community.”33
Many teachers are beginning to utilize this philosophy in their classrooms, replacing the
32
Kushnir, Tamar. “Learning About How Young Children Learn.” Cornell.edu (2011) Ithaca, New York: Cornell University.
Accessed October 2013.
33
Siegel, Marjorie, Raffaella Borasi, and Judith Fonzi. 1998. “SupportingStudents' Mathematical Inquiries Through Reading.”
Journal for Research in Mathematics Education 29 (4) (Jul.): 378-413.

14
commonly used “techniques curriculum,” which portrays math as a collection of facts and
procedures. This style of teaching reinforces the commonly held myths about learning math
which are counterproductive for learners who see the subject as boring, repetitive, and concrete
in nature.
Inquiry-based learning, on the other hand, encourages students to get involved in the
“experience” of math. As Marjorie Siegel of Columbia University puts it, inquiry learning allows
the learners to “experience and appreciate first hand the ambiguity, nonlinearity, and ‘conscious
guessing’ associated with the mathematical thinking of professional mathematicians.”34
When
teachers take advantage of this capability, they can present math in its natural and true form, one
which involves creativity and problem solving, in addition to the equations and formulas which
are also associated. As demonstrated by the popularity and success of programs such as the Math
Circle, which take full advantage of constructivism, it seems appropriate that math classrooms
that operate in a similar manner would meet equal amounts of success.
A distinct advantage of these classes is that reading opens up a whole world of
opportunities for learning. Language as a whole becomes incredibly important to the learning
process, as meanings and representations are created in the learners’ world. As opposed to
traditional math classrooms where techniques and formulas are merely explained and repeated,
students need to communicate to formulate their own meaning and understanding. Language
becomes more than just a channel through which previously existing knowledge can be
transferred, language becomes a powerful tool.35
As alluded to earlier, in a traditional classroom,
reading is often viewed as an obstacle; though it is necessary to reach the “expert’s message,”
one can only interpret this message if they have proper reading skills. Writing, then, is the means
34
Siegel, “Students' Inquiries,” 378-413.
35
Ibid

15
of demonstrating what has been learned. On the other hand, in the appropriate classroom
environment, specifically a more inquiry-based one, reading, writing, and even speaking can take
on new roles which will actually enhance a student’s experience with the subject, giving them
even more knowledge than other classroom formats could offer.
So what is “knowledge” exactly? Looking to the study of the natural sciences, and the
process involved, most modern scholars have rejected the belief that knowledge is a stable mass
of information, and instead replaced it with the belief that knowledge is a “dynamic process of
inquiry in which the doubt arising from an anomaly sets in motion the struggle to settle doubt
and fix belief.”36
The scientific processes of learning and forming knowledge can apply just as
well to mathematics as any of the other sciences. So classes which operate through inquiry allow
the students to be active members helping discover knowledge in the field of mathematics. Much
like labs in science which involve testing hypotheses and experimentation to discover new
knowledge, so too can a math class allow students to discover knowledge for themselves. It only
requires an environment that encourages this type of learning. The assumptions which define a
classroom as inquiry-based are:
1- Knowledge is reflexively constructed through a process of inquiry that is
motivated by ambiguity, anomalies, and contradictions and undertaken within a
community of practice
2- Learning is a generative process of meaning-making, requiring both social
interaction and personal construction in a purposeful situation.
3- Teaching is establishing a rich environment for inquiry and establishing the
conditions that support a community of learners.37
36
37
Ibid

16
Of course, these assumptions must be understood as contributing to a long-term
engagement with the subject. While brief encounters will still be beneficial, it is through the
continued implementation of this process which will transform students from passive learners
into active participants in unveiling mathematical knowledge. Similarly, it should be noted that
executing this philosophy requires a lot of effort on the part of the teachers who have to carefully
plan lessons, while also being very flexible and patient as the students make most of the progress
on their own. And, because the popularity of this belief is relatively new, there are not as many
resources to help teachers, as there are for other learning styles. However, the benefits from this
type of learning still remain, and students will have a much better appreciation and
understanding of the subject upon completion of the class.
Dr. Siegel proposes inquiry cycles as one possible way to help cultivate this type of
learning environment. An inquiry cycle is comprised of four stages: problem sensing, problem
formation, search, and resolution.38
As mentioned above, doubt plays a major role in this process
as anomalies, and contradictions lead to questions and eventual exploration of the topic. In a
classroom, the students become the focal point. They are the primary members and explorers
who all share responsibility in helping decide how to proceed with the inquiry, and reaching
eventual conclusions from their exploration. Expanding on the basic stages of an inquiry-cycle to
be more accommodating for mathematics, Dr. Siegel presented the steps of a “mathematics
inquiry cycle” to be used in a classroom: “setting the stage; developing and focusing one’s
question; identifying appropriate approaches, resources, and tools for exploring the question;
carrying out the research; collaborating with other inquirers; reflecting on and expanding the
results of one’s inquiry; communicating with outside audiences; identifying problems and
38

17
planning strategy instruction; and offering invitations for new beginnings.”39
As the study was
carried through, these steps were then regrouped and morphed into four chronological phases,
“Setting the stage and focusing the inquiry, carrying out the inquiry, synthesizing and
communicating results from the inquiry, and taking stock and looking ahead.”40
So how does reading come into play in these types of math classrooms? What does
reading have to do with inquiry-cycles? In the study performed by Dr. Siegel, along with two
University of Rochester Professors Dr. Raffaella Borasi and Dr. Judith Fonzi, they operated
under the assumption that literacy skills of reading, writing, and talking offer a range of
opportunities for students to become engaged in the inquiry-cycle. In a 1975 study, linguist Dr.
Michael Halliday found that language serves at least seven different functions in our lives
(instrumental, regulatory, interactional, personal, heuristic, imaginative, and informative).41
Our
education system, however, tends to heavily emphasize the informative function, allowing the
remainder of the functions to fall on the wayside. Language educators, as a result, have begun to
call for instructional environments that provide students with more opportunities which allow
them to use reading, writing, and talking for purposes that reflected the nature of language
outside of the school setting.
In a similar study, linguist Dr. Shirley Heath identified a variety of functions that reading
and writing serve outside of classroom settings such as building and maintaining relationships,
learning about the news, enjoyment, or accomplishing an array of simple tasks (paperwork
e.g.).42
Most of these functions are taken for granted in our daily lives. In the classroom,
however, the roles of reading and writing tend to be aimed primarily at accomplishing the same
39
Ibid
40
41
Ibid
42
Ibid

18
repeated tasks, namely we read for meaning, and write to communicate our learning. Again, as a
result, language educators called for learning environments which helped bridge the gap between
reading and writing functions in the outside world, and in a classroom setting. Bridging both
gaps addressed in these studies demonstrate that the uses of language and literacy in math
classrooms is far more expansive than was ever previously considered. Reading, of course, as
argued in this essay, needs to be expanded beyond the typical notion of reading that is applied in
math classrooms. It goes beyond learning mathematical symbols and gaining strategies for
tackling word problems, to encompass all sorts of math-related texts including but not limited to
historical essays, diagrams or even literature.
Looking at one case study of an inquiry-cycle used in a classroom, the added value from
reading becomes incredibly apparent. In fact, after the completion of the study, there were 30
various functions of reading that were identified, 27 of which were all present in just one of the
three observed courses: the narrative of the “Taxi-Geometry.”43
This unit was a part of a
semester-long course entitled “Alternative Geometries” offered at an alternative urban public
high school. The students were 10th – 12th graders who had completed at least two high school
level math courses, and had all been previously exposed to reading strategies encouraging sense-
making and discussions. Taxi-geometry, as suggested by its name, is
made up of a grid where only horizontal and vertical movements are
allowed (like a taxi-driver navigating blocks in a big city).44
Although
this world seems trivial enough, as it essentially simplifies the real
world, many aspects of geometry that we take for granted no longer
hold. For example, the shortest distance between two points is rarely a
43
44
Ibid
Figure1: As can be noted,
all three paths above are of
equallength,thus all three
could be considered the
shortest distance

19
straight line (see figure 1). The shortest path would only be a straight line if the given points
were perfectly vertical or horizontal to one another, otherwise, alternative steps up or down
would be necessary, and often times there would be multiple “shortest paths.” Because this
situation is easily graspable, the student’s challenges arise from their mathematical
understanding of definitions, formulas, proofs, and truth, rather than from a conceptual
understanding of the material. The simplicity of the taxi-geometry scenario similarly allowed for
more time on reflection, and was later used as a springboard for other mathematical explorations
later in the semester. Of course, it should be noted, that this structure was designed for these
exact purposes.
In the first phase of this process, setting the stage and focusing the inquiry, students were
asked to answer questions which made them reflect on some mathematical concepts and issues
that they most likely wouldn’t encounter on their own. Already, a function of reading
(challenging student’s initial concepts and knowledge of the topic being explored) reared its
head.45
The next step in this phase involved reading even more directly. The class spent several
periods reading an essay, “Beyond Straight Lines,” by J Sheedy, which discussed his own
explorations with the subject. In the essay, Sheedy even addressed his discomfort with the idea
of alternate geometries and gave a reassurance that this discomfort is a natural stage in the math
exploration process. This reading not only demonstrated to students that it is normal to encounter
hesitations and concerns in the process they are about to engage in, but it also introduced the
subject to the class – generating interest and knowledge of the subject they were about to
explore.46
Both of these demonstrations were later categorized into 2 of the 30 formal reading
functions in the inquiry-based learning math classrooms.
45
46
Ibid

20
Rather than reading the essay at once in its entirety, the students read smaller sections at a
time, using specifically-chosen assigned reading strategies, such as writing a journal response, or
reading aloud to another student, to help them benefit the most from the experience. Some of the
following notes from students after the completion of the exercise demonstrate the “richness of
the thinking generated by this reading activity.”
Jolea – Who is to determine the accuracy and what becomes law in math?
Math is humane just like us in the respect that it changes because it is not always
complete and accurate
Char – “Completeness and perfection are ideals” [-] that kind o struck me as really
Interesting. It’s true now that I think of it, but I never realized it before.47
The next reading in the class was a fictional story, “Moving Around the City,” again by J
Sheedy, where the protagonist navigates a grid-patterned city and encounters several problems,
specifically the non-intuitive consequences of the geometry in this world.48
Rather than have the
students merely read the whole story again, the solutions to the problems were removed from the
text, allowing the students to try and solve them for themselves first, and again write a journal to
reflect on their experience. During the discussion of reflection, one student claimed that this
geometry was the same, just with a new rule – leading to the first in depth exploration of the
subject – is this geometry our normal geometry with a new rule, or a completely new one by
itself? The proceeding discussion led the students to their first inquiry, “what do familiar shapes
look like in this world?” Through reading and responding to the appropriate texts, the students
stumbled upon a subject that they found exciting and worthy of further investigation,
demonstrating the ability of literature to grab students’ interests and, again, revealing another
47
48
Ibid

21
formal function of reading in a mathematics classroom; to generate specific questions and
conjectures, and find resources to help make sense of these conjectures.49
Soon the class came to a fork in the road, and stumbled upon an incredibly important, and
oftentimes necessary, skill to have in mathematics: interpreting a definition. The class, trying to
make sense of a circle in this world, encountered the textbook definition that defined a circle as
“a set of points in a plane that are a given distance from a given point [the center] in a plane.”50
Of course, this definition also needed to take into account the means of measuring distance in
this world, which again meant travelling only in straight horizontal or vertical lines, and not “as
the crow flies.” Eventually the students reached a consensus about the new image of a circle in
this world (see figure 2). This investigation forced the students to think deeply about the use of
definitions in mathematics, and as mentioned by Sheedy, doubtful results; i.e. for example,
following the definition of a circle, the resulting shape is no longer round.51
Student’s eventual excitement with this discovery led them to the
formulation of more inquiries with regards to what other shapes would look
like in this world, and what other means of measuring distance exist. Little
did they know, this seemingly simple concept of measuring distance is
actually a branch of topology where different systems of measuring distance
are referred to as metric spaces. Keeping on top of student interest, the instructor provided more
readings about these subjects, several of which left much to be desired by the students who then
took researching into their own hands.
Finally, holding true to a constructivist-teaching format, the students were given control
over the conditions of their final project for the unit. One student built a geoboard, two others
49
Ibid
50
51
Ibid
Figure2: A circle of
radius 2 in a taxi-cab
geometry

22
constructed a “taxi-globe” by rotating a taxi-circle around the vertical axis to construct a three
dimensional figure. Another student, inspired by the story “Moving Around the City” wrote his
own story about a similar city and read it aloud to his classmates. In all of these examples,
students used some form of “reading” (being loose with the definition of reading to also include
diagrams and other nonverbal texts) to come full circle and demonstrate their understanding of
the material and present results from their investigation.52
Students were then presented with a few more articles to read in tandem with their
reflection on the experience. They were asked to answer questions about the readings, and the
impact they had on their exploration. Reading strategies that the teacher had encouraged were
brought up again as a reminder, and then they were asked how effective they felt each strategy
had been. The answers to the question “What did reading this story [Moving around the City] do
for us?”, which were posted on a wall along with much of the student’s other work, included
responses such as: helping understand the geometry better, made the student think about how a
city is planned, and helped pique student interest by putting them in the shoes of the protagonist
trying to solve the encountered problems.53
During this discussion, the question of what would
happen if the surface were a sphere, as opposed to a flat grid led perfectly into another inquiry
cycle – one in which students even drew from their own sources to help make sense of the new
problems posed in the readings handed out by the instructor. Thus the new inquiry cycle began.
Along the entire course of the taxi-geometry inquiry cycle, many more functions of
reading were discovered and recorded, only a few of which were alluded to in this overview of
the study. In fact, all but 3 of the 30 defined reading functions were identified somewhere in the
three different inquiry cycles observed for the study, and both of the other two other cycles (not
52
53
Ibid

23
discussed in this paper) included at least 15 functions.54
The abundance of these functions
indicates the important connection between reading and mathematics that is present, especially in
inquiry-based classrooms.
Upon a completion of the study, the list of observed functions was grouped into two
distinct parts: chronological and embedded. The chronological functions were connected to
specific stages in the cycle, whereas embedded functions cut across the stages and were present
throughout.55
Both groups could find a place in any mathematics classroom. One could certainly
argue that many of the functions primarily help to construct and carry out the inquiry cycle, for
example using articles to inspire students to create their own investigations, or reflecting on the
inquiry process. While some of these may not be as useful outside the setting of an inquiry cycle,
there were many other functions which transcend the classroom context. Many would work just
as well in a traditional, non-constructivist classroom. Reading to both generate interest and gain
background knowledge, for example, was prevalent in the study and could easily be generalized
to a larger audience when trying to introduce new ideas or concepts to students. Similarly, many
of the readings helped encourage students when they ran into doubt or frustrations, since they
were shown many other people who encountered similar difficulties. And in case those two
benefits weren’t enough, the readings also addressed a deeply-rooted problem with mathematics
by encouraging students to “rethink their conceptions of mathematics and learning mathematics
by appreciating the humanistic dimensions of this discipline.”56
In spite of the cultural
perceptions of the subject, through reading, students can begin to see math in a new light; as a
discipline which goes beyond mere formulas and calculations.
54
55
Ibid
56
Ibid 400

24
After completion of the study, during a reflection on their work, the researchers Dr.
Siegel, Dr. Borasi and Dr. Fonzi also found that the functions of reading used in the math
classroom also aligned with many reading theories as well. For example, Dr. Louise Rosenblatt’s
transactional theory of reading, a reader-response theory which places importance on individual
reading and interpretation, “provide[s] an apt description of reading experiences identified in
Setting the Stage and Focusing the Inquiry.”57
At this early stage of the Inquiry-cycle, the
primary objective of the texts was personal exploration through prior knowledge and personal
experience which, ideally, leads to questions for inquiry. These types of reader-response theories
are also present in the final stages of the cycle dealing with reflection and potential future topics
for investigation. Since everyone interacts with the texts in a unique manner, each individual’s
reflection and interests will lead to a diverse exploration of the topics being addressed. And
similarly, each one of the embedded functions was associated with specific reading practices laid
out in earlier research.
The problem with this observation, however, lies in the fact that our education system
places the most (if not all) of the emphasis of math education on what is essentially the carrying
out the inquiry stage. The reading which takes place during this time tends to be more technical
and text-based, which is where most analysis of math-reading takes place; researchers spend
most of their time trying to figure out how students understand the content of their math books
and similar texts. While this type of reading is important, and does account for most of the
reading which takes place in traditional math courses, it doesn’t account for many of the possible
benefits which can be gained if we implement these reading functions in the classroom. There is
still much to investigate with regards to bringing literature into the classroom, but already we
57

25
have shown that there are many more connections between the two subjects than most people
would imagine.
That being said, there still remains the concern that reading only works in an inquiry-
based setting. Before directly addressing that issue, it should be noted that in this example,
reading was not a supplementary activity but rather the primary focus. It was the entire means of
carrying out the inquiry cycle, thus the classroom learning only occurred because of the reading,
and without it, no investigations would have taken place. Reading played a role at each stage in
the cycle, helping drive the investigation forward and continually keeping the students engaged
with the material. So when the students in this course gained an appreciation for the subject and
became more fluent in mathematics, they did so solely through the context of reading. One could
certainly argue that this context is specialized, and one could similarly argue that reading isn’t
necessary for students to learn. Both of these arguments are valid, though it is clear that in this
case study, the reading was more than effective, it was the entire foundation of the learning, and
to ignore the numerous benefits to be gained would be foolish. Teachers could certainly continue
teaching without implementing reading into their classroom, but I believe that by doing so, they
are missing out on major instructional opportunities for their students.
~~~
Having explored the pre-existing connections between reading and mathematics, I would
now like to begin a more thorough investigation into the possible benefits of this relationship. To
recount, I want to examine mathematics classrooms at the three primary stages in which I
divided our mathematical learning into: elementary, where we are just beginning to grasp
concepts such as shapes and numbers; basic math, which includes standard topics such as algebra
through calculus; and advanced math which encompasses topics like number theory or

26
combinatorics. Similarly, I argued that there are a couple ways, at each level, in which literature
can be brought into the classroom, and I would now like to begin exploring this claim.
Perhaps the most important time period to begin developing student’s fascination with
mathematics would be at the elementary level. If students are introduced to mathematics in ways
that draws them in, it will be much easier to keep them interested. This would ease the challenge
of convincing students that math can be interesting after they have developed a dislike for it. In
fact, making this introduction at the elementary level actually allows for some of the most
interesting elements of math to be explored in fun and non-formulaic ways. Early on in students’
mathematical experience, each aspect they encounter is new and exciting, and their
understanding of arithmetic will be minimal at best. This blank slate of knowledge offers up the
perfect opportunity to make math appealing, giving students a positive first experience.
The typical pattern of learning mathematics, specifically arithmetic, begins by using
physical objects, allowing the students to interact with the world while they are learning.58
When
children can feel, see, and interact with the concrete objects, they can more easily make
connections with the ideas. Early on in their education, most students will have participated in
some sort of activity which involved counting and moving around blocks or tiles, helping them
understand the connection between the abstract numbers and the physical objects they are
manipulating. The idea of “two,” for example, only makes sense if kids have two objects to
associate the idea with (aka two things to count). The next common step moves away from
concrete objects, onto pictorial representations.59
This small step is the first level of abstraction
from the concrete world. The students have images they can count and manipulate, but the
images are not actual things, a difference which takes time getting used to.
58
Lowe, Joy L. Matthew,Kathryn I. 2000. “Exploring Math with Literature.” Book Links 9 (5) (05): 58-59.
59
Ibid

27
Continuing along this process of learning mathematics, children are introduced to another
abstract concept, numerals (1,2,3, etc).60
Most often, the first interaction with these symbols deals
with counting purposes – assigning meaning to the arbitrary figures – because the leap from
physical/countable objects to a symbolic representation can be a big one. In fact, even after many
students have become familiar with this abstraction, many of them will continue to rely on
concrete visualizations as they make the move towards basic arithmetic. Greg Tang observed
students learning addition in classrooms with dominoes were actually counting the number of
dots on the dominoes to reach the final sum, rather than simply adding the numbers together.61
Likewise, we can all attest to witnessing young children still counting on their fingers rather than
performing mental math in their head. This step is, of course, the final prerequisite to mastering
basic arithmetic, and it requires a wholly abstract grasp on what is occurring. There is no
physical connection between the symbol 4, and four apples on a table, aside from the meaning
which human kind has given to the symbol 4, or the word “four.” This should be obvious since
the words “cuatro,” in Spanish, or “cat” in French both have the same meaning, but share no
physical or harmonic similarities.62
Or the various ways we can print the number 4, such as
roman numerals IV, or the Chinese character 四, the only similarity between these symbols and
sounds is the significance of their human-assigned meaning. The process of performing
mathematics has made its first step entirely out of the concrete world, and into one of abstraction.
The importance of this fact is that very early in the learning process, visuals and imagery
already play major roles. This means something as simple as using pictures, which appeal to the
60
Lowe, “Exploring Math,”58-59.
61
62
Saussure, Ferdinand de. Course in general linguistics. New York: Philosophical Library, 1959: 80-90

28
students, can help draw them in and keep them interested.63
And what better way to introduce
these math concepts visually than in children’s literature? Not only can these books use
illustrations to grab student’s attention, they can also place the math concepts in real-world
situations that the characters find themselves in. As mentioned above, this method of combining
math and English involves literature based on mathematical concepts, and there is far from a
shortage of these types of books. Another major benefit is that there is sure to be some book on
every introductory math concept; from counting to pattern recognition, from shapes to grouping
digits, some children’s book covers it. In fact, there is a book series dedicated to just this goal of
blending math with literature. The Hello Reader! Math series contains dozens of books for
various levels of math ability, covering preschool through first grade.64
And each children’s
book, regardless of whether they are in the Hello Reader or not, comes fully equipped with
illustrations to further demonstrate the math concepts being introduced.
A perfect example of this type of synthesis for elementary level mathematics is Big
Numbers and Pictures that Show Just How BIG They Are, by Edward Packard. Dealing with the
concept of large numbers, the book follows the common thread of a pea to illustrate how big
numbers can get.65
Pete, the main character, first sees one individual pea on a plate, followed by
10 peas on the next page, then 100, until there are 100,000 peas overflowing onto the table. This
visualization brings the readers back to the stage of pictorial representations, and even though
they are unlikely to count all 100,000 peas, the image still drives home the message; 100,000 is a
very large number. To further illustrate this concept, Packard has Pete, accompanied by his dog
and cat, travel out to the moon (240,000 miles away) and eventually even further. The threesome
goes far enough into space to eventually allude to the idea of infinity. At a certain point, after
63
64
Hopkins, Gary. "Math and Reading Do Mix!" Education World.
65
Ibid

29
travelling far enough into outer space (10 to the 27th power miles away) they all look back
towards the Earth, which now looks like the size of a pea.
While travelling in a space ship thousands of miles may not be something children are
going to experience in their own daily lives, many other books contain elements which show the
kids how people encounter math in everyday life as well. Seeing the math concepts in the real
world helps them understand math and its importance. It is worth noting here that it is essential
for the books to first be read for pleasure, and to later introduce the mathematics and problem
solving.66
This way the books can be enjoyed for what they are, fun children’s books, rather than
becoming a chore. If, however, children aren’t interested in math-related books at a young age,
there is still another strategy to introduce the same ideas; taking non-mathematical books and
extracting mathematical concepts from them.
With a little bit of creativity, any children’s book can become a source of inspiration for a
number of math related activities. For example, a favorite among many children, The Giving
Tree, by Shel Silverstein has a universal appeal across the world, and has been translated into
over a dozen different languages. Using the appeal of this book as a springboard, teachers and
parents alike could create activities stemming from events in the story. For instance, at one point
the young boy in the story picks all of the tree’s apples to sell them for money. After reading the
book, an activity dealing with apple counting or figuring out the finances of selling the apples
could easily rear its head. The benefits of this synthesis is that no matter what types of books
interest a child, some element of math can be found inside it. Utilizing the internet can expedite
the whole process, as thousands of sample activities already exist, and can be found merely by
Googling the book’s title and “math activity” afterwards. Hundreds of ideas and samples can be
found with almost no effort at all.
66
Lowe, “Exploring Math,”58-59.

30
As mentioned earlier, this stage of learning is the most crucial, but also the easiest to
improve. Greg Tang acknowledges that when he visits schools and takes polls of who loves
math, nearly all young kids will raise their hands. It is only when they get older and begin the
second stage of math understanding that they begin to dislike it.67
What this indicates is that at
one time, almost everyone loves math. If we take advantage of this by encouraging students to
not just read, but to read math related books, then the beauty and mystery of abstract math
concepts, and the fun of problem solving that arises from these concepts will present themselves
to the children. Or, on the other hand, if teachers can tailor assignments towards students’
previously existing fascinations, they can construct math related activities from non-
mathematical stories, exhibiting some applications in the real world and, again, demonstrating
the fun that exists in the subject.
The importance of enhancing a child’s pre-existing fascination with the world of
mathematics increases due to the following stage of mathematic development, namely the basic
mathematics concepts. This stage includes all the math one is likely to study from roughly 2nd
grade through the end of high school: algebra, geometry, trigonometry, statistics, pre-calculus,
and eventually calculus. Some, or rather many, students will not even complete all of these
foundational courses, and for those who do, it is very often the case that they don’t finish them
all until college. Unfortunately, this stage is where most students begin to despise math, and the
separation between students who “understand math” and those who don’t becomes established
and solidified. With a firm introduction to mathematics through children’s literature, students at
this stage should no longer need to be convinced that they can enjoy the subject, rather they will
merely need to maintain that viewpoint. Again, using literature can be a way to keep students
interested and engaged.
67

31
Before addressing the benefits which can be gained at this level of math education, I
think it would be helpful to first look into the reason many students begin to dislike the subject
all together. As mentioned earlier, the cultural view on math remains the same, “math is
difficult.” When adults claim to dislike math, their children are very likely to adopt this similar
attitude, meaning it can be difficult to entice a student who has pre-determined they will not
enjoy the subject.68
Especially after the enchantment of math at younger ages wears off, students
are more prone to join the masses in the revolt against the pleasures of math. Similarly, because
of the nature of most of these concepts, it can be very difficult for a teacher to inspire learning in
the students. There are so many rules and formulas to memorize, all of which lack the attractive
creativity of real mathematics. As Greg Tang, and the Kaplans have hypothesized, it could very
well be the manner of instruction that makes kids lose interest.
Even if the problem lies more with the content than the teaching procedure, there is still a
necessity to revise and improve the method of teaching mathematics, specifically, with regards to
reading math textbooks. In a 2006 study, Magnus Österholm of University of Umeå, revealed
that reading mathematical texts with symbols requires a different set of skills than normal
reading comprehension.69
Their investigation was inspired by the universality of textbooks used
to teach mathematics, and the common use of symbols inside these texts. Prior to this study,
most studies of math comprehension focused primarily on the problem-solving aspect of math,
and tackled their research with the mindset that reading more often presented an opportunity for
misinterpretation and misunderstanding. What Österholm wanted to argue, on the other hand, is
that reading comprehension could be viewed as an essential part of math ability, rather than a
weak relation of it.
68
Hopkins, Gary. "Math and Reading Do Mix!"
69

32
The procedure of the study was to let students read a one-page math text about group
theory with either symbols or natural language explanations, and were all also given a one page
historical text. After each reading, the subjects were then given a test of their reading
comprehension. The data collected took into account outside factors such as prior knowledge,
college or high school enrollment, etc., and they judged the results by recreating “mental
representations” (as defined earlier) based on student responses to the post-reading questions.
The results showed that reading comprehension of the math text without symbols was highly
correlated with reading comprehension of the history text, but not related to the math text with
symbols.70
What this relationship demonstrates is that the content of the text makes no difference
with regards to comprehension, and suggests that we need another whole skill set when we read
texts with symbols in them (essentially every single math textbook).
Although the reasons for this difference is unclear, there are several possibilities that
Österholm presented. One of them relates to our expectation when we see symbols in a text.
When symbols are on the page, we more often expect some sort of procedural demonstration to
follow, which we internalize differently. Another hypothesis was since symbols can be used in so
many different contexts, our brains need to figure out which context we find ourselves in at
every encounter. Or another possible explanation is because humans have a tendency to skip
over the parts of texts containing symbols with the intention of returning to them later. These
theories all have some potential truth to them, however as Österholm admits, more research on
this would be necessary before reaching any solid conclusions. The article did make clear the
researchers do not mean to suggest that math texts should only be printed in natural language.
The use of symbols in mathematics, Österholm says, is necessary and a major advantage of the
subject. Rather than changing our texts, it would be more beneficial (and practical) to recognize
70

33
the other skills necessary, and help students to develop this ability. In this way, reading and math
would both benefit. I propose that bringing more literature into math classrooms would be an
excellent way to increase this skill.
Following the same pattern set out, the first strategy to synthesize math and literature is to
have students read texts that revolve around and introduce mathematical concepts. The trouble
here is that often books of this type are not nearly as abundant as with introductory level
concepts. Algebra does not always make for the most exciting plot lines, whereas the extensive
amount of freedom in young children’s books make for an easier synthesis. It has been done,
however. The book, “Do the Math; Secrets, Lies and Algebra,” by Wendy Lichtman has taken a
stab at this daunting task.71
The main character in the book, Tess, likes the concreteness of math
but has her world shaken a bit with the introduction of variables in her classes. But, as she begins
to learn algebra, she begins applying things she learned in class to her everyday life. Though the
book is a little juvenile (it would probably not be well received by high school seniors for
example), it does introduce algebra in a purely literary form. Not only does it provide an
opportunity to springboard out of the book into a discussion of algebra, it also demonstrates real
world applications of the subject. This means that before students have time to ask, “when will I
ever need to know this,” they will already have some examples floating around in their head.
At the intermediate stage of math development, the line between books about math
concepts, and extracting math from non-mathematical texts becomes blurred. The concepts being
learned do not necessarily inspire very exciting stories, but minor examples of math can be found
in an array of books for all reading levels. Whether these should be grouped together with the
literature about math, or with examples from non-mathematical texts is not a crucial distinction
71
Pestro, Annie. 2008. Mathematics Teaching in the Middle School 14 (1) (AUGUST):p. 63.

34
though, as the eventual goal remains the same. Many books are full of mathematics, which could
help inspire and interest in mathematics of some sort. Some examples include The DaVinci
Code, Flatland, or even Sherlock Holmes.
To look specifically into one area of mathematics, geometry, there are numerous
examples of age-appropriate books chock full of real world examples of math problems. Take,
for example, Sherlock Holmes, specifically the story Adventure of Musgrave Ritual. In this
particular story, Sherlock Holmes uses geometry to help recreate one of his old classmate’s
family rituals, to better understand its significance. Using mathematical terms such as “parallel,”
“fixed point,” and even “trigonometry,” the story makes no attempt at hiding the importance of
math in solving the case. Actual geometric calculations are even used in the story itself; “If a rod
of six feet threw a shadow of nine, a tree of sixty-four feet would throw one of ninety six, and the
line of the one would of course be the line of the other."72
Through these types of stories, many teachable moments can arise on their own, helping
to spark students’ interests. Better yet, when the math concepts can already be found in a good
story, the material can be seamlessly woven into the classroom. These stories show how math
terms can be used naturally outside of the textbook setting, and the multitude of genres allow all
students to find something that resonates with their pre-existing interests. One way to utilize
these texts for their mathematical connections is through reading strategies, such as “coding the
text.” This reading strategy directs students to make notes, predictions, and other connections
while they read, often encouraging them to use their own math knowledge to problem-solve
before the teacher even becomes involved.73
In the series Crime Files: Four-Minute Forensic
Mysteries, when students used text-coding to record important events and approaches to solve
72
Wallace, “Geometry Sleuthing,” 154-9.
73
Ibid

35
the mysteries, the majority of the noteworthy clues were math-related – meaning that the
students are already beginning to recognize math concepts and their importance in the real world.
Going beyond the in-text applications, however, many other works can inspire other activities to
welcome an even stronger understanding and appreciation of the field of mathematics. In one
example, inspired by the mystery novel Artifacts, teachers Dr. Faith Wallace, Mary Evans, and
Megan Stein set up Cartesian coordinates inside their classrooms and divided the students into
small groups to explore the importance of this seemingly simple concept. They then asked the
students to complete basic tasks such as using coordinates to measure distances (without a ruler),
comparing their results based on the different measurement sizes, and determine the significance
of defining the location of the origin on a coordinate system.74
Activities like this not only allow
the students to recreate the mathematics they encountered in the stories, but also get them
involved in the action of real-life problem solving and applications of mathematics.
Even in middle school or high school when English and mathematics are separated into
completely different classes, teachers still have the opportunity to co-plan lessons and take an
interdisciplinary approach; something that is already highly encouraged in Middle Schools
across the country. As the National Council of Teachers of Mathematics (NCTM) says,
opportunities for interesting math problems can be found in all sorts of everyday experiences,
including reading.75
This inspired Donna Christy, EdD from Boston University, and her
colleagues at Rhode Island College to compile a list of books, and math activities stemming from
them, with hopes of inspiring other teachers to follow suit. The way they see it, both subjects will
benefit from this relationship. The activities and assignments would enhance the experience of
the students who have read the books, and potentially motivate those who haven’t to read it on
74
75
Christy, Donna, Christine Payson, and Patricia Carnevale. 2013. “TheBridge to Mathematics and Literature.” Mathematics
Teaching in the Middle School 18 (9) (May):572-7.

36
their own.76
Since these activities do not require the students to have already read the books – as
long as the teachers are careful not to spoil anything from the story – both English and math
teachers alike have something to gain. As Christy puts it, integrating math and literature presents
the opportunity to “ignite the imagination and creativity of students and teachers.”
The four examples that are given in their article are The Westing Game, The BFG, The
Red Pyramid, and The Hunger Games; none of which make explicit references to mathematics,
unlike the texts mentioned above. The sample activities, though, still meet both NCTM standards
as well as Common Core State Standards (listed in the article), demonstrating the possibility of
beneficial activities inspired from the text.77
Looking at the Hunger Games, for example, Christy
and her colleagues used a scene where two characters, Katniss and Rue, are hiding in the treetops
with their gear and food. The activity sheet provided, which prints the passage on the top, then
creates a scenario where their total weight is being balanced between two halves of the tree. The
student’s job is to figure out the unknown weight of the food and supplies when the weights of
Katniss, Rue, water, medicine, and weapons are given. This basic algebra problem hardly
resembles the formulaic equation sheets that most students would likely be used to seeing,
making the assignment more enjoyable and less of an abstraction. As a more concrete example, it
will help students better understand, since, as discussed previously, math is first learned through
real-world examples before it becomes abstracted. Returning occasionally to tangible problems
will help reinforce the concepts being taught.
As previously stated, this stage of math development is the most important for students
learning the subject. The knowledge that the students acquire in algebra, geometry, and even
calculus will be utilized in all sorts of areas that many would never have even considered. Nearly
76
Christy, “Bridge to Mathematics and Literature,” 572-7.
77
Ibid

37
all sciences, computer programming, finances, and even basic business functions require some
level of mathematical understanding; making sure that students don’t take for granted the
information they learn during this stage is crucial to their futures in mathematics. The NCTM
encourages reading across the curriculum, and the reason for this is most likely because reading,
when used appropriately can inspire and enhance student’s experiences in almost all disciplines.78
Programs such as the Math Circle have proven the possibility to stimulate student interest in a
subject that many of them will grow to despise. Since attendance at a Math Circle program is not
an option for every student, as the cost of attendance is expensive and the program locations are
limited, teachers need to utilize other possible means of getting students’ fascinated. Co-
curricular activities, inspired by reading, are this great alternate option that can be utilized by any
teacher in any location.
If student’s are lucky enough to move beyond these foundational courses, or able to take
more advanced/pure math courses simultaneously, then the use of literature becomes less of a
chore, and instead helps enhance the learning by addressing some, for the most part, already
thought-provoking ideas. As David Foster Wallace mentioned in his literature review, the
foundational courses are boring and formulaic. While reading literature may help make the
material more tolerable (for those who don’t enjoy it already), the more advanced stages of
mathematics don’t often require outside sources to make the subject interesting; the material is
already interesting. The skills used at this level include problem solving, imagination and
creativity, as opposed to memorization and calculation. For many people, these topics may no
longer even resemble math. The perception of mathematicians is so misconstrued because people
rarely encounter this aspect of the subject due to the inconvenience of wading through all of the
foundational learning in the intermediate level. What this means for advanced math topics, then,
78

38
is that the use of reading can only help to inspire new ideas, enhance explorations, and address
incredibly fascinating ideas already present in the respective fields. Thus I would argue that at
this level of mathematics, though rarely required in an upper division course, classes could
certainly still benefit by integrating math-related literature into the classroom.
For some math-averted students, there already exists the perfect amalgamation of math
and literature at Arcadia University in a course that can either fulfill a core requirement or be
taken out of pure enjoyment. The class “Truth and Beauty: Mathematics in Literature,” which
counts as either math or literature credit, was initiated by Marion Cohen who claims that while
science has led to the genre science-fiction, math has similarly led to an analogous genre.79
The
goal of her course is not to teach mathematics through literature, but rather to use literature to
cultivate an appreciation for the subject, with hopes that students will learn a little bit of math
along the way. Going beyond novels and stories, Cohen even utilizes poetry in the second half of
the semester. She claims, surprisingly, that the amount of material to draw from, for both fiction
and poetry, is incredibly extensive. She has taken things from various anthologies of the genre
such as Fantasia Mathematica, and Strange Attractors: Poems of Love and Mathematics.80
The
fact that so many examples exist allows her to pick from an array of topics, as well as select
better-written pieces of literature so that neither math nor English has to suffer as a result of the
relationship. Similarly, since the course has no math prerequisites, and many students often have
an aversion to math, Cohen tries to pick math topics which are not too complicated or obscure,
but at the same time are not so trivial that the math majors enrolled in the course become bored.
Each unit begins with reading either a piece of fiction or a poem, which Cohen prints for
every student, so no textbook is required. Initially, the emphasis is focused on the literature
79
Cohen, Marion D. 2013. “Truth and Beauty:Mathematics in Literature.” The Mathematics Teacher 106 (7) (March): 534-9.
80
Cohen, “Truth and Beauty,” 534-9.

39
aspect of the story, as that is more universal and easier to discuss. Then, after the first read-
through, the actual math ideas make their way to the foreground. This occurs first in homework
assignments and eventually in class discussions. Each piece of literature that students read comes
with two assignments, one literature-based one math-based, and the class culminates with a
project where students compose their own poem or short story dealing with math. In her four
years teaching the course, Cohen has found that the whole classroom atmosphere is brightened
by the presence of literature. Her lectures and the class discussions have become so fruitful that
she believes that this strategy (using literature to stimulate student math-interest) could be used
in any math course at any level. Cohen essentially argues that even in high school, middle
school, or elementary school, math classes could follow a very similar path and meet an equal
amount of success. As she states, students are “never too young to experience mathematics in
emotional ways.”81
On the first day of the course, Dr. Cohen begins by reading a story out loud to her
students, easing them into the new class and letting them reflect on what they are hearing. This
activity allows the students to dive into the material without actually demanding very much from
them. The story she favors for this introduction, An Old Arithmetician, written by Mary Eleanor
Wilkins Freeman in 1885, deals with an old woman who has a gift of solving “sums.” Of course,
as a work of fiction, this gift also ends up being a curse; the old woman becomes so absorbed
trying to solve a summation problem that her granddaughter goes missing while she is
distracted.82
Using this story as a catalyst, Cohen immediately asks the class who can tell her the
sum of the first 100 integers? The students immediately begin working on the math problem, and
once they have an answer, Cohen provides them with more problems to solve; the infinite sum
81
82
Freeman,Mary Eleanor Wilkins. An Old Arithmetician. Charlottesville, Va.: University of Virginia Library, 1995.

40
1 + 1 2⁄ +1 4⁄ + 1 8 + ⋯⁄ , and then the more complicated infinite sum 1 + 1 3⁄ +1 9⁄ +
1 27 + ⋯⁄ both of which (as math-inclined students are likely to notice) hint at the geometric
series. Then, as a bonus, for the students who are interested, she mentions that the sum ∑ 1
𝑛2
∞
𝑛=1 =
𝜋2
6
. This structure brilliantly introduces the simple idea of repeated sums.83
Everyone already has
an understanding of addition, and these summations are merely the repetition of this basic
arithmetic idea. Even when Cohen introduces infinite sums, which may be difficult to solve, the
idea is still incredibly graspable. It is also important, of course, to note the entire discussion
originated out of a fictional story.
With some of her other assigned stories, Dr. Cohen has addressed topics including
probability, logic, the Pythagorean theorem, modular arithmetic, all the way up through a brief
mentioning of Godel’s Theorem about the nonexistence of complete axiomatic systems. This
theorem states that no set of axioms (an axiom is an argument that is accepted as true without
proof) is sufficient to prove that all facts are true; a fundamental idea in the philosophy of
mathematics. Running into a theorem like this, which is incredibly complicated to prove but
fairly easy to understand, can certainly be a first step into very high-level abstract mathematical
thinking. Similarly, exposure can lead to an interest in the subject, personal investigations, and
further explorations in related areas of mathematics. If, on the other hand, a student merely finds
the problems boring and monotonous, at the very least they are interacting with the material in a
more exciting manner.
In fact, the culmination of the course, students’ composition of their own work, more
often than not leads to student reflections on their own life-encounters with mathematics. Cohen
tries to keep this conversation, regarding math in the real-world, especially relevant to her
83

41
students’ lives throughout the semester. For example, she asks students about family members
who are math enthusiasts, or to remember their favorite math teachers in high school. To keep
things light, she starts with “life questions” before making the transition back to mathematics in
the students’ lives. As one student explained, “in most courses there’s just one day when the
teacher asks us to talk about ourselves, but by then we’re so burned out… we just don’t want to.
But [she does] that throughout the semester, and [she’s] gotten students who normally don’t talk
much to say things in class.”84
Cohen adds, they don’t just talk about anything, but math things.
Most college math professors are likely to scoff at the suggestion of incorporating an
element of reading to their syllabus. Bringing literature into a class whose focus is on an obscure
concept, such as number theory, would take up valuable class time; especially since every field
of mathematics contains an endless number of rabbit holes for further investigation. Why waste
time putting effort into a completely different subject altogether? This argument is valid since
there is so much information to learn, and so little time to learn it. However, the fact that there
are so many areas for further investigation leads to a perfect argument for bringing in literature.
Students could find topics they wouldn’t normally encounter, or run into questions which pique
their curiosity, on their own. Similarly, bringing in related books don’t necessarily have to take
up as much class time as it did in Cohen’s course. Reading could be an activity to take place
outside of class and be based on student’s own interests. Because there are so many examples of
mathematical literature out there, students could pursue something that they are interested in,
greatly enhancing their experience with the material. Just as middle school teachers are pushing
for interdisciplinary studies by bringing literature into the classroom, so too could college
professors. Even if minimal amount of class time was spent on the actual books, I believe their
mere introduction could still be greatly beneficial.
84

42
David Foster Wallace’s classification of the sub-genre, “math-melodrama,” is just one
example of an additional resource that could help students take more out of the class. The rise in
the popularity, and abundance, of math-inspired media shows that the demand for the material
already exists.85
The success of books like Fermat’s Last Theorem, by Amir Arzel, or even A
Beautiful Mind by Sylvia Nasar further exemplify that people are better relating to the plight of
the mathematician, so why not take advantage of it? The “math-melodrama,” as described by
Wallace, is a sub-genre often depicting the life of a Prometheus-like character who views pure
math as a “mortal quest for divine truth.” This new perception and handling of math could help
inspire students to change their view of the subject. Even in a lower level course, the portrayal of
this eventual goal could give a student a new respect for the subject matter. Then, in an advanced
course, it would help student’s appreciate the material they are about to encounter. As David
Foster Wallace puts it, these books could “bring the subject to life and demonstrate its beauty
and passion. Both readers and math itself stand to gain” (Wallace).
While not all of these books are exactly successful at synthesizing the two subjects, as it
can be difficult, the more mathematical knowledge a student has, the more they “stand to gain”
from reading the book. David Foster Wallace notes the paradox that with many books, the
authors are most likely gearing their texts towards those who would already enjoy the
mathematics. Unfortunately, these people are also the most likely to be disappointed by the way
in which the math concepts are covered. Typically the subject ends up being glossed over,
handled vaguely, or overtly imaginary (which doesn’t have to be a problem, as long at the
writing is good enough to still inspire the same message). However, these novels all still have
something to offer. Even if the math concepts are glossed over, a student could likely gain a
desire to know more; to further their understanding of what is taking place in the book, and their
85
Wallace, “Math Melodrama.” 2263-2267

43
math classroom is the perfect environment for initial inquiry. Thus, when students read these
types of novels while learning about the concepts, they will not only better enjoy the book, but
will also begin to change their perception of math due to its positive portrayal in the book.
Take, for example, the book White Light by Rudy Rucker. Rucker was a professor at the
State Colleges in New York during the 70s where he did research on Cantor’s continuum
hypothesis (to oversimplify, he essentially dealt with the different sizes of infinities). His
research inspired his novel whose protagonist struggles with trying to solve the exact same
problem.86
The notion of infinity becomes a major thread throughout this book, as it brings up
many interesting properties and hypothetical scenarios, taking advantage of the abstract nature of
infinity. For students about to enter a course on set theory, or any other course dealing with
infinity, many ideas presented in the novel are sure to baffle and inspire them. For example, at
one point in the novel, after the protagonist, Felix, has already managed to travel to infinity in
four hours through an infinite acceleration (one billion miles in 2 hours, then the next billion in
one hour, then the next billion in half hour, then ¼ hour, etc., which places them an infinite
distance from earth in four hours), they find themselves at “alef-null,” the most basic, aka
countable, form of infinity.87
Already this idea is a bit paradoxical, traveling an infinite distance in a finite amount of
time, but when they reach Hilbert’s Hotel, a famous mathematical paradox, even more fun with
infinity begins. This infinite hotel is already full when Felix arrives, so the question is posed,
how can they fit this new guest? Since the hotel in infinite, Felix figures out the solution: have
every inhabitant move one room over. This means the person in room #1 moves to room #2, #2
moves to room #3, etc., leaving room #1 completely open. A little bit later, the hotel has an
86
Rucker, Rudy v. B.. White light. New York: Four Walls Eight Windows, 2001.
87
Ibid

44
infinite number of guests arrive, all wanting to enter the full hotel, and again Felix has an answer
to fit them all in: have each current guest double their room number, and move to that new room
instead. So room #1 will move to #2, #2 moves to number 4, #3 moves to #6, and so on. This
leaves all the odd room numbers empty, now allowing an infinite number of guests to check into
the hotel.88
This paradox demonstrates that when dealing with the infinite, our notion of a “full”
hotel and a hotel with “no available rooms” are no longer identical. Not only can one new guest
check in, but also the hotel can make room for an infinite number of new inhabitants, something
only possible through the nature of infinity.
Assigning a reading like this outside of class, even as early as the first week, could very
well inspire students’ curiosity about the subject. What are the mathematical principles that make
these events possible? What other properties of infinity exist? Students who have a solid
understanding of math are more likely to find the enjoyment from this type of novel, as the
“magic” of infinity seems to be present in nearly all mathematical fields and the more one learns
about it, the more abstract and interesting this concept becomes. Just as earlier levels of
mathematics utilize literature to help inspire learning, pique the curiosities of students, and
dangle interesting problems in front of them, pure math classes can use reading for the same
goals. True, more class time should probably be spent on the actual material itself, but an outside
assignment exploring some of these books could very well heighten a student’s experience in the
class. Even if the subject matter is already exciting, students rely solely on their teachers to
present them with thought-provoking ideas. Teachers and professors ultimately have the final say
on the topics being covered, and students inevitably obey and follow. Assignments completed
outside of class, and exposure to new ideas, especially when presented through literature, can be
a great inspiration to students as new ideas rear their heads. Even if the works are fictional, they
88
Rucker, White light.

45
can help paint a better picture of what a true mathematician actually does, as opposed to the
commonly held belief that they merely do what most people think “math” is made up of:
formulas and calculations.
Much of the United States is guilty of continuing to further the belief that math is
inherently difficult, and accepting math illiteracy to prosper. Many students struggle to find the
necessity of learning math skills as technology makes calculations available at the click of a
mouse. But there is much more to math than mere arithmetic. Mathematics should be about
problem solving, critical thinking, and being creative; not about formulas, equations, and
number-crunching. This view is too often lost because students are not exposed to the real world
applications of their learning. By showing them how crucial this information will be to their
daily lives, students should, if nothing else, begin to see how important mathematics can be. The
government continually pushes for students to study math and sciences, complaining that we are
not the top performing country in these disciplines. Rather than trying to force students to pursue
something they are not passionate about, I propose teachers should instead try to cultivate this
passion for mathematics in students – leading to an overall improvement in student learning.
Though it may seem counterintuitive, by bringing literature into mathematics classrooms, at all
levels of education, students should begin to gain an appreciation for the subject that they too-
often learn to despise. If we can once again present mathematics in an interesting light, the result
will be a perception change in society and better mathematical understanding in students. No one
should plead that they have a math-deficiency. The sooner we begin integrating literature into
math classrooms, the sooner we will begin cultivating student interest and promoting better
understanding of this fascinating and indispensable subject.

46
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Cohen, Marion D. 2013. “Truth and Beauty: Mathematics in Literature.” The Mathematics
Teacher 106 (7) (March): 534-9.
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Schatzberg, Eric. 2012. “From Art to Applied Science.” Isis 103 (3) (September): 555-63.
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