Writing in the Math Classroom

8/9/2019 Writing in the Math Classroom

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Integrating Writing into the Mathematics Classroom

Integrating writing into your mathematics classroom can be easy for you and beneficial for yourstudents. Communicating about mathematics helps strengthen student learning, which can builddeeper understanding. It provides students an opportunity to organize their thoughts related to themath topic, which helps clarify their thinking.

Student writing can also provide valuable insight for you into their mastery of math concepts.Teachers can use writing assignments as either an informal or formal assessment tool. Writing oftenreveals gaps in learning and misconceptions, which can help inform your instructional planning andintervention strategy.

First StepsWriting activities in math class can take several forms, ranging from frequent, quick, and informalactivities, to creative writing assignments, to more involved, long term assignments involving

research, expository writing, and/or cooperative projects. You can use writing activities in math classto diagnose learning difficulties, assess student mastery of concepts, and to enable students toexpress their thoughts and feelings about math in reflective or creative ways. Writing also provides aninteresting and varied instructional activity for your students.

Guidelines for Assigning Writing

Let your students know ahead of time whether or not the writing activity will be evaluated.

Adhere to the same expectations for composition, written expression, and usage and

mechanics that are expected for traditional English class assignments. Even though it's mathclass, students should still be expected to utilize grade-level expectations for writing skills.

Remember, writing clearly and preciselyan important benefit of writing in math classshouldalways be expected of your students.

Determine the timeframe for the written assignment. This can range from fast and frequent

five minutes, everydayto week-long assignments, given several times a semester, to longerassignments, given once a semester.

You may want to use study groups or cooperative learning groups for some assignments,

which can further strengthen the learning.

Tip:

If your students are struggling with a writing activity, don't hesitate to model desirable strategies for completing theassignment and a sample high quality final product. Present a sample final product for a written assignment to your

class. Discuss with your students the thought processes you went through to complete the assignment. Point out the

critical elements of your final product and describe how they met the expectations for the assignment.

Ideas for Mathematics Writing ActivitiesIntegrating writing can be quick and easy. Here are several activities that are a snap to incorporate,and can kick-start writing in your math class. As you feel more comfortable, try incorporating a few

longer, more involved writing activities.

Math Journals. Math journals are a great way to begin class. Display a writing prompt on an

overhead projector or white board for your students to read as they enter the classroom.Students should spend five to ten minutes writing on the daily topic. Math journals can also beused to assess background knowledge when beginning a unit, and then used as a means ofassessing acquired learning at the end of the unit. Make sure your students know ahead oftime if their journal assignment will be read by you and/or evaluated. If so, determine whenand how often you will collect and read your students' journals. You will also need to decide if


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you will devote class time to permit students to share their journal writingwhich many loveto do!

Math Journal Topics

Explain a formula.

Write an explanation of a recently-learned concept, as if you were explaining it to a younger sibling or

friend.

Write about a time that you were really confused in math class. What did you do? Who did you get help

from? How did you explain what was confusing you?

Write about a time that you helped explain something to a classmate. What was your classmate having

difficulty with? How did you help your classmate?

Write everything you know about probability. (A great way to start a chapter! Have your students write a

similar entry at the end of the chapter, and then have them compare this with their initial entry.)

Present a graph from a newspaper or magazine and have your students write a paragraph about the graph.

Write as many examples of a ratio that you can think of in five minutes.

Creative/Expressive Writing Activities. These activities can be short or long-termassignments. Either way, they'll be quite fun and insightful for your students (and for you).

o Write a Vocabulary ParagraphAssign a list of math vocabulary words to your

students, then have them write a paragraph that incorporates all of the words on thelist. Your students will have fun generating some clever ideas for their paragraphs!

o Create Missing Numbers StoriesSimilar to the vocabulary paragraph activity, have

your students write a creative story that incorporates a variety of numbers. After your

students have written the paragraph, have them turn their paragraph into a puzzle bywriting a new version of the paragraph with blanks where each number appears. Havethe students include a table with the numbers used at the top of the paragraph, thenexchange paragraphs with partners, and try to place each number in its correct placein the paragraph. This can be a beneficial activity when your students are studying orreviewing rational numbers or the set of real numbers. If desired, you can tell yourstudents that they must include an integer, a fraction, a decimal, a percent, and anirrational number in their story.

o Word PuzzlesHave your students create a word puzzle with vocabulary words for

their current chapter (this can be a great summary activity for the end of a chapter).Students should create word puzzles such as crosswords or word jumbles that requirethem to write clues. This will ensure that students are applying their knowledge of themath terms, such as definitions and examples.

o PoetryWriting and sharing poems is a popular way for middle school and high school

students to share ideas and feelings. The creative process involved in writing poetryrequires students to apply their understanding of math concepts to the task. Yourstudents may enjoy presenting their poetry in a "Math Poetry Slam" event for otherclasses. A fun and easy poetry assignment is to have your students write haiku poemsfor geometric solids. (Haiku, and its three line, five syllable, seven syllable, fivesyllable format is quite appropriate for a math activity!) Take this haiku, for example:


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Triangular Prism

Five faces, all flat

Your straight edges count to nine

Trianglesa must!

o Advice ColumnsHave students write fictitious advice columns, as one might find in a

newspaper, except these are math advice columns. Have your students think of math-related names to use for their advice column, for example "Dear Algy" (short foralgorithm), or "Dear Doctor Pi." You can either assign a topic for the advice column, ortry having your students think up possible math situations when someone might needadvice, such as "I keep getting my cosine confused with my tangent. Please help mestraighten this out," or "I can't remember how to find the slope of a line."

o Research ActivitiesCan be longer-term assignments, usually lasting a week or two,

and can be completed individually, or in small groups. For a research activity, preparean assignment handout that lists the required elements, how the assignment will beevaluated, and when it is due. You may want to include a rough draft milestone,especially if it is an initial written assignment.

Research Activities Ideas

Biographies of Famous MathematiciansNewton, Fermi, Pascal,

Galileo, Euclid, and of course, Albert Einstein, are just a few of the mathematicians

your students can research and write reports about. These reports can be assigned as

traditional biographies, or for a more creative assignment, have your students write

an obituary as it might appear in a newspaper.

Careers That Require the Use of MathematicsHave smallgroups research various careers and write a report that they will present to class.

Have students include specific examples of mathematics used in the career they

research. Possible careers include: architect, chemist, physicist, engineer, statistician,

chef, engineer, landscape designer, fashion designer, graphic designer, and football

coach. Have students conduct interviews, research college courses required for

applicable degrees, read magazine and newspaper articles, and read traditional

reference books on each career.

Conduct a SurveyThe math strands of data, statistics, and

probability lend themselves to interesting research and writing activities. One

example is to have small groups design and conduct a survey. You may want to

begin this activity by sharing a few examples of published surveys with your

students and discussing the survey questions. Have your students discuss whether ornot the survey questions were clearly written and easy to answer. Your students will

need to determine a survey topic, decide on an appropriate sampling technique, write

the survey questions, and finally, assure there is no bias in their survey or sample

population before conducting their survey. Along with appropriate statisticalmeasures, have your students write a detailed summary of the process they

undertook, as well as a summary of their findings. Make sure your students include

at least one graph in their summary.


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Teacher Tip

If your students are struggling with a writing activity, don't hesitate to model desirable strategies for completing theassignment and a sample high quality final product. Present a sample final product for a written assignment to your

class. Discuss with your students the thought processes you went through to complete the assignment. Point out the

critical elements of your final product and describe how they met the expectations for the assignment.

This article was written by Heidi Janzen, a former classroom teacher and mathematics specialist. She

now works as an educational consultant in the areas of professional development, curriculum,

standards, and assessment.


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Journaling in the Math Classroom

Sample Prompts for Journals/Blogs

Reflect on your participation in class today and complete the following statements:

o I learned that I...

o I was surprised that I...

o I noticed that I...

o I discovered that I...

o I was pleased that I...

Describe how you feel about solving _________ problem.

Explain in your own words what subtraction means.

Explain what is most important to understand about fractions.

How and When to Use Journal Writing

1. When new material has been introduced.

Ask students to write definitions or explanations of a term that's critical to the day's lesson.

Sample Direction: "Explain in your own words the meaning of the term

____________."

2. When the class looks disengaged or confused.

Ask students to write an explanation of something you were doing or a term you used. Have

them share journal entries aloud, and redirect the lesson accordingly.

Sample Direction: "Write down two questions you have about the work

you are doing/the lesson we're working on."

3. When collaboration with fellow students is appropriate.

Have students form small groups and work together to solve a problem on paper. This willget them to talk to each other-to ask questions and give explanations-all with the common

goal of solving the problem.

4. When teaching the value of revising their work.


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Occasionally ask students to pick a journal entry and revise it. This helps emphasize that

journal writing is an initial effort that can be rethought and improved upon-the end product is

less important than the process.

Sample Direction: "Review the last three entries in your journal. Select

one to revise." Specific suggestions might include, "Write a clearer

explanation," or "Draw a picture to express your idea in this journalentry."

Sample Journal Questions/Writing Prompts

Writing prompts can take many different forms. We have found that students respond best

when the prompt is clear and can be approached in different ways. We recommend prompts

that do the following:

1. Pinpoint a confusing or easily misunderstood mathematical idea

For Example: "Do 0.2 and 0.020 equal the same fraction? Explain youranswer."

Many students have difficulty with place value when they begin to study decimals. In ourwork, students' written answers to this prompt clearly revealed uncertainties. As one student

responded: "The zeroes don't matter, so .2 equals .2." This student does not appear to have agood understanding of place value, having over generalized the "hint" to ignore certainzeroes. Another student drew two grids in response to this prompt. In one grid she colored in

two rows of tenths and in the other grid she colored in two hundredths. She concluded that

0.2 was "way more" than 0.020. Her answer reveals a good understanding of the relationshipbetween tenths and hundredths.

2. Can be solved using different strategies

For Example: "Allison's team won 8 out of 10 games. Jennifer's team

won 15 out of 18 games. Whose team won a greater fraction of its

games? Explain your answer."

Students used different strategies to approach this problem . One student found a least

common denominator and then compared the two teams' performance. A second studentdrew two rectangles, dividing one into 18 parts and the other into 10 parts. He then colored in


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15 and 8 parts, respectively, of each rectangle. The student did not know how to proceed, but

he did show a good understanding of how fractions could represent the win/loss records of

the two teams.

3. Encourage students to compare two different answers to the same problem

For Example:

"Who is correct? The problem: Which fraction is biggest? 1/3 or

2/5?"

Jamar's solution: 2/5 is bigger because 15 is the LCD and 1/3

equals 5/15. 2/5 equals 6/15. So 2/5 is biggest.

Bill's solution: I used the calculator. I made them decimals andthen compared the decimals. For 1.3, I divided 1 into 3 and got

3.0. Then I divided 2 into 5 to get 2.2. 3.0 is bigger than 2.2, so1/3 is biggest.

This prompt encourages students to consider two very different approaches to the sameproblem: the least common denominator (LCD) method taught in the text and a calculator.

The two offered solutions also model fairly clear explanations. In this case a correct and an

incorrect solution are offered. As students become more skilled at comparing two responses

the differences between the solutions can be more subtle. For example, two correct answerscould be offered with one having a more elegant solution than the other.

Encourage your students to use drawings and graphs to explain their thinking.

Research shows that using simple visual aids (diagrams, graphs, etc.) improves mathematical

problem-solving ability, especially in female students.

As student writing progresses, ask students to write about their small group work.

Ask the group to write a summary of how they reached a solution, including any "false

starts" or "dead ends."

Ask each individual to write an explanation of the group's work on a problem. Have the small

groups discuss the individual explanations.

After a small group assignment, have students "explain and illustrate two different

approaches to solving a problem."


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Managing Math Journals: Helpful Tips

1. Provide students with thin, inexpensive journals. College "blue books" work well: Students

feel important using college materials, and additional books can be stapled on as students fill

them up.

2. Keep journals in class. Collect math journals each day so as not to lose them.

3. Decide whether you want students to "decorate" their journals, or reserve them for writing

only.

4. Decide on a system for identifying journal entries. Rather than having students take time to

copy the writing prompt, have them number or date the entries.

5. Develop system for distributing and collecting journals each day. So as not to interrupt classinstruction, have a second adult distribute and collect journals, or choose a "journal student" who

attends class regularly to do so.

6. Use a timer for some journal assignments. This will help keep students writing. Using clear

time limits for writing makes the assignment seem more "scientific," more important to students.

Encouraging Students as They Write

1. Be patient. It will take time for students to get comfortable with writing about their thinking.

2. Tell students you understand how new and different this is for them. Remind them that thereare no "wrong" answers in writing about thinking.

3. If students indicate they have no more to say:

Read over what they've written. Ask questions such as: "What other questions do you

have about this topic that you haven't written about?" or "What's another way this couldhave been said?"

Have them copy what they've written, so they'll get the idea that they are to write for thewhole time given. (Often, they'll get bored with copying and begin writing somethingnew.)

4. Ask students to choose a journal entry to revise.


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Some students will use this revision exercise to rethink math ideas; others will work on

writing more clearly. Whatever their focus, revision tells students their thoughts are

important and worth developing.

5. Provide feedback.

Let students know you took time to read their journals.

You won't have time for in-depth comments on each journal for every assignment, so try

other kinds of feedback, too:

Stars

Stickers

Smiley Faces

Put stars by sentences that helped you see their thinking.

6. Clearly communicate to students the purpose of writing in math class.

Explain how their writing helps teachers to understand how students think.

Other purposes of writing: Writing is a concrete way to show students' thinking that they

can look at and think about. Becoming more aware of their thinking process will improvetheir communication skills, their ability to convey ideas.

7. Use students' writing samples to help them refine their writing.

Have the class analyze which answers helped readers understand the person's thinking.

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Writing in the Math Classroom