Thinking Mean in Math

by Amy Shultz

Is it your life-long desire to be a Mean Teacher? I’m not talking about a run-of-the-mill-average teacher who only requires students to show their work. I’m talking about a really-truly-wicked-teacher, who actually calls for students to think! Do you get a thrill each time you evoke terror in your students by inquiring of them, “Explain how you got that answer,” or “Do you think that answer is reasonable?” Must you suppress an evil giggle whenever you require your pupils to show more than one way to solve the problem?

I confess I long to be a Mean Teacher. And I’m not alone! It seems there are other Mean Teachers out there who strive to stimulate mathematical thinking in their students. For many of these teachers, regularly including writing (and talking) in math instruction, is one of the best ways to torture...I mean engage students in their own learning.

Joan Kenney observes, “Writing in mathematics helps students think....allows students time to wonder and to process.” (p. 49) “Written explanations in mathematics are about what is being done and why it works. The type of thinking involved in justifying a strategy or explaining an answer is quite different from that needed to merely solve an equation. The process of writing about a mathematics problem will itself often lead to a solution.” (p. 27)

Some Mean Teachers have also discovered how highly effective student writing is in informing their instruction. Author and teacher Marilyn Burns shares, “Not only did I see how writing helped students think more deeply and clearly about mathematics, but I also discovered that students’ writing was an invaluable tool to help me assess their learning.” Marilyn goes on to illustrate four different writing assignments she employs and her purposes behind them:

Journals or logs are places for students’ ongoing reflection about what they’re doing and learning in math. Suggestions for writing or drawing include:

• What you did in class today.
• What did you learn?
• What are you unsure about, confused by, or wondering about?
• Describe what was easy and what was difficult for you.

Solving math problems give students opportunities to apply a variety of mathematical strategies. Writing about why solutions make sense teaches students to reflect upon their own problem-solving processes. You may challenge your students to:

• Write about or draw different ways to solve the same problem.
• Consider whether the problem or the solution would make sense in real life.

By asking students to explain mathematical ideas in essay form (or for younger students, orally), a teacher gains insight into their understandings and misunderstandings of concepts. This can be done as pre-assessment, formative assessment, or summative assessment. You might ask:

• What do you know about fractions?
• Share what you’ve learned about fractions.
• Explain fractions to a younger student/your parents.

Writing about learning processes encourages students to reflect upon and become responsible for their own learning. You may guide your students to draw or write:

• What they liked the most and the least about a unit of study.
• Directions to a math game.
• A favorite problem-solving approach.

If you think that some of the writing assignments mentioned above will elicit groans from your students, you are right. They will grumble over not being able to get by with just giving an answer, or by only remembering the tricks and the steps to get a right answer. It will become increasingly difficult for your students to go through the motions of math, as they will be forced to improve the real-life skills of problem solving and communication. And consequently, you will be successful in your endeavor to be considered a Mean Teacher!

The National Council of (Mean) Teachers of Mathematics has included writing as a necessary element in math instruction, stating “written communication should be nurtured” (p. 62) and that math instruction should enable preK-12 students 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. (p. 60)

With a whole nation of Mean Teachers behind you, what do you have to lose? Mak’m think you’re mean. Mak’m work. Mak’m write. (And someday, they will remember with fondness and gratitude how their Mean Teacher made them think in math!)

References:

Some content adapted from:

 

Burns, Marilyn.

“Writing in Math.” Educational Leadership October 2004

Kenney, Joan.

Literacy Strategies for Improving Mathematics Instruction. Alexandria: Association for Supervision and Curriculum Development, 2005.

National Council of Teachers of Mathematics. (2000).

Principles and standards for school mathematics. Reston, VA: Author. Available: http://standards.nctm.org

Amy Shultz

Amy Shultz, former fourth grade teacher, works as a facilitator for the Buddy Teaching and Learning Center. She also writes for The Write Connection newsletter and The Writing Site, under the Buddy System Project.

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.