Writing in Mathematics: Common Objections & FAQs

by Stephanie Krajicek

Anytime a teacher decides to try something new, s/he is likely to have concerns. Writing in math is no exception. Here are some common concerns math teachers have when the subject of writing in math comes up in conversation:

I’m a math teacher, not an English teacher.

True. Remember, however, that just because you teach math doesn’t mean your students don’t rely on language to solve problems. O’Malley and Chamot indicate that students must use language skills in math classes – especially as they reach higher-level math classes (1994). “Though much mathematics instruction focuses on representing ideas with symbols and manipulating those symbols, students still understand mathematics by linking those forms with meaning (Kessler, 1987).” “…[M]ore is required than symbol manipulation, particularly at higher levels” (Clarkson and Thomas, 1993).

The National Council of Teachers of Mathematics (NCTM) acknowledges the dependence of mathematics literacy on language by advocating the cultivation of communication in math classes. The communication standard states that students should be able to:

• organize and consolidate their mathematical thinking through communication;
• communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
• analyze and evaluate the mathematical thinking and strategies of others;
• use the language of mathematics to express mathematical ideas precisely (NCTM, 2006).

Additionally, Indiana academic standards for communication in mathematics support the use of writing as a means to math literacy:

The ability to read, write, listen, ask questions, think, and communicate about math will develop and deepen students’ understanding of mathematical concepts. Students should read text, data, tables, and graphs with comprehension and understanding. Their writing should be detailed and coherent, and they should use correct mathematical vocabulary. Students should write to explain answers, justify mathematical reasoning, and describe problem-solving strategies (Indiana Department of Education, 2006).

Being able to meet the communication standard requires students to have and utilize a mathematics register, “a set of specialized vocabulary and preferred (or dispreferred) syntactic and rhetorical devices/structures, used by specific socio-professional groups for special purposes” (Schiffman, 1997).

The language of mathematics is highly specialized and includes specific vocabulary, syntax, and discourse that must be mastered before students can be successful (Kang and Pham, 1995).

I like to think of this unique shift in teaching roles as the transitive property of language learning. If a = math teacher; b = guides students towards use of specialized oral and written language to communicate content; and, c = English teacher then. . .

a = b and b = c, therefore a = c

Not only do you teach students math, you are teaching them to speak, read, and write a specialized language that English teachers can’t and don’t teach. You could say that you’re a de facto English teacher. Other often heard comments include:

I’m not qualified to teach or grade writing.

That’s ok. What is important is what is written, not how it is written (Burns, 2004). This doesn’t mean that grammar and language conventions can be thrown out; it just means that you don’t have to teach your students about dangling modifiers and comma splices. However, all writing, even math writing, needs to be fluent. You will have set a standard for your students’ writing. Their work can’t be so riddled with errors that it isn’t comprehensible. Think of it as practice for the I-STEP.

Remember that writing is a tool. The key to using writing in mathematics is to remember the purpose: writing to learn.

Writing to learn allows students to accomplish many things: It requires students to organize, clarify, reflect on, explore, and extend their ideas (Burns, 2004; Fortescue, 1994). It reinforces learning of specific content (Armes & Sullenger, 1986); provides teachers with alternative assessment opportunities; and increases recall and understanding of information (Evans, 1984; McGee, 1982; Fortescue, 1994).

I don’t have time to do writing in my class.

Sister Brandenburg, a math teacher in Illinois “…learned that students in [her] upper-level classes could work the problems when [she] taught the material, but ‘putting it together’ seemed incredibly difficult. Students found it hard to combine or apply techniques. In addition, they couldn’t use the material in unfamiliar situations. When talking to other math teachers, [she] discovered that these were common problems” (2002).

If students are not able to apply their knowledge, it isn’t very useful. I have found that forgoing comprehension and depth in favor of breadth has not been successful in my own classroom. What good does knowing a little about a lot do if there are no connections between the information? Using writing is one way to help students make the connection between school and “real life.” Exploration and extension activities allow students to apply math skills in ways that are meaningful and rooted in every day experiences instead of relying on the teacher to provide problems and solutions. Students take ownership of their learning and are better able to find ways to use it outside of the classroom.

How am I supposed to actually implement this?

Here is what math teachers who have used writing in their classrooms have to say about writing in math:

• Start small. It takes a long time to grade writing, especially if you have large classes or teach multiple courses. “Start with one class or use a journal for a specific unit” (Brandenburg, 2002).
• Manage student writing. Decide “when and how many writing assignments will need to be assessed” (Pugalle, DiBiase & Wood, 1999). Create rubrics for your writing assignments.” Simple is better. (Brandenburg, 2002). Not every writing assignment must be graded by you: allow students to both self-assess and assess their peers (Pugalle, DiBiase & Wood, 1999; Fortescue, 1994; Burns, 2004; Evans 1984).
• Be firm. Students will be resistant to writing in classes other than English. Hold your ground. Make sure that your students know what your expectations for writing are. (Brandenburg, 2002)
• Teach students how to “talk and write mathematics.” Students need experience using the language of mathematics before they can write about it effectively. Spend time modeling both oral language and written language in addition to modeling the math skill. Encourage students to “talk mathematics” during class discussion and small group work so they can develop a coherent math vocabulary and practice using the math register. (Fortescue, 1994).
• Establish the purpose for writing in math class. Students should know that writing “support[s] their learning and …help[s] you assess their progress” (Burns, 2004).
• Post math vocabulary for students to refer to as they work and write (Burns, 2004).
• Use prompts to guide writing and promote critical reflection (Burns, 2004; Brandenburg, 2002; Pugalle, DiBiase & Wood, 1999).

What kinds of writing activities should I have my students do?

• Guided response strategy: A problem-solving device that requires students to rewrite problems in their own words, come up with a plan for solving it, solve and analyze their strategy (McGehe, 1991).
• Problem writing: Have students write math problems using the skill that is being learned in class.
  Example prompts:
  • Write an addition problem that has an answer for 465.
  • Write a math problem to go with a picture.
  • Write a story problem that involves multiplication and subtraction.
  • Write and illustrate a story problem for a 2nd grader (McGehe, 1991).
  • Write a step-by-step explanation of how to solve an equation or graph a function for a student who was absent.
• Explanations: Have students explain how they solved a problem. Have students write a “how to” piece for another student (Burns, 2004; Fortescue, 1994; Brandenburg, 2002; Evans, 1984).
• Definitions: Have students write definitions in their own terms (Evans, 1984).
• Troubleshooting: Have students explain their errors (Evans, 1984).
• Math essays: Ask students to write about a mathematical concept (Burns, 1995).
• Cubing: A writing strategy that “allows students to examine a problem from six viewpoints.” “Each of the viewpoints is written on one face of a cube. … [T]he prompts can be modified to meet the objectives of many learning situations…” Students write informal responses to share with their classmates. (Pugalee, DiBiase & Wood, 1999)
  1. Describe it (the process, event, features, traits)
  2. Compare and contrast it
  3. Associate it (analogies, makes me think of?)
  4. Analyze it (composed of? Steps? Procedures?)
  5. Apply it (how can it be applied to other situation?)
  6. Argue for or against it (support decision)
• Essay tests: Example questions: What are three methods for solving the sides and angles of a triangle? What information do you need for each? How can you tell which method to use? If you were given an angle with a terminal ray passing through the point (-3,8), how would you find the six trigonometric values for the angle? Don’t do any calculations (Brandenburg, 2002).
• Math journals / math logs: Keep track of what students are doing and feeling in class. You may choose to use prompts to guide student responses.
• Math portfolios: Save students’ quizzes and unit tests; save student work and their reflections about the work; or require students to summarize concepts in each unit and demonstrate them mathematically.
• Math pal: Pen pals for math students can be in the same class, in different grades, and even different schools. This is an opportunity to incorporate technology, also (Tichenor & Jewell, 2001).
• Word webs: Gathering ideas about concepts (definitions, uses, ways to write or express the concepts, how the concept connects to other math skills, feelings about the concept) (McGehe, 1991)

Teachers who have upper-level mathematics classes might consider taking writing one step further. Students who may pursue mathematics and / or science curricula in college may benefit from learning to write in the formal mathematics register. It’s time that we let ourselves in on the secrets of writing in math. Pick up a pencil and jump in – it’s a worthwhile endeavor.

Here are a few resources that may be useful for teachers of upper-level math courses:

Lee, K. (n.d.) Guide to college math writing.

Retrieved October 30, 2006 www.stat.ualberta.ca/~wiens/purdue1_write.pdf
A student handbook designed to help undergraduate students learn how to write formal mathematics papers

Crannell, A. (1994). A guide to writing in mathematics classes.

Retrieved October 30, 2006 server1.fandm.edu/departments/Mathematics/writing_in_math/guide.html

Crannell, A. (1994). How to grade 300 mathematical essays and survive to tell the tale.

Primus 4 (3), 193-201. Retrieved October 30, 2006 server1.fandm.edu/departments/Mathematics/writing_in_math/checklist.html
A checklist for students writing math papers

Crannell, A. (n.d.). Writing in mathematics.

Retrieved October 30, 2006 server1.fandm.edu/departments/Mathematics/writing_in_math/writing_index.html Writing assignments for pre-calculus – Calculus III

Bibliography Resource

Brandenburg, M.L. (2002).

Advanced math? Write! Educational Leadership, 60 (3), 67-68.

Burns, M. (1995).

Writing in math class? Absolutely! Instructor, 104 (7), 40-47.

Burns, M. (2004).

Writing in math. Educational Leadership, 62 (2), 30-33.

Chamot, A. U. & O’Malley, J. M. (1994).

The CALLA Handbook: Implementing the Cognitive Academic Language Learning Approach. New York: Addison-Wesley Publishing Company, Inc.

Evans, C. S. (1984).

Writing to learn in math. Language Arts, 61, 828-35.

Fortescue, C. M. (1994).

Using oral and written language to increase understanding of math concepts. Language Arts, 71, 578-80.

Indiana Department of Education. (2006).

Indiana’s academic standards: High school mathematics. IDEANet. Retrieved October 31, 2006 www.doe.state.in.us/standards/HS-Mathematics.html

Kang, H. & Pham K. T. (1995).

From 1 to Z: Integrating math and language learning. Long Beach, CA: Teachers of English to Speakers of Other Languages. (ERIC Document Reproduction Service No. ED 381 031)

McGehe, C. A. (1991).

Mathematics the write way. Instructor, 100 (8), 36-38.

National Council of Teachers of Mathematics. (2006).

Principles and standards for school math. Retrieved October 30, 2006 standards.nctm.org/document/appendix/process.htm#bp3

Pugalee, D. K., DiBiase, W. J. & Wood, K. D. (1999).

Writing and the development of problem solving in mathematics and science. Middle School Journal 30(5), 48-52.

Schiffman, H. (1997).

Linguistic register. Retrieved November 11, 2006 ccat.sas.upenn.edu/~haroldfs/messeas/regrep/node2.html

Tichnor, M.S. & Jewell, M. J. (2001).

Using e-mail to write about math. The Educational Forum 65 (4), 300-308.

Stephanie Krajicek

Stephanie Krajicek is a certified secondary English and French teacher who has been teaching in Indiana public schools for five years and is a facilitator for the Buddy project and a trainer for the Buddy Technology Learning Center (BTLC).

This featured article appeared in Volume 2, Number 2 issue of the Write Connections quarterly newsletter. View other archived newsletters , a topical organization of all newsletters, or sign-up to receive notification when the next newsletters are ready to download.