Writing in Mathematics

Using Writing in Mathematics
to Deepen Student Learning

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Acknowledgements
The following McREL staff members contributed to this publication.
Kathleen Dempsey, M.Ed.
Matt Kuhn, M.A.
Heather Martindill, M.S.

© 2009 McREL
20090609

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Using Writing in Mathematics
to Deepen Student Learning
by
Vicki Urquhart

“Writing in mathematics gives me a window into my students’
thoughts that I don’t normally get when they just compute
problems. It shows me their roadblocks, and it also gives me,
as a teacher, a road map.”
–Maggie Johnston
9th-grade mathematics teacher,
Denver, Colorado

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Introduction
INTRODUCTION
Writing is the ability to compose text effectively for different purposes and audiences.
When many of us reflect on our own school experiences, we recall writing in English
and history classes, but not in mathematics. Math classes previously relied on skill-
building and conceptual understanding activities. Today, teachers are realizing that
writing during a math lesson is more than just a way to document information;
it is a way to deepen student learning and a tool for helping students gain new
perspectives.

They recognize, too, that students whose strengths are language-based—and many
are—use writing as the key to understanding other disciplines, especially mathematics.
For example, Dr. David K. Pugalee (2004) conducted a study with 9th-grade algebra
students to determine if journal writing can be an effective instructional tool in
mathematics education and found that it may have a positive effect on problem
solving because the writer must organize and describe internal thoughts.

Like most things, learning to write well requires instruction and practice. In this
booklet, I aim to nudge secondary math teachers who are thinking about using
writing in their classrooms more extensively and to encourage those who want
to begin. Perhaps you will come to the same conclusion as mathematics educator
Marilyn Burns, who said, “I can no longer imagine teaching math without making
writing an integral aspect of students’ learning” (p. 30).

Section One gives a brief background that answers the question you may be
wondering: Why write in mathematics? Section Two describes the existing role of
writing in the mathematics curriculum, and Section Three provides strategies and
ideas to put into practice right away.

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Section One
SECTION ONE:
What we know from research about writing in the content areas
Researchers agree that, like reading, improving student’s writing skills improves
their capacity to learn (National Institute for Literacy, 2007). We also know that
writing fosters community in a classroom and, because writing is a social act, it is a
vehicle for students to learn more about themselves and others. Researcher Donna
Alvermann (2002), an expert in adolescent literacy, studies students’ self-efficacy and
engagement. She urges all teachers, despite their content area expertise, to encourage
students to read and write in many different ways. She does so because she believes
that writing raises the “cognitive bar,” challenging students to problem solve and
think critically. What other single action requires students to be so grounded in a
viewpoint that they can convince others, to know a process so thoroughly that they
can explain it to someone else, or to grasp the nuances of an idea so deeply that they
can convey it in a way that provokes thought and sparks discussion?

I know that writing does this Why are we writing in math class?
for me each time I draft an David Pugalee (2005), who researches
article or prepare a workshop the relationship between language and
presentation. Until I read what mathematics learning, asserts that writing
I have written, I don’t see the supports mathematical reasoning and problem
holes in my logic, the missing solving and helps students internalize the
steps, or the rambling thoughts. characteristics of effective communication. He
Writing informs me that I only suggests that teachers read student writing for
have a cursory knowledge of evidence of logical conclusions, justification of
answers and processes, and the use of facts
the content when I need a deep
to explain their thinking.
one. Simply put, it doesn’t let me
cut corners. Whenever I have
conducted workshops on using writing in mathematics, math teachers, quick to see
the parallels with problem solving, have rallied to the idea. Happily, teachers who
want to begin infusing writing in their instruction or who want to increase their
use of it don’t have to start from scratch. They can begin with their own well-crafted
lessons and add a writing activity that will enhance student engagement and heighten
cognitive demands.

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In Writing Next, researchers Graham and Perin (2007) identify the following 11
elements of current writing instruction that help young people learn to write well
and to use writing as a tool for learning.
1. Teach students strategies for planning, revising, and editing.
2. Explicitly and systematically teach students how to summarize texts.
3. Use instructional arrangements in which students work together on writing.
4. Assign students specific, reachable goals for their writing tasks.
5. Use computers and word processors as instructional supports for writing
assignments.
6. Teach sentence combining as a way to construct more complex, sophisticated
sentences.
7. Engage students in prewriting activities to generate ideas for composing.
8. Use inquiry activities where students analyze immediate, concrete data to
develop ideas and content for a particular writing task.
9. Use the writing process to provide extended writing opportunities.
10. Provide opportunities to read, analyze, and emulate models of good writing.
11. Use writing as a tool for learning content material.

There are many formal and informal ways to make these elements actionable in
schools. For example, a school undertaking a writing initiative might adopt one
element a month for a year. Or, if teachers already meet regularly for book studies,
they could meet to share their ideas, concerns, and successes about implementing one
of these writing elements. I encourage you to try, share, and try again. You will get to
know your students in ways you never have before, and you will most certainly know
who is and isn’t learning mathematics content.

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Section Two
SECTION TWO:
Writing as part of the mathematics curriculum
Writing is not a separate entity from the mathematics curriculum; it is part of it.
Among the learning goals that the National Council of Teachers of Mathematics
(NCTM) has set for all students is
to communicate their mathematical Principles and Standards for School
thinking. Mathematics
NCTM recommends that writing about “Reflection and communication are
intertwined processes in mathematics
mathematics be nurtured across grades.
learning…Writing in mathematics can also
NCTM suggests that students write help students consolidate their thinking
explanations about how they solved a because it requires them to reflect on
problem, solutions to exercises as if they their work and clarify their thoughts about
were writing a textbook, essays about the ideas” NCTM (2000), p.61.
what it means to prove something,
or reports describing the significant
contributions of well-known mathematicians (2000). Joan Countryman (1992), who
explores the relationship between mathematics and writing, offers the following four
benefits of writing in mathematics class:
Students write to keep ongoing records about what they’re
doing and learning.
While they’re writing, students can restate new material in their own words, identify
computations that are easy or difficult, or reflect on aspects that confuse them, as in
this note from a student to his math teacher.

Dear Mr. Kuhn:

Today we talked a lot about equations. I understand what an equation is. I
have used them many times. But I don’t really understand how an equation can
be turned into a sentence. I know how to do the math but not how to explain
it. Would you please spend some more time tomorrow teaching us how to make
sentences out of equations?

Thanks,
Sammy

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Students write in order to solve math problems.
Students can write the facts they need to answer a question beforehand and afterwards,
then check their computations against their written facts. This also helps them see
different ways to arrive at an answer. When doing a unit on slope, one of Maggie’s
students wrote down her thought process this way:

In order to solve the problem, I need to find the rate of change in the sale of blue
jeans by subtracting the amount sold in 1992 from 1996 and then add the costs on
top of the cost in 1992 until it reaches this year.

Another student wrote:

I need to find the slope, which is the rate of change, and then next find B and
finally solve the problem. The rate of change is the jeans.

Students write to explain mathematical ideas.
When students write explanations of their work and give examples, teachers can
better assess student understanding and progress throughout time. Writing is an ideal
vehicle for formative assessment, providing teachers with the information they need
to adjust their instruction.

Three kinds of writing prompts reflect three aspects of learning mathematics:
1) content, 2) process, and 3) affective. Content prompts deal with mathematical
concepts and relationships, process prompts focus on algorithms and problem
solving, and affective prompts center on students’ attitudes and feelings. Content
prompt examples include these:

• Define parallel in your own words.
• How would you describe a number line?
• Write a paragraph about the graph in the news.
• Write one sentence that describes an equation.
• How do you know that 1/4 is greater than 1/5? Explain your thinking.
• Write as many examples of a square that you can think of in five minutes.
• What properties do triangles have?
• Write everything you know about money.
• What were the key points in today’s lesson?

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Students write to describe learning processes.
Writing about problem solving requires students to monitor and reflect on the
strategies and processes they select. Maggie explains why she uses writing to enhance
the metacognitive aspect of learning in mathematics: “If there’s no writing in math
class, all they’re doing is the evaluation-execution portion of learning. Orientation
and organization come before execution, and that’s what writing gets at. That’s the
most valuable piece of writing in mathematics class,” she said.

Maggie develops the reflective writing prompts she uses with a learning objective in
mind. Frequently, it includes a metacognitive piece, which will require her students
to organize a problem, do the problem, and rethink it. This is how it looks in her
classroom:

Maggie shows the class an example problem from her Algebra 2 class: 2 log4 x - 5
log and asks, “Does anyone know how to do this problem?”

She waits for a few minutes, sensing students’ hesitancy to respond. Maggie has
anticipated this, so she removes the problem from the overhead, replacing it with a
writing prompt she has prepared.

“Here’s the writing prompt: When I see this problem, my first reaction is. . . Here
are your options:

1. I realize why I hate math.
2. I’m a little afraid, but I know that condense means to make something smaller.
3. I’m not exactly sure how to do this problem, but we’ve been learning about logs.”

Maggie has set the stage for learning by providing students a vehicle for describing
their learning processes. The rest of the class period includes whole-class brainstorming
about what students already know about solving similar problems, time to work
alone and with a partner, and sharing learning processes and outcomes. To keep the
workload down, Maggie uses only two or three writing prompts with each unit and
tries to connect big ideas from each unit through writing. “Once they write about
those big ideas, it really enhances their understanding, especially at the high school
level,” said Maggie.

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Section Three
SECTION THREE:
Strategies and ideas for writing in mathematics
Not only should teachers be aware of the instructional strategies that are most effective
in improving student writing (National Institute for Literacy, 2007; Graham & Perin,
2007); they also need ideas for implementation. In this section, I address that need by
returning to the work of Joan Countryman (1992), who observes that writing in the
mathematics classroom generally looks like one of six types: Free writes; biography
and autobiography; learning logs, blogs, and journals; summaries; word problems; and
formal writing. With an understanding of these forms, strategies for implementation,
and practical ideas for integrating technology tools, all teachers—regardless of their
own comfort levels with writing—can enhance their mathematics lessons.

1. Free writing
Free writing involves writing nonstop for a fixed amount of time, usually just a few
minutes. Free writes don’t allow time for students to agonize over grammar or spelling;
rather, they encourage students to think freely and raise questions about a topic or
idea. When you first ask students to free write, give them high-interest topics, so they
can begin to write immediately. For example, students usually have strong opinions
about whether or not they will ever use advanced mathematics in “real life,” why they
should use calculators during high-stakes assessments, or whether an additional year
of math should be required in the high school curriculum. Once they are used to
writing on broad topics, ask them to write on math-related topics, such as predicting
the effect of one rotating object on another or comparing methods of analyzing data
sets. Finally, develop prompts that relate specifically to the content you are covering
in class by asking students to summarize their learning or describing steps in solving
a problem.

Implementation Idea: The Journalists’ Questions1
Once students have become comfortable writing for short periods, introduce “The
Journalists’ Questions” (who? what? when? where? why? how?). Explain that this
traditional reporters’ style of writing is a way of identifying essential information.

When studying units of measure, for instance, ask students to write the general
topic “the metric system” on their papers and list the six questions, leaving room
for a response to each. Give them a few minutes at the beginning or end of class to
answer as many as they can. Collect and look over responses, and you will quickly
discern what information or misinformation students already have. Here’s how the
six questions might apply to the topic “the metric system.”

1
For more writing strategies, see Urquhart, V. & McIver, M. (2005). Teaching Writing in the Content Areas.
Alexandria, VA: Association for Supervision and Curriculum Development.

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The Metric System
Who? Only three countries have not adopted the metric system: the
United States, Liberia, and Myanmar. All the sciences use it,
however.

What? It is an international system of measurement with proportional
graduations that uses naturally occurring standards as base
units.
When & It was first adopted in 1791 in France and spread throughout
Where? Europe.
Why? France wanted a standardized system of measurement that
would help unify the country with a single currency and
countrywide market. It can be reproduced any time by any
country.
How? It is based on the number ten, so it is easy to go from one unit
to another. You just multiply or divide by 10.

The next day, have a class discussion to clear up any misconceptions. Give students
the option to write a paragraph describing the metric system or defending its use in
science and mathematics. If you have access to technology, a fun way to apply this
strategy is to pair it with a Web site that you can check out ahead of time. Assign a
topic, ask students to complete as many of the Journalists’ Questions as they can, and
write a summary paragraph on the topic.

2. Biography & autobiography
This type of narrative non-fiction writing encourages students to write descriptively,
and to identify significant events, personality traits, turning points, and impacts on a
person’s life. The life stories of important mathematicians will intrigue some of your
students, and there are many Web sites with biographies, such as Omnibiography.
com; allmath.com/biography.php; or even Simpsonsmath.com, where students can
read the math biographies of the show’s writers.

To extend this writing opportunity, encourage students to write letters or e-mails
to the mathematicians (or the Simpson creators) they learned about. Alternatively,
ask students to illustrate in the form of a pie chart the percentage of the person’s life
devoted to the activity that made him or her famous. You also can use a variation of
autobiography called a “mathography” to learn more about your students’ attitudes,
perceptions of their effort and abilities, and to know the kind of support they think
they need.

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Implementation Idea: Write Your Mathography
At the beginning of a year, ask students to write about their experiences learning
mathematics, describing the strategies their instructors used to help them learn. Or,
provide a choice of writing prompts, such as these:

• What early math accomplishments do you remember? (e.g., When and how did
you learn to count? Who taught you? How did he or she teach you? Did you
“show off” this new talent to others?)
• When you were in elementary school, what did you like (or not like) about
math?
• What do you remember about learning to add and subtract? Which did you
think was more fun? Why?
• Was math ever your favorite subject? If so, why? If not, why?

3. Learning logs, blogs, & journals
Over time, the lines distinguishing learning logs and journals have blurred, but
students still can use these writing vehicles to respond to class discussions, make
connections between real-life and the content, and to reflect on themselves as
learners. Learning logs should focus on content, whereas journals might focus on
students’ ideas and questions about a broad range of general topics. Students use
each differently. While journaling, they might reflect on anything they consider
relevant, carry on conversations with their teachers, or both. Learning logs, on the
other hand, are less about “feeling” and more about understanding content. Similarly,
blogs allow students to share ideas and solutions in real time with each other, other
classes, and the teacher.

Although both kinds of insights are valuable,
teachers should assign learning logs, blogs, Algebra I Learning Log
and journals with different intent. Students • Date:
should write frequently in their logs and
• Name of topic, presenter,
blogs for several minutes at a time at least
chapter title, program/video:
once a week and should use an established
template for entering information. Journal • Pages read, length of discussion/
writing can be less frequent, perhaps every explanation or program/video:
two weeks. Here is one example of a learning • Main points:
log template that you can adapt and provide
• Summary of main points:
students.

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Implementation Idea: Climbing and Diving
This is a good strategy to use when students are writing in their learning logs. As
students move back and forth between climbing and diving (into a topic), they
internalize the process and the content. For example, following a unit on the area
of polygons, students spend 10 minutes writing everything they learned, including
formulas and descriptions. They then read over their writing and select one idea to
explore further, such as why the formula to determine the area of a triangle works for
all triangles, regardless of type. The second 10-minute writing allows them to justify
their thinking or reflect on their understanding. If you have access to technology, ask
students to journal electronically or keep a class e-learning log or blog. (For more
on Climbing and Diving, see Teaching Writing in the Content Areas by Urquhart &
McIver.)

Implementation Idea: Double-entry Journals
A double-entry journal is a long-standing popular activity for any content area.
Frequently, teachers pair it with a reading assignment where students summarize
on the left, which represents literal information from the text, and respond to the
summary on the right, which represents inferential and critical thinking. One way to
use a double-entry journal focusing on problem solving is to have students write the
problem in the left column and the details for solving it in the right column. To adapt
the journal, ask students to create a third column and write a personal reflection that
describes what was frustrating or easy, or to draw a horizontal line two-thirds of the
way down the paper to provide a section for summarizing the process.

4. Summaries
Because students often find summary writing difficult, teachers should explicitly
teach summary skills and provide plenty of opportunities for practice. Journals and
learning logs are ideal places for students to practice summarizing. Students should
understand they must identify main ideas, discriminating between information
that is essential and information that is merely interesting. Here are some practical
suggestions for using summary writing:

• Teach students how to organize key ideas into logical patterns using webs,
charts, or diagrams, such as a Venn Diagram, which visually represents common
elements, or a concept map, which presents relationship among a set of
connected ideas.
• Use summary writing when students are learning large amounts of information
and vocabulary terms.
• Allow students to write collaboratively or summarize together as a whole class.

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Venn Diagram

Types of Numbers

Prime Even

103 4 18
17
2
3 11 6
23 600

Concept Map

9 - 4 = 5
See how many A bird found 9
things you have Equation
beetles. He ate
to begin with. 4. At the same
Then take away time, 5 beetles
How does Story
some. Count how
it work?
Subtraction hid under a
many things you rock. Then the
have left, and
Drawing bird flew away.
that is your
answer.

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Implementation Idea: Magnet Summaries
A great way to explicitly teach summary writing is with the “Magnet Summary”
strategy.

Sample steps for using Magnet Summaries
• When studying equations, provide students a written selection (e.g., a textbook
section, Web site, or teacher-created document) that explains how to solve an
equation.
• Read the selection ahead of time and develop a list of key vocabulary words that
appear, such as inverse, variable, logarithm, exponent, etc.
• Provide students with the same number of index cards as total number of words
on the list.
• Write the magnet word list on the board, overhead transparency, or PowerPoint,
and ask students to write each word on an index card.
• Distribute the text selection, and ask students to read it. Working on their
own, they should reread and look for the magnet words, identifying key words
or phrases in the text that help explain or directly relate to the magnet word.
Explain that these are the words or phrases that the magnet words “attract,” and
students can highlight them with a marker, if it will help them remember the
meaning of the words.
• On the back of each index card, students then write a summary sentence
in their own words that defines, describes, or expresses the main idea of the
magnet word.
• Students read their sentences and organize the cards in a logical order.
• Students write a summary paragraph, adding transitional words and phrases.
• Students read their summaries to others, and revise for clarity and cohesion,
using peer feedback.
5. Word problems
Words are tools for thinking in mathematics, just as they are in other disciplines.
Good word problems promote thinking and encourage students to use their own
language, thus owning their ideas. Pugalee cites the research of Winograd (1992),
suggesting that students, when asked to write original word problems, will write
more interesting and challenging ones than textbook problems.

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Implementation Idea: Explicitly Teach Relevant Vocabulary
Whether writing their own word problems or preparing to write constructed responses,
students need to be comfortable with certain words, know their definitions, and be
able to use them in writing tasks. There are six concrete steps for learning a new word
(Paynter, Bodrova, & Doty, 2005):

1. Identify the new word and elicit students’ background knowledge (e.g., the term
“probability model”).
2. Explain the meaning of the new word (e.g., tell students that a probability
model is a technique for representing the chances of something occurring, and
that they will use a model, or something they can manipulate, to determine the
chances of two students each drawing a red chip from a bag of five blue and
five red chips. Show them two colored charts, one representing each student’s
chances, and a third chart representing the chances of both of the students
drawing a red chip.
3. Monitor students as they work in small groups to generate their own
explanations. If they have difficulty, you might need to provide a sentence stem
or ask questions or provide tools, such as dictionaries or thesauruses.
4. Ask students to create a visual representation of the new word. If you have access
to technology and the Internet, encourage students to find clip art, photos, or
interactive models (see a selection of mathematics and science interactives at
http://www.explorelearning.com).
5. Provide an experience to use the new word (e.g., discuss the probability that
students will win the state lottery).
6. Engage students in activities (e.g., vocabulary baseball or vocabulary bingo) to
help them remember the word and its meaning.

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In addition to teaching mathematics-specific vocabulary, teach students terms they
will see on state tests. Several of the most-used terms on constructed response items
appear in the chart that follows. You can assign the writing task on the chart or adapt
it to use with your students.

Common Constructed Response Terms with Definitions and
Mathematics Writing Tasks
Term Definition Mathematics Writing Tasks

Analyze Break down a topic into Examine a set of economic
its parts and examine statistics and write an editorial on
how each part functions the cause and effect relationship
in relation to the whole. between high wages and inflation.
Describe Represent a person, Write a detailed description of a
object, or idea in words. model so that someone else can
re-create it.
Evaluate General: Determine Write an article for a student
the significance, worth, newspaper about the benefits of
or quality of objects or taking extra math courses in high
ideas. school.
Specific to Evaluate the expression for x =
mathematics: Evaluate 5, y = 3. Work it out, and write an
an expression for a explanation for someone else to
given amount. follow.
Narrate Write a sequence of Relate the story of the evolution
actions occurring over of the abacus through ancient,
time. middle, and modern times.
Reflect/ Present to readers the Think about a different method of
Question same questions you ask solving the same problem that still
yourself. results in an accurate answer, and
explain it.
Summarize Briefly restate others’ Write a report compiling highlights
ideas in your own of the research on a mathematical
words. question that intrigues you.
Synthesize Combine information Write the final rubric criteria for a
and ideas from multiple math writing assignment.
sources.

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6. Formal writing
Formal writing should always be graded. When students write formally, they go
beyond the kinds of short writings they might have been doing in learning logs,
blogs, journals, or free writes to write research reports and essays. Formal writing can
still be done collaboratively, however.

Implementation Idea: Conduct a Research Project and Write a Report

Research topics can cover a wide range of students’ interests—Aristotle’s contributions
to the field of mathematics, the reason gas prices go up or down just before an election,
or differences in attitudes towards mathematics in other countries. Whatever students’
interests, when it is time to write the report, explain that formal mathematics research
papers include several sections, although not all papers contain all sections. A basic
format to adapt and share follows.

1. Title: Use it to catch the attention of the reader and reflect the content of the
paper.
2. Abstract: This is a summary paragraph that explains the basic purpose of the
paper, states the question(s) answered, and tells the reader what was proved.
3. Literature Review: When researchers consult existing literature and extend the
ideas they find there, they include a literature review. To complete this section,
ask questions such as, “What kind of relevant studies or techniques should I
know about in order to do the project?” “How have others gone about trying to
solve the problem, and how is my approach different?”
4. Statement of the Problem: This “sets the stage” for the paper. A brief
introduction gives the reader some context. What inspired you to explore this
problem? Is it a modification of some other question? Why is this problem
important or interesting to you?
5. Body of the Report: This takes the reader on a trip through the research project.
Using your learning log, write the body of the report as narrative non-fiction,
including your initial ideas. Include nonlinguistic representations and examples
as support.
6. Ideas for Further Research: State any questions that surfaced that are beyond the
scope of the project.
7. References. You must credit the people whose work you use. The Internet is a
great resource for this. Writing labs at colleges or universities, in particular, offer
online user-friendly guidance.

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Final
FINAL THOUGHTS
Standards have long been a kind of road map for teachers. For Maggie Johnston,
the mathematics teacher quoted at the beginning of this booklet, writing also is a
road map, and perhaps a richer, more detailed one. Teachers who include writing
experiences in their classrooms set the stage for active problem solving, invention and
discovery, increased reading, and improved content learning. Students get a chance
to express new knowledge and skills in their own words, organize their thinking
about the content, share their ideas, experience a creative side of mathematics, and
learn to value the act of writing; teachers get a tool that can motivate and engage
students, instant evaluations about students’ learning, and a way to participate in
interdisciplinary collaboration. Whatever the purpose, writing should be as much at
home in a mathematics class as in an English class.

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References

REFERENCES

Alvermann, D. E. (2002). Effective literacy instruction for adolescents. Journal of Literacy
Research, 34(2), 189–208. Retrieved April 1, 2009, from http://www.coe.uga.edu/
reading/faculty/alvermann/effective2.pdf
Bergman, S. (1992). Exploratory programs in middle level schools: A responsive idea.
In J. Irvin (Ed.), Transforming middle level education (pp. 179–192). Boston: Allyn
and Bacon.
Burns, Marilyn. (2004, October). Writing in math. Educational Leadership, 30–33.
Countryman, J. (1992). Writing to learn mathematics. Portsmouth, NH: Heinemann.
Graham, S. & Perin, D. (2007). Writing next: Effective strategies to improve writing of
adolescents in middle and high schools. New York: Alliance for Excellent Education.
Mizelle, N. B. (1995, April). Transition from middle school into high school: The student
perspective. Paper presented at the Annual Meeting of the American Educational
Research Association, San Francisco.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and
standards for school mathematics. Reston, VA: Author.
National Institute for Literacy. (2007). What content-area teachers should know about
adolescent literacy. Washington, DC: Author.
Paynter, D. E., Bodrova, E. & Doty, J. K. (2005). For the love of words: Vocabulary
instruction that works. San Francisco: Jossey-Bass.
Pugalee, D. K. (2004). A comparison of verbal and written descriptions of students’
problem-solving processes. Educational Studies in Mathematics, 55, 27–47.
Pugalee, D. K. (2005). Writing to develop mathematical understanding. Norwood, MA:
Christopher-Gordon.
Urquhart, V. & McIver, M. (2005). Teaching writing in the content areas. Alexandria,
VA: Association for Supervision and Curriculum Development.
Winograd, K. (1992). What fifth graders learn when they write their own math
problems. Educational Leadership, 64(4), 64–66.

info@mcrel.org 19

Workshops
Essential Skills for Academic and Lifelong Success
Because mathematics and literacy skills are fundamental to student success, McREL
provides educators with services and products that translate rigorous research into
practical classroom applications. Learn more about McREL’s mathematics workshops
and training at http://www.mcrel.org/topics/Mathematics.
• Doing the Right Things Right in Mathematics
• Increasing Mathematical Understanding Through Literacy
• Making Afterschool Count: Mathematics Learning in Afterschool
• Mathematics Leadership Institute (six 2-day sessions)
• Meeting Learning Standards for Preschool and Kindergarten Children: Literacy
and Mathematics
• Technology in the Content Areas: Elementary Mathematics
• Technology in the Content Areas: Secondary Mathematics
• What Research Says about Improving Mathematics Achievement

Products
E-mail us at info@mcrel.org to request a product catalog for ordering
these popular manuals:
•
•
For the Love of Words: Vocabulary Instruction that Works
Remove Limits to Learning With Systematic Vocabulary Instruction•
• Scaffolding Literacy Development in the Preschool Classroom
• Scaffolding Literacy Development in the Kindergarten Classroom
• Teaching Reading in the Content Areas: If Not Me, Then Who? 2nd ed.
• Teaching Reading in Mathematics
• Teaching Writing in the Content Areas
• EDThoughts: What We Know About Mathematics Teaching and Learning, 2nd ed.

Contact Us
Mid-continent Research for Education and Learning
4601 DTC Boulevard, Suite 500
Denver, Colorado 80237
Phone: 303.337.0990, Fax: 303.337.3005, E-mail: info@mcrel.org

20 www.mcrel.org

Mid-continent Research for Education and Learning
4601 DTC Blvd., Ste. 500, Denver, CO 80237-2596
P: 800-781-0156 • F: 303-337-3005
E-mail info@mcrel.org • Web site www.mcrel.org

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