July Challenge #10 Writing in the Math Classroom

Many years ago I read the book Writing to Develop Mathematical Understanding by David Pugalee.  I want to use this post to record some of the important points.

Pugalee wrote that

“The goal of writing in mathematics is to engage students in ways that require them to think deeply about the mathematics they are encountering.”

He suggested that, writing, or more generally, communication, happens along a continuum.



This continuum “is not about writing ability but about the level of cognitive engagement of the student.”

He offers many practical suggestions for incorporating writing into the daily routine of math classrooms.

Beginning of the lesson suggestions (pages 36-38):

  • Use a prompt such as “Write what you know about ________.”
  • Have students write a short description of how they solved a particular homework problem.

Middle of the lesson suggestions:

  • Have students write an example or draw a diagram or other illustration to demonstrate a key idea or concept.
  • Have students write a question about a concept or problem, then turn to another classmate and exchange questions.
  • If students are taking notes, pause and have them write a summary of an idea or concept in the margin.

End of the lesson suggestions:

  • Write the main idea from the day’s lesson.
  • Write definitions in your own words. This might also apply to a procedure or property.
  • Have students exchange notes, a practice problem, or another task.  Students can identify common elements and approaches as well as differences.

He shares a list of 50 Activities for Writing in Mathematics…a few of my favorites include:

  1. Construct test or quiz questions
  2. Write freely on any topic
  3. Create a dialogue between one student and another
  4. Defend a decision or action
  5. List characteristics or steps
  6. Write a mathematics word problem
  7. Prepare an outline of a lesson
  8. Identify personal goals for mathematics learning
  9. Write about what gave you difficulty on a particular task
  10. Write about how two problems are similar or different

Pugalee discusses the importance of creating a safe environment for communicating in the classroom.  He offers suggestions for promoting this culture.

Struggling writers might need “a framework or skeleton” as entry points into a communication task.  This might look like:

I need to…

I notice…

This means…

So, I need to… because…

Therefore, the…

A couple of quick ideas that I use for incorporating writing into lessons that were inspired by this book:

  • I might put these words on the board:  hypotenuse, Pythagorean Theorem, leg.  And then ask students to write 2-3 sentences using these words.
  • I like to create fill-in the blank responses.  So students have to make sense of what’s already on the paper…and how best to complete the sentences.

There is soooooo much out there on this topic.  But I don’t think enough of it has trickled down to implementation in the classroom.

I’m going to continue to add to this list below…but here are a few additional resources for learning about writing in the math classroom.



3 thoughts on “July Challenge #10 Writing in the Math Classroom

  1. I recall clicking on this post, but I tend to be bad for leaving comments unless I think I can further discussion in some way. I didn’t at the time, though I’m coming back to it now that you’ve mentioned writing from one of my posts. I agree that (a) writing can help with deeper understanding, and (b) there’s so much out there on the topic. The latter is something that always seems to lead to paralysis for me in teaching – except in the statistics course I have, where language is kind of key.
    I often assume students can just “pull in knowledge from other courses” then just reapply it to mathematics. But either they’ve compartmentalized “math” and “english” somehow, or there really is a different manner of thinking at play… I don’t know, nor do I have answers, hence being hesitant to even say something. Food for thought though, maybe. I suppose I can admit to having a “communication” style question on all my tests (even outside of the statistics course, eg. “Given this situation explain how you know …”), to prevent math from being all about numbers and word problems.


  2. I’ve found that providing a word bank (you mentioned writing a few words on the board and having students write sentences using them–good idea) really helps, as does requiring them to practice being more specific. My students started out really struggling to formulate math ideas into words and were very vague when pressed to do it. A few things that helped:

    1. When having them talk me through a problem on the board, I would (kindly) refuse to understand their intended meaning if they didn’t actually communicate it. I would write down what they said and let them realize that it wasn’t what they meant (e.g., they say 3x but mean 3^x). Other times, I would point out how vague they were being and try to get them to specify (e.g., they say “Take that number,” I say, “What number?” hopefully leading them toward something like “The coefficient of x.”)

    2. We would regularly take a day to play a math vocab Catch Phrase game. A lot of difficulties in communication and retention lie in not knowing/remembering the right words.

    3. We worked up to a technical mathematical writing project that had to be turned in as a draft and revised to be more clear. The task of having to describe a complex process with only written words, and then having to revise for clarity helped things click for some. (I work with older students–this last one might be a stretch for middle schoolers, but you may know how to adjust it)


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