58
USI NG
LI T ER AT U RE
TO
T E AC H
M E A SU REM EN T
William P. Bintz
¯
Sara D. Moore
¯
Pam Wright
¯
Lyndsie Dempsey
Interdisciplinary teaching and learning is often messy but also exciting.
This article shares one lesson that integrates literacy and mathematics,
and the results are encouraging for both students and teachers.
If teachers address isolated content areas, a school day
will never have enough hours for them to teach both
literacy and mathematics adequately and thoroughly.
However, by creating connections between the two,
teachers can help ensure that students have
ample opportunity to develop both areas.
(Altieri, 2009, p. 346)
L
yndsie (fourth author) is the
fourth-grade mathematics
teacher at a departmentalized
elementary school. For several
years now, she has taught mathematics with textbooks and worksheets. Each
year, she struggles to teach all of the content in her mathematics curriculum, and her students
struggle to learn all of it. In particular, her students
struggle with measurement concepts, especially fractional measurement. She stated,
I spend lots of time on measurement because it is
important and it always appears on the state test. Each
year, my students have a difficult time grasping it, particularly understanding increments within each inch. I
relate the increments to number lines and fractions, but
[the students] still become confused when using a ruler.
R T
The Reading Teacher
Vol. 65
Issue 1
pp. 58–70
I show them how to measure an object with a ruler and
review increments within each inch. I also have them
measure the object starting at the edge of the ruler and
record results. And yet, after analyzing their work, I’m
always disappointed with the results. [The
students] are still confused and don’t feel confident about measuring objects. This year, I
want to try something different. I want to use
literature to integrate literacy and math. I hope
literature will help my students get better at
mathematics, especially measurement. I need
your help.
Like many teachers, Lyndsie understands that measurement is a difficult
concept for many children to learn. Over
William P. Bintz is a professor in the Department of Teaching, Learning,
and Curriculum Studies at Kent State University, Ohio, USA; e-mail
[email protected].
Sara D. Moore is Director of Mathematics and Science at ETA/Cuisinaire,
Vernon Hills, Illinois, USA; e-mail [email protected].
Pam Wright is the District Title I Coordinator for Paducah Independent
Schools, Kentucky, USA; e-mail [email protected].
Lyndsie Dempsey is an elementary teacher for Paducah Independent
Schools; e-mail [email protected].
DOI:10.1598/RT.65.1.8
© 2011 International Reading Association
59
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
“Students should do more reading, writing,
and discussing ideas in the math classroom
and learn mathematical ideas in
real-world contexts.”
the past 25 years, National Association
of Educational Progress trend data have
indicated that student achievement with
measurement is at best disappointing
given the amount of instructional time
it receives in grades K–5 (Kamii, 2006;
Thompson & Preston, 2004). Lyndsie
also understands that measurement is
a difficult concept to teach. Fortunately,
she is an inquirer, a risk taker, and a
teacher researcher. In this instance, she
is interested in integrating literacy and
mathematics, specifically investigating
the use of literature to teach measurement. She invited us to help, and we
gladly accepted.
This article reports on the lesson
developed by the author team in
response to Lyndsie’s request. We
describe a lesson that integrates reading, writing, drawing, and literature to
teach linear measurement to the inch,
and fractional measurement. We begin
with a rationale for integrating literacy
and mathematics and share a collection of literature that is based on major
mathematical content strands. Then, we
describe research that supports using literature to teach measurement. Next, we
identify literacy and mathematics standards that are embedded in this lesson,
describe materials and procedures used,
and share samples of student work that
resulted. We end with lessons learned
from the experience.
Integrating Literacy
and Mathematics
Literacy is important to mathematics learning (Draper, 2002), particularly
to the National Council of Teachers of
Mathematics (NCTM). In Principles and
Standards for School Mathematics, NCTM
(2000) recommends that students
should do more reading, writing, and
discussing ideas in the math classroom
and learn mathematical ideas in realworld contexts. In response, increasing
numbers of teachers are integrating literacy and mathematics for several
reasons, two of which are particularly
noteworthy.
First, there is growing recognition
that literature, especially trade books,
is a powerful tool for integrating literacy and mathematics (Burns, 2004;
Shatzer, 2008) and that reading, writing, and even drawing are important in
mathematics learning (Adams, 2003).
According to Crespo and Kyriakides
(2007), “drawing can be a powerful way
of engaging many students, especially
young ones, in representing and communicating their mathematical ideas”
(p. 118). It also helps students support,
solidify, and extend mathematical ideas
(Carter, 2009).
Second, there has been, and continues to be, a proliferation of high-quality
and award-winning literature that
teaches mathematical concepts (Griffiths
& Clyne, 1988; Thiessen & Matthias,
1992; D.J. Whitin & P.E. Whitin, 1996;
D.J. Whitin & Wilde, 1995). This proliferation clearly indicates that literature is
important for integrating mathematics
and literacy. From a literacy perspective,
literature provides “wondrous tales”
(Malinsky & McJunkin, 2008, p. 410),
and from a mathematical perspective,
it allows children to enjoy reading and
learning mathematics at the same time.
More specifically, literature provides a human perspective by showing
students how people use mathematics to solve problems (D.J. Whitin &
Wilde, 1995), helps students connect
the abstract language of mathematics to real-world contexts (D.J. Whitin
& P.E. Whitin, 1996; P. Whitin & D.J.
Whitin, 1997), captures children’s imagination, stimulates their mathematical
thinking and reasoning (Burns, 1992),
and reinforces new concepts. Literature
also enhances and further explains concepts and skills being studied in math
textbooks (Olness, 2007), provides visualizations of mathematical concepts
through vivid illustrations (Guiett, 1999;
Murphy, 1999), and engages learners in
meaningful conversations and investigations in mathematics (Hunsader,
2004). In short, good things happen
Pause and Ponder
■
■
■
In what ways can teachers collaborate on
developing, implementing, and assessing
interdisciplinary, classroom-based, action
research projects?
In what ways can administrators best
support teachers who are interested in
interdisciplinary teaching and learning?
In what ways can teachers assess student
learning in an interdisciplinary curriculum?
www.reading.org
R T
60
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
■
How great are the resources needed
to help readers benefit from the
book’s mathematics?
Table 1 illustrates a collection of
trade books that meet these criteria. We
share this collection not only because
they meet the criteria but also because
they are based on the five major content
strands found in Principles and Standards
for School Mathematics (NCTM, 2000).
These strands include numbers and
operations, geometry, algebra, data and
probability, and measurement.
Measurement and Literature
when literacy and mathematics are integrated. One example is that math scores
increase when standards-based math
strategies are combined with highquality literature (Jennings, 1992).
It is important to note, however,
that not all literature will work well in
classrooms. Simply because a piece of
literature is published, and promoted
by publishers and recommended by
teachers as a good resource to integrate literacy and mathematics, these
are not guarantees that the piece is good
literature for teaching important mathematical concepts accurately, correctly,
and effectively. Schiro (1997) stated,
Advocates of the mathematics and children’s literature connection write as
though children’s literature is a collection of marvelous books that grip the
imagination of students and teachers so
strongly that merely using those books
will guarantee children wonderful learning experiences—because of the power
of the literature itself. Unfortunately, not
all children’s trade books are superb literature, a fact readily acknowledged in the
field of children’s literature, but almost
R T
www.reading.org
never mentioned by those writing about
linking mathematics and literature. (p. 14)
Only literature that is rigorously and
systematically assessed for its quality and
value for teaching mathematics will do
(Schiro, 1997). Hunsader (2004) developed a rubric that can be used to assess
and establish the value of mathematics
trade books. We used this rubric to assess
the value of a variety of mathematics
trade books and focused on the following
criteria (Hunsader, 2004, p. 621):
■
Is the book’s mathematics content
correct and accurate?
■
Is the book’s mathematics content
visible and effectively presented?
■
Is the book’s mathematics content
intellectually and developmentally
appropriate for its audience?
■
Does the book facilitate the reader’s
involvement in, and use and transfer of, its mathematics?
■
Do the book’s mathematics and
story complement each other?
In this lesson, we wanted to integrate
literacy and mathematics with a particular focus on measurement. Principles
and Standards for School Mathematics
(NCTM, 2000) defines measurement as
“the assignment of a numerical value
to an attribute of an object, such as the
length of a pencil” (p. 44). High-quality
literature is an important context for
and springboard into learning a variety of measurement concepts (Austin,
Thompson, & Beckman, 2005). Table 2
illustrates a variety of literature that can
be used to teach different measurement
concepts.
Literature can help students understand and use measurement tools
accurately in real-world contexts
(Wickett, 1999), distinguish between
standard and nonstandard units of measurement, and recognize different kinds
of rulers and how to use them for different measurement purposes (Clarkson,
Robelia, Chahine, Fleming, & Lawrenz,
2007). Literature can also help students
understand linear relationships between
measurement and data analysis (Joram,
Hartman, & Trafton, 2004), explore
algebraic patterns (Austin & Thompson,
1997), and understand fractional measurement (Moyer & Mailley, 2004).
61
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
Table 1 Suggested Children’s Literature for Integrating Literacy and Math
Math concept
Algebraic thinking and
algebra readiness
Literature
Campbell, S.C. (2010). Growing patterns. Honesdale, PA: Boyds Mills.
Murphy, S.J. (1997). Elevator magic. New York: HarperCollins.
Murphy, S.J. (2003). Less than zero. New York: HarperCollins.
Neuschwander, C. (2007). Patterns in Peru: An adventure in patterning. New York: Henry Holt.
Area and perimeter
Burns, M. (2008). Spaghetti and meatballs for all! A mathematical story. New York: Scholastic.
Murphy, S.J. (2002). Bigger, better, best! New York: HarperCollins.
Murphy, S.J. (2002). Racing around. New York: HarperCollins.
Neuschwander, C. (2006). Sir Cumference and the Isle of Immeter. Watertown, MA: Charlesbridge.
Pollack, P., & Belviso, M. (2002). Chickens on the move. New York: Kane.
Data and probability
Einhorn, E. (2008). A very improbable story. Watertown, MA: Charlesbridge.
Herman, G. (2002). Bad luck Brad. New York: Kane.
Leedy, L. (2007). It’s probably Penny. New York: Henry Holt.
Murphy, S.J. (2001). Probably pistachio. New York: HarperCollins.
Van Allsburg, C. (1981). Jumanji. Boston: Houghton Mifflin.
Division
Harris, T. (2008). Splitting the herd: A corral of odds and evens. Minneapolis, MN: Millbrook.
McElligott, M. (2007). Bean thirteen. New York: G.P. Putnam’s Sons.
Murphy, S.J. (1997). Divide and ride. New York: HarperCollins.
Pinczes, E.J. (1993). One hundred hungry ants. Boston: Houghton Mifflin.
Pinczes, E.J. (1995). A remainder of one. Boston: Houghton Mifflin.
Turner, P. (1999). Among the odds and evens: A tale of adventure. New York: Farrar Straus & Giroux.
Geometry
Adler, D.A. (1998). Shape up! New York: Holiday House.
Burns, M. (1994). The greedy triangle. New York: Scholastic.
Ellis, J. (2004). What’s your angle, Pythagoras? A math adventure. Watertown, MA: Charlesbridge.
Friedman, A. (1994). A cloak for the dreamer. New York: Scholastic.
Friedman, M., & Weiss, E. (2001). Kitten castle. New York: Kane.
Murphy, S.J. (2001). Captain Invincible and the space shapes. New York: HarperCollins.
Neuschwander, C. (1997). Sir Cumference and the first round table: A math adventure. Watertown, MA: Charlesbridge.
Neuschwander, C. (1999). Sir Cumference and the dragon of pi: A math adventure. Watertown, MA: Charlesbridge.
Neuschwander, C. (2001). Sir Cumference and the great knight of Angleland: A math adventure. Watertown, MA: Charlesbridge.
Neuschwander, C. (2005). Mummy math: An adventure in geometry. New York: Henry Holt.
Pilegard, V.W. (2000). The warlord’s puzzle. Gretna, LA: Pelican.
Rocklin, J. (1998). Not enough room! New York: Scholastic.
Rocklin, J. (2000). The incredibly awesome box: A story about 3-D shapes. New York: Scholastic.
Graphing
Bader, B. (2003). Graphs. New York: Grosset & Dunlap.
Dussling, J. (2003). Fair is fair! New York: Kane.
Glass, J. (1998). The fly on the ceiling: A math myth. New York: Random House.
Leedy, L. (2005). The great graph contest. New York: Holiday House.
Nagda, A.W., & Bickel, C. (2000). Tiger math: Learning to graph from a baby tiger. New York: Henry Holt.
Ochiltree, D. (1999). Bart’s amazing charts. New York: Scholastic.
Penner, L.R. (2002). X marks the spot! New York: Kane.
Measurement
Adler, D.A. (1999). How tall, how short, how far away. New York: Holiday House.
Herman, G. (2003). Keep your distance! New York: Kane.
Kellogg, S. (2004). The mysterious tadpole. New York: Puffin.
Leedy, L. (2000). Measuring Penny. New York: Henry Holt.
McCallum, A. (2006). Beanstalk: The measure of a giant: A math adventure. Watertown, MA: Charlesbridge.
Sweeney, J. (2002). Me and the measure of things. New York: Dragonfly.
Multiplication
Birch, D. (1988). The king’s chessboard. New York: Dial.
Calvert, P. (2006). Multiplying menace: The revenge of Rumpelstiltskin. Watertown, MA: Charlesbridge.
Demi. (1997). One grain of rice: A mathematical folktale. New York: Scholastic.
Leedy, L. (1995). 2 × 2 = boo! A set of spooky multiplication stories. New York: Holiday House.
Losi, C.A. (1997). The 512 ants on Sullivan Street. New York: Scholastic.
Neuschwander, C. (1998). Amanda Bean’s amazing dream: A mathematical story. New York: Scholastic.
(continued )
www.reading.org
R T
62
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
Table 1 Suggested Children’s Literature for Integrating Literacy and Math (continued)
Math concept
Number sense and
place value
Literature
Driscoll, L. (2003). The blast off kid. New York: Kane.
Fisher, V. (2006). How high can a dinosaur count? And other math mysteries. New York: Schwartz & Wade.
Friedman, A. (1994). The king’s commissioners. New York: Scholastic.
LoPresti, A.S. (2003). A place for zero: A math adventure. Watertown, MA: Charlesbridge.
Love, D.A. (2006). Of numbers and stars: The story of Hypatia. New York: Holiday House.
Pilegard, V.W. (2001). The warlord’s beads. Gretna, LA: Pelican.
Schmandt-Besserat, D. (1999). The history of counting. New York: Morrow.
Thompson, L. (2001). One riddle, one answer. New York: Scholastic.
Ratio and proportion
Clement, R. (1995). Counting on Frank. New York: Houghton Mifflin.
McCallum, A. (2006). Beanstalk: The measure of a giant: A math adventure. Watertown, MA: Charlesbridge.
Pilegard, V.W. (2003). The warlord’s puppeteers. Gretna, LA: Pelican.
Schwartz, D.M. (1999). If you hopped like a frog. New York: Scholastic.
Table 2 Suggested Children’s Literature for Teaching Measurement
Aber, L.W. (2001). Carrie measures up. New York: Kane.
Allen, P. (1980). Mr. Archimedes’ bath. New York: Puffin.
Anno, M. (1976). The king’s flower. New York: Collins.
Axelrod, A. (1999). Pigs in the pantry: Fun with math and cooking. New York: Aladdin.
Briggs, R. (1970). Jim and the beanstalk. New York: Coward-McCann.
Hightower, S. (1997). Twelve snails to one lizard: A tale of mischief and measurement. New York:
Simon & Schuster.
Hoban, T. (1985). Is it larger? Is it smaller? New York: Greenwillow.
Howard, E. (1993). The big seed. New York: Simon & Schuster.
Hutchins, P. (1991). Happy birthday, Sam. New York: Greenwillow.
Johnston, T. (1986). Farmer Mack measures his pig. New York: Harper & Row.
Keenan, S. (1996). The biggest fish. New York: Scholastic.
Kellogg, S. (1976). Much bigger than Martin. New York: Dial.
Lasky, K. (1994). The librarian who measured the Earth. Boston: Little, Brown.
Leedy, L. (2003). Mapping Penny’s world. New York: Henry Holt.
Ling, B. (1997). The fattest, tallest, biggest snowman ever. New York: Scholastic.
McCarthy, R.F. (2001). The inch-high samurai. Tokyo, Japan: Kodansha International.
Morimoto, J. (1988). The inch boy. New York: Puffin.
Murphy, S.J. (1996). The best bug parade. New York: HarperCollins.
Murphy, S.J. (1999). Super sand castle Saturday. New York: HarperCollins.
Myller, R. (1991). How big is a foot? New York: Dell.
Pluckrose, H. (1995). Length. Danbury, CT: Children’s.
Puharich, T. (1998). How do you measure a dinosaur? Walton-on-Thames, UK: Nelson Thornes.
Russo, M. (1986). The line up book. New York: Greenwillow.
Walpole, B. (1995). Distance. Milwaukee, WI: Gareth Stevens.
Wells, R.E. (1993). Is a blue whale the biggest thing there is? Morton Grove, IL: Albert Whitman.
Wells, R.E. (1995). What’s smaller than a pygmy shrew? Morton Grove, IL: Albert Whitman.
Mathematics and
Literacy Standards
The lesson was intentionally developed
as a standards-based lesson. It focused
on using literature to teach measurement and integrated both literacy and
mathematics standards. Integrating
R T
www.reading.org
these standards is important because
they complement each other in powerful
ways, as well as offer a means for mathematics and language skills to develop
simultaneously as learners listen, read,
write, and talk about mathematics
(Hellwig, Monroe, & Jacobs, 2000).
Specifically, the lesson was based
on mathematics expectations for
grades 3–5, as described in Principles
and Standards for School Mathematics
(NCTM, 2000):
■
Students understand such attributes
as length, area, weight, volume, and
the size of an angle and select the
appropriate type of unit for measuring each attribute.
■
Students understand the need for
measuring with standard units
and become familiar with standard
units in the customary and metric
systems.
■
Students understand that measurements are approximations and how
differences in units affect precision.
For example, the lesson focused
on the attribute of length, and inches
as the unit for measuring length. The
lesson focused on the inch as a standard unit in the customary system and
for illustrating problems with nonstandard measurements. Finally, the lesson
focused on fractional measurements
and how they increase accuracy and
precision.
The lesson was also based on
national literacy standards delineated
63
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
within Standards for the English Language
Arts (International Reading Association
& National Council of Teachers of
English, 1996):
■
Students read a wide range of literature from many genres.
■
Students employ a wide range of
strategies as they write and use different writing process elements
appropriately to communicate with
different audiences for a variety of
purposes.
■
Students use spoken, written, and
visual language to accomplish their
own purposes (e.g., learning, enjoyment, persuasion, exchange of
information).
materials; clarifying and elaborating on
lesson instructions; working with students in small groups, particularly with
those who were struggling with instructions and applications; and recording
field notes in our research journals. The
lesson involved the following seven
stages.
Stage 1: Getting Started
To get started, we felt that it was important to assess what students already
knew about measurement. Lyndsie
began by inviting students to respond
to the following prompt: “Please tell me
how you would measure the length of
something—a carrot, a pencil, etcetera.
I want you to tell me by using writing,
drawing, and numbers. Tell me as much
as you can.” Two student samples caught
our attention.
James (all student names are pseudonyms) wrote that he would measure
a pencil by laying a ruler next to the
pencil. His illustration (see Figure
1) depicts a ruler marked in whole
Figure 1 A Fourth Grader’s Record of What He Already Knew About Measurement Prior
to the Lesson
The lesson used a range of literature,
including poetry and realistic fiction.
This literature was read aloud, and students were invited to respond verbally
to the readings. The lesson engaged
students in oral retellings, making connections between texts, and exploring
measurement through writing, drawing,
and sharing their work with others.
Instructional Lesson
Each day, Lyndsie teaches three classes
of fourth-grade mathematics, with each
class period lasting two hours. For this
lesson, she was able to work with her
colleagues and principal to schedule
one of her math classes for a three-hour
block of time. The lesson was collaboratively planned, designed to teach linear
measurement to the inch and fractional
measurement, and conducted in a 180minute class period, with a 15-minute
break in the middle of the lesson. A total
of 20 students participated.
As the regular classroom teacher,
Lyndsie took the lead on teaching the
lesson. We assisted her by organizing, distributing, and collecting lesson
www.reading.org
R T
64
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
numbers and measures the pencil to be
“about 8 inch tall.” His measurement of
the carrot is also in a whole number.
Jenny would use her thumb to measure a short object like a dime, but a
ruler for a larger object like a pencil or
table. Like James’s, her illustration (see
Figure 2) depicts rulers marked in whole
numbers.
Stage 2: Creating Interest
Next, we wanted to create student interest in measurement. We used poetry for
several reasons: Children enjoy hearing
poetry read aloud, especially poems that
rhyme; poetry is a powerful tool to teach
content area material; reading and discussing math poems is an effective way
to integrate literacy and mathematics
Figure 2 A Fourth Grader’s Record of What She Already Knew About Measurement Prior
to the Lesson
and an efficient use of time; and we
enjoy poetry ourselves.
One of our favorite poets is J. Patrick
Lewis because he writes both enjoyable
and informative poems across content areas. Arithme-Tickle (Lewis, 2002)
is a good example. The book includes
poems with rhyming text and appealing illustrations based on a variety of
math problems. Lyndsie read aloud two
poems from this book that deal with
different ways to measure: “Pardon
My Yardstick” and “How to Hand-le a
Horse.” Afterward, she asked students
how these poems showed the difference
between standard and nonstandard
measurement. One student stated,
In the first poem, the whole poem was
based on a yardstick. It didn’t say how
long a yardstick was, but I know it is
exactly 36 inches long. It also asked
how much is one half a yardstick, and
I know that is exactly 18 inches long. A
yardstick is an example of standard measurement. The inches stay the same no
matter who is using it to measure stuff.
The second poem is different. It’s about a
man who is a horse trainer, and he is telling a little boy how to measure a horse
by hands. The man says one hand is
four inches, but if the man measures the
horse with his hands and the boy measures the same horse with his hands,
they aren’t going to get the same measurement because the man’s hands are
bigger than the boy’s. Hand is an example of nonstandard measurement. That’s
the difference.
Next, Lyndsie read two more poems
that deal with measurement from the
book Where the Sidewalk Ends by Shel
Silverstein (1974): “One Inch Tall” and
“The Longest Nose in the World.” After
reading, Lyndsie invited students to
talk about measurement concepts, tools,
and words in the poems. Students identified and discussed words like longest
(length), tall (height), yardstick (standard
measurement), hand (nonstandard mea-
R T
www.reading.org
65
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
15-minute break. Afterward, let’s use
him to measure things from the story.”
Stage 4: Applying the Concept
of an Inch
surement), counted (addition), and inch
(measurement).
Stage 3: Exploring the Concept
of an Inch
Now, Lyndsie wanted to use a readaloud to focus student attention on the
concept of an inch. First, she asked,
“How long is an inch?” The students’
answers varied. To show the length of
an inch, Lyndsie introduced her “human
inch.” Students seemed puzzled at first.
She showed them one of her thumbs
and measured it with a ruler. She measured the length of her thumb from
its tip to the first knuckle. It measured
approximately an inch. She explained
that she called it her human inch
because it always goes with her, so she
always has a way to measure something
in inches with her thumb whenever she
does not have a ruler available. Students
spent time measuring small objects with
Lyndsie’s thumb and later with one of
their own thumbs.
Next, Lyndsie read aloud Inch by Inch
by Leo Lionni (1960), which is a story
about a clever inchworm who measures
parts of different predators (e.g., a flamingo’s neck, a toucan’s beak, a heron’s
leg) to escape from being eaten. After
the reading, students orally retold and
discussed the story with a partner.
From the discussion, we noticed
that they clearly understood the story,
enjoyed finding the inchworm on each
page, and recognized how clever it was
to keep from being eaten. One student noted that “the inch worm was
useful because it could measure things.”
Lyndsie quickly stated, “That’s right.
He was useful. I think we can really
learn some things from him about measurement, but first, let’s take a quick
“To show the length
of an inch, Lyndsie
introduced her
‘human inch.’”
Lyndsie extended the concept of an inch
by having students apply it to a character in the story. To do this, we made
a photocopy ahead of time of the page
in the book that illustrates the legs of
the heron and gave each student one
copy. Then, Lyndsie gave the students
a handful of different colored, rubber
inchworms. She showed that each of
the rubber inchworms were one-inch
long and invited students to use them to
measure the length of the straight leg of
the heron.
She told the students to measure
the distance of the leg from the bottom
of the heron’s ankle to the bottom of
its knee. She selected this distance
because in this illustration, the heron’s
leg is vertical, reasonably straight, and
approximately five inches long—a whole
number instead of one with a fraction.
To set boundaries for the measurement, Lyndsie instructed the students to
make a line at the ankle and at the knee
on their sheet and then use individual inchworms to measure the distance.
Afterward, all of the students agreed
that the distance was five inchworms, or
five inches.
To confirm our measurement,
Lyndsie gave each student an inchworm ruler. She used this ruler because
it complements Inch by Inch and continued the focus of the lesson. Students
placed the ruler next to the heron’s leg
to confirm their measurements. Some
kept the ruler in place but experimented
with different sizes and combinations
of inchworms by placing them on top of
the ruler. Once again, the students concluded that the length of the heron’s leg
is five inches.
www.reading.org
R T
66
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
Stage 5: Exploring the Concept
of an Inch and a Half
Lyndsie wanted to make a transition
from whole numbers to fractional measurements, specifically from an inch
to an inch and a half. To this end, we
planned to read Inchworm and a Half
by Elinor Pinczes (2001). Before reading, Lyndsie asked students, “What
happens when we measure something, and it’s not in an exact number
of inches? For example, what happens
when we measure the leg of a heron,
and it is not exactly five inches?” One
student answered, “Well, we would just
have a different number of inchworms.”
Another said, “We would just have a
little less or a little more than five inchworms.” Lyndsie then stated, “Well, let’s
see how this book helps us with this
question.”
Inchworm and a Half is a story that
takes place in a garden, is told in rhyme,
and is designed to introduce fractional
measurement. One day, an inchworm
measures a bean. The bean is not an
inch in length, so the inchworm has a
little bit left over. Then, a worm half her
size measures it and, as a result, introduces readers to the concept of fractions.
The story continues with the worms getting smaller and smaller (e.g., one half,
one third, one fourth). Each illustration reinforces the concept of fractions
by showing the relationship between the
different worms’ lengths and what they
are measuring.
After reading this story, Lyndsie
asked the class, “Let’s think about how
our two books are similar. What is similar about Inch by Inch and Inchworm
and a Half?” One student responded,
“Both books have inchworms in them.”
Another stated, “The inchworms in
each story used themselves to measure
things.” Lyndsie then read the rest of
the story.
R T
www.reading.org
Afterward, she asked, “How are
our two books different?” One student
responded, “In this book, not everything the inchworms measured was an
inch.” Another stated, “The first inchworm only had to hop once to measure
the celery, the second inchworm had to
hop twice, the third inchworm had to
hop three times, and the last inchworm
had to hop four times.” Lyndsie noted
that the word fraction was used in the
story and that the second inchworm was
one half, the third inchworm was one
third, and the fourth inchworm was one
fourth the size of the first inchworm,
which was one inch. She stated, “Now,
we have to find a way to be more exact
with our measurements.”
Stage 6: Introducing
and Applying
Fractional Measurement
Lyndsie gave each student a ruler to use
for fractional measurement and drew
the students’ attention to the difference
between the two rulers. The students
quickly recognized that the first ruler
measured in whole inches, and the
second ruler measured in whole inches
and fractions, specifically one fourth,
one half, and three fourths.
Then, she gave students a data collection sheet to record their measurements
of objects. She invited them to browse
around the classroom and find objects
to measure with the ruler. The students
were encouraged to select objects that
they predicted or suspected would not
have a measurement in whole inches.
Lyndsie reminded the students that they
were learning how to measure more
exactly and required objects whose measurement was in fractions. The students
went right to work.
Figure 3 is one student’s data collection sheet. This student estimated the
length of a variety of objects (human
and nonhuman) in whole numbers,
and the actual measurements in inchworms are also recorded in whole
numbers. When using a ruler, the
student recorded the actual measurements in whole numbers and fractional
measurements.
Figure 3 A Fourth Grader’s Data Collection Sheet of Objects Measured in the Classroom
67
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
Stage 7: Recording What
Students Learned
Figure 4 A Fourth Grader’s Record of What He Learned About Measurement During
the Lesson
Lyndsie ended the lesson by inviting the
students to record what they had learned
about measurement. Basically, she used
the same prompt at the beginning of the
lesson, so we could make some beforeand-after comparisons. We looked at the
work of James and Jenny once again.
James illustrated a move from whole
to fractional measurement (see Figure
4). Specifically, he shifted from using an
approximate measurement (“this pencil
is about 8 inch tall”) to increasing his
precision. He used a ruler to measure a
paintbrush because then he could “measure something more exacly.” He also
included increments on the ruler so that
he could “look at the next half” to measure the paintbrush.
Similarly, Jenny moves from whole to
fractional measurement (see Figure 5).
Her first ruler was marked only in whole
numbers, but her new ruler included
fractional divisions. She recognized that
this kind of ruler allows her to be “more
accurate and exact.”
Lessons Learned
We learned several lessons from this
experience and share them here in two
ways: from an interdisciplinary perspective and from a disciplinary perspective.
We discuss literacy and mathematics
separately with some hesitation. On the
one hand, we described an interdisciplinary lesson designed to integrate, not
separate, literacy and mathematics. By
sharing lessons learned in literacy and
mathematics separately, we do not want
to perpetuate a “disciplinary divide”
(Donahue, 2003, p. 24) between these
two disciplines or any others.
On the other hand, we share lessons learned from each discipline
because much professional literature has
discussed how connecting mathematics and literature helps children learn
mathematics, but has “hardly mentioned how connecting mathematics
and literature can help children develop
literary concepts and skills” (Schiro,
1997, p. 10). As a result, we begin with
lessons learned from integrating literacy
and mathematics, then from mathematics, and finally from literacy.
From integrating literacy and mathematics, we learned once again the
importance of good literature for teaching mathematics. The trade books used
had important similarities and differences and invited students to make
intertextual connections. In terms
of similarity, each book provided an
understandable context that made measurement real and relevant and made
the tools for measurement, like thumbs
and rulers, practical and useful.
In terms of difference, the inchworm in Inch by Inch is illustrated as
www.reading.org
R T
68
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
Figure 5 A Fourth Grader’s Record of What She Learned About Measurement During
the Lesson
a single object. Throughout the story,
the inchworm is shown moving in a
single, one-inch increment as it escapes
from one predator after another. The
inchworm is not shown making multiple movements and moving multiple
inches. In Inchworm and a Half, however, there are multiple inchworms, and
each is a different length. These inchworms are shown to illustrate the length
of different-sized objects by making
multiple loops and measuring the different sizes of the loops. We believe that
both books worked nicely together to
help students make a seamless transition from whole-number measurement
to fractional measurement.
At the same time, we offer a caveat.
Inchworm and a Half includes inchworms
and measurements that deal with simple
fractions: one half, one third, and one
fourth. We like moving from wholenumber measurement to the fractional
measurements of one half and one
fourth. We worry, though, that students
may develop a misconception about the
measurement of one third, specifically
by seeing increments on a ruler as “½,”
R T
www.reading.org
“1⁄3,” and “¼.” That said, we suspect that
Inchworm and a Half is a better book
for teaching fractions than for teaching
fractional measurement.
From the perspective of mathematics,
we learned once again that measurement is difficult for young students to
learn. This lesson helped them focus
on the mathematics and use measurement to move from estimation and
approximation to precision and exactness. We also learned the importance of
mathematics lessons that involve using
language, numbers, and drawing. For
example, we noticed on the students’
data collection sheets that the students’
drawings were not to scale. That is, the
“Reading aloud entertaining
and informative poems
sparked student interest in
posing and solving math
problems.”
drawings did not show the relative sizes
of the objects measured. Next time, we
want to help students draw different
objects according to scale.
From the perspective of literacy,
we learned that in addition to being
enjoyable and entertaining, poetry
effectively generated student interest
in mathematics and, in this case, measurement, a math concept that many
students do not find particularly interesting. In this instance, reading aloud
entertaining and informative poems
sparked student interest in posing and
solving math problems. For example,
while reading aloud, the students were
actively involved and constantly commented about how the poems connected
to mathematics, especially how they
described and illustrated the difference
between standard and nonstandard
measurement. In this sense, these
poems functioned as “way-in” (Keene
& Zimmermann, 2007, p. 145) pieces
of literature. That is, they functioned
as an entertaining, understandable,
and informative way into the topic of
measurement.
Poetry also functioned as a way to
support vocabulary growth and development. After reading aloud, students
responded by providing short retellings,
describing the mathematics, and evaluating the language (e.g., “I like the way
the poem rhymes. It makes it easy to
understand”). The class also responded
by identifying specific words in the
poems that connected to measurement
concepts. The students recognized that
the word longest connected to length,
yardstick and inch indicated standard
measurement, and hand indicated nonstandard measurement.
In the end, however, Lyndsie perhaps
best captured the important lessons
learned:
69
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
Before this experience, I always struggled
to teach measurement. I’ve tried different ways to teach it but haven’t been very
successful. This experience, however, has
helped me in so many ways. It has given
me a new set of eyes not only on how to
teach measurement but also how to teach
mathematics. This has helped me better
understand the value of integrating literacy and mathematics. It has also helped
me in that, instead of feeling frustrated, I
now feel confident and competent, even
empowered by the whole experience. I
feel like I’m a better and more effective
teacher. I also feel rejuvenated and even
inspired and can’t wait to start using literature to teach other concepts in my
mathematics curriculum.
Like Lyndsie, we hope this experience will help other teachers see
literature as a tool to teach measurement
as well as other math concepts that are
difficult for students to understand. We
also hope that it will inspire other teachers to start new conversations and ask
new inquiry questions not only about
how to integrate literacy and mathematics but also to investigate and reflect on
the power and potential of an interdisciplinary curriculum.
R E F E R E NC E S
Adams, T.L. (2003). Reading mathematics: More
than words can say. The Reading Teacher,
56(8), 786–795.
Altieri, J.L. (2009). Strengthening connections
between elementary classroom mathematics
and literacy. Teaching Children Mathematics,
15(6), 346–351.
Austin, R.A., & Thompson, D.R. (1997).
Exploring algebraic patterns through literature. Mathematics Teaching in the Middle
School, 2(4), 274–281.
Austin, R.A., Thompson, D.R., & Beckman, C.E.
(2005). Exploring measurement concepts
through literature: Natural links across disciplines. Mathematics Teaching in the Middle
School, 10(5), 218–224.
Burns, M. (1992). About teaching mathematics: A
K–8 resource. Sausalito, CA: Math Solutions.
Burns, M. (2004). 10 big math ideas. Instructor
Magazine, 113(7), 16–19.
Carter, S. (2009). Connecting mathematics and
writing workshop: It’s kinda like ice skating.
The Reading Teacher, 62(7), 606–610.
Clarkson, L.M.C., Robelia, B., Chahine, I.,
Fleming, M., & Lawrenz, F. (2007). Rulers of
different colors: Inquiry into measurement.
Teaching Children Mathematics, 14(1), 34–39.
Crespo, S.M., & Kyriakides, A.O. (2007). To
draw or not to draw: Exploring children’s
drawings for solving mathematics problems. Teaching Children Mathematics, 14(2),
118–125.
Donahue, D. (2003). Reading across the great
divide: English and math teachers apprentice one another as readers and disciplinary
insiders. Journal of Adolescent & Adult Literacy,
47(1), 24–37.
Draper, R.J. (2002). School mathematics reform,
constructivism, and literacy: A case for literacy instruction in the reform-oriented
math classroom. Journal of Adolescent & Adult
Literacy, 45(6), 520–529.
Griffiths, R., & Clyne, M. (1988). Books you can
count on: Linking mathematics and literature.
Portsmouth, NH: Heinemann.
Guiett, D. (1999). From alphabet to zebras: Using
children’s literature in the mathematics
classroom. Ohio Media Spectrum, 51, 32–36.
Hellwig, S.J., Monroe, E.E., & Jacobs, J.S. (2000).
Making informed choices: Selecting children’s trade books for mathematics instruction. Teaching Children Mathematics, 7(3),
138–143.
Hunsader, P.D. (2004). Mathematics trade books:
Establishing their value and assessing their
quality. The Reading Teacher, 57(7), 618–629.
International Reading Association & National
Council of Teachers of English. (1996).
Standards for the English language arts.
Newark, DE: International Reading
Association; Urbana, IL: National Council of
Teachers of English.
Jennings, C.M. (1992). Increasing interest and
achievement in mathematics through children’s literature. Early Childhood Research
Quarterly, 7(2), 263–276.
Joram, E., Hartman, C., & Trafton, P.R. (2004).
“As people get older, they get taller”: An
integrated unit on measurement, linear
relationships, and data analysis. Teaching
Children Mathematics, 10(7), 344–351.
Kamii, C. (2006). Measurement of length: How
can we teach it better? Teaching Children
Mathematics, 13(3), 154–158.
Keene, E.O., & Zimmermann, S. (2007). Mosaic
of thought: The power of comprehension strategy
instruction. Portsmouth, NH: Heinemann.
Malinsky, M.A., & McJunkin, M. (2008).
Wondrous tales of measurement. Teaching
Children Mathematics, 14(7), 410–413.
Moyer, P.S., & Mailley, E. (2004). “Inchworm
and a half”: Developing fraction and measurement concepts using mathematical representations. Teaching Children Mathematics,
10(5), 244–252.
Murphy, S.J. (1999). Learning math through stories. School Library Journal, 45(3), 122–123.
National Council of Teachers of Mathematics.
(2000). Principles and standards for school
mathematics. Reston, VA: Author.
Olness, R. (2007). Using literature to enhance content area instruction: A guide for K–5 teach-
ers. Newark, DE: International Reading
Association.
Schiro, M. (1997). Integrating children’s literature
and mathematics in the classroom: Children as
meaning makers, problem solvers, and literary
critics. New York: Teachers College Press.
Shatzer, J. (2008). Picture book power:
Connecting children’s literature and mathematics. The Reading Teacher, 61(8), 649–653.
Thiessen, D., & Matthias, M. (1992). The wonderful world of mathematics: A critically annotated list of children’s books in mathematics.
Reston, VA: National Council of Teachers of
Mathematics.
Thompson, T.D., & Preston, R.V. (2004).
Measurement in the middle grades: Insights
from NAEP and TIMSS. Mathematics
Teaching in the Middle School, 9(9), 514–519.
Whitin, D.J., & Whitin, P.E. (1996). Fostering
metaphorical thinking through children’s literature. In P.C. Elliott (Ed.), Communication in
mathematics: K–12 and beyond (pp. 228–237).
Reston, VA: National Council of Teachers of
Mathematics.
Whitin, D.J., & Wilde, S. (1995). It’s the story that
counts: More children’s books for mathematical
learning, K–6. Portsmouth, NH: Heinemann.
Whitin, P., & Whitin, D.J. (1997). Inquiry at the
window: Pursuing the wonders of learners.
Portsmouth, NH: Heinemann.
Wickett, M.S. (1999). Measuring up with the
principal’s new clothes. Teaching Children
Mathematics, 5(8), 476–479.
L I T E R AT U R E C I T E D
Aber, L.W. (2001). Carrie measures up. New York:
Kane.
Adler, D.A. (1998). Shape up! New York: Holiday
House.
Adler, D.A. (1999). How tall, how short, how far
away. New York: Holiday House.
Allen, P. (1980). Mr. Archimedes’ bath. New York:
Puffin.
Anno, M. (1976). The king’s flower. New York:
Collins.
Axelrod, A. (1999). Pigs in the pantry: Fun with
math and cooking. New York: Aladdin.
Bader, B. (2003). Graphs. New York: Grosset &
Dunlap.
Birch, D. (1988). The king’s chessboard. New York:
Dial.
Briggs, R. (1970). Jim and the beanstalk. New York:
Coward-McCann.
Burns, M. (1994). The greedy triangle. New York:
Scholastic.
Burns, M. (2008). Spaghetti and meatballs for all! A
mathematical story. New York: Scholastic.
Calvert, P. (2006). Multiplying menace: The
revenge of Rumpelstiltskin. Watertown, MA:
Charlesbridge.
Campbell, S.C. (2010). Growing patterns.
Honesdale, PA: Boyds Mills.
Clement, R. (1995). Counting on Frank. New York:
Houghton Mifflin.
Demi. (1997). One grain of rice: A mathematical
folktale. New York: Scholastic.
Dussling, J. (2003). Fair is fair! New York: Kane.
www.reading.org
R T
70
U SI NG L I T E R AT U R E T O T E AC H M E A S U R E M E N T
Driscoll, L. (2003). The blast off kid. New York:
Kane.
Einhorn, E. (2008). A very improbable story.
Watertown, MA: Charlesbridge.
Ellis, J. (2004). What’s your angle, Pythagoras?
A math adventure. Watertown, MA:
Charlesbridge.
Fisher, V. (2006). How high can a dinosaur
count? And other math mysteries. New York:
Schwartz & Wade.
Friedman, A. (1994a). A cloak for the dreamer.
New York: Scholastic.
Friedman, A. (1994b). The king’s commissioners.
New York: Scholastic.
Friedman, M., & Weiss, E. (2001). Kitten castle.
New York: Kane.
Glass, J. (1998). The fly on the ceiling: A math
myth. New York: Random House.
Harris, T. (2008). Splitting the herd: A corral of
odds and evens. Minneapolis, MN: Millbrook.
Herman, G. (2002). Bad luck Brad. New York:
Kane.
Herman, G. (2003). Keep your distance! New York:
Kane.
Hightower, S. (1997). Twelve snails to one lizard:
A tale of mischief and measurement. New York:
Simon & Schuster.
Hoban, T. (1985). Is it larger? Is it smaller? New
York: Greenwillow.
Howard, E. (1993). The big seed. New York:
Simon & Schuster.
Hutchins, P. (1991). Happy birthday, Sam. New
York: Greenwillow.
Johnston, T. (1986). Farmer Mack measures his pig.
New York: Harper & Row.
Keenan, S. (1996). The biggest fish. New York:
Scholastic.
Kellogg, S. (1976). Much bigger than Martin. New
York: Dial.
MORE TO EX PLORE
ReadWriteThink.org Lesson Plans
■ “Bridging Literature and Mathematics by
Visualizing Mathematical Concepts” by David
Whitin and Phyllis Whitin
■ “What If We Changed the Book? Problem-Posing
With Sixteen Cows” by David Whitin and Phyllis
Whitin
IRA Book
Literacy + Math = Creative Connections in the
Elementary Classroom by Jennifer L. Altieri
■
IRA Journal Article
“Picture Book Power: Connecting Children’s
Literature and Mathematics” by Joyce Shatzer,
The Reading Teacher, May 2008
■
R T
www.reading.org
Kellogg, S. (2004). The mysterious tadpole. New
York: Puffin.
Lasky, K. (1994). The librarian who measured the
Earth. Boston: Little, Brown.
Leedy, L. (1995). 2 × 2 = boo! A set of spooky multiplication stories. New York: Holiday House.
Leedy, L. (2000). Measuring Penny. New York:
Henry Holt.
Leedy, L. (2003). Mapping Penny’s world. New
York: Henry Holt.
Leedy, L. (2005). The great graph contest. New
York: Holiday House.
Leedy, L. (2007). It’s probably Penny. New York:
Henry Holt.
Lewis, J.P. (2002). Arithme-tickle: An even
number of odd riddle-rhymes. San Diego, CA:
Harcourt.
Ling, B. (1997). The fattest, tallest, biggest snowman ever. New York: Scholastic.
Lionni, L. (1960). Inch by inch. New York:
Scholastic.
LoPresti, A.S. (2003). A place for zero: A math
adventure. Watertown, MA: Charlesbridge.
Losi, C.A. (1997). The 512 ants on Sullivan Street.
New York: Scholastic.
Love, D.A. (2006). Of numbers and stars: The story
of Hypatia. New York: Holiday House.
McCallum, A. (2006). Beanstalk: The measure of
a giant: A math adventure. Watertown, MA:
Charlesbridge.
McCarthy, R.F. (2001). The inch-high samurai.
Tokyo, Japan: Kodansha International.
McElligott, M. (2007). Bean thirteen. New York:
G.P. Putnam’s Sons.
Morimoto, J. (1988). The inch boy. New York:
Puffin.
Murphy, S.J. (1996). The best bug parade. New
York: HarperCollins.
Murphy, S.J. (1997a). Divide and ride. New York:
HarperCollins.
Murphy, S.J. (1997b). Elevator magic. New York:
HarperCollins.
Murphy, S.J. (1999). Super sand castle Saturday.
New York: HarperCollins.
Murphy, S.J. (2001a). Captain Invincible and the
space shapes. New York: HarperCollins.
Murphy, S.J. (2001b). Probably pistachio. New
York: HarperCollins.
Murphy, S.J. (2002a). Bigger, better, best! New
York: HarperCollins.
Murphy, S.J. (2002b). Racing around. New York:
HarperCollins.
Murphy, S.J. (2003). Less than zero. New York:
HarperCollins.
Myller, R. (1991). How big is a foot? New York:
Dell.
Nagda, A.W., & Bickel, C. (2000). Tiger math:
Learning to graph from a baby tiger. New York:
Henry Holt.
Neuschwander, C. (1997). Sir Cumference
and the first round table: A math adventure.
Watertown, MA: Charlesbridge.
Neuschwander, C. (1998). Amanda Bean’s amazing dream: A mathematical story. New York:
Scholastic.
Neuschwander, C. (1999). Sir Cumference and the
dragon of pi: A math adventure. Watertown,
MA: Charlesbridge.
Neuschwander, C. (2001). Sir Cumference and the
great knight of Angleland: A math adventure.
Watertown, MA: Charlesbridge.
Neuschwander, C. (2005). Mummy math: An
adventure in geometry. New York: Henry Holt.
Neuschwander, C. (2006). Sir Cumference
and the Isle of Immeter. Watertown, MA:
Charlesbridge.
Neuschwander, C. (2007). Patterns in Peru: An
adventure in patterning. New York: Henry
Holt.
Ochiltree, D. (1999). Bart’s amazing charts. New
York: Scholastic.
Penner, L.R. (2002). X marks the spot! New York:
Kane.
Pilegard, V.W. (2000). The warlord’s puzzle.
Gretna, LA: Pelican.
Pilegard, V.W. (2001). The warlord’s beads.
Gretna, LA: Pelican.
Pilegard, V.W. (2003). The warlord’s puppeteers.
Gretna, LA: Pelican.
Pinczes, E.J. (1993). One hundred hungry ants.
Boston: Houghton Mifflin.
Pinczes, E.J. (1995). A remainder of one. Boston:
Houghton Mifflin.
Pinczes, E.J. (2001). Inchworm and a half. Boston:
Houghton Mifflin.
Pluckrose, H. (1995). Length. Danbury, CT:
Children’s.
Pollack, P., & Belviso, M. (2002). Chickens on the
move. New York: Kane.
Puharich, T. (1998). How do you measure a dinosaur? Walton-on-Thames, UK: Nelson
Thornes.
Rocklin, J. (1998). Not enough room! New York:
Scholastic.
Rocklin, J. (2000). The incredibly awesome box: A
story about 3-D shapes. New York: Scholastic.
Russo, M. (1986). The line up book. New York:
Greenwillow.
Schmandt-Besserat, D. (1999). The history of
counting. New York: Morrow.
Schwartz, D.M. (1999). If you hopped like a frog.
New York: Scholastic.
Silverstein, S. (1974). Where the sidewalk ends: The
poems and drawings of Shel Silverstein. New
York: Harper & Row.
Sweeney, J. (2002). Me and the measure of things.
New York: Dragonfly.
Thompson, L. (2001). One riddle, one answer.
New York: Scholastic.
Turner, P. (1999). Among the odds and evens: A
tale of adventure. New York: Farrar Straus &
Giroux.
Van Allsburg, C. (1981). Jumanji. Boston:
Houghton Mifflin.
Walpole, B. (1995). Distance. Milwaukee, WI:
Gareth Stevens.
Wells, R.E. (1993). Is a blue whale the biggest thing
there is? Morton Grove, IL: Albert Whitman.
Wells, R.E. (1995). What’s smaller than a pygmy
shrew? Morton Grove, IL: Albert Whitman.