Teaching

Finding ways to get students to write about mathematics has played a pivotal role in my development and growth as a math teacher.  Mathematical writing challenges students to express their ideas clearly and efficiently; it forces students to stop thinking of mathematics as merely equations and answers; and it opens up a new and unexpected dialogue between math teacher and student.

I have always found great value and pleasure in writing.  It is a valuable skill, a necessary tool of scholarship, and a powerful creative outlet.  And now I see its value as a math teacher.  The more my students write, the more useful and interesting we all find it.

In this post, I’ll discuss some strategies for making writing part of the culture of the math classroom.

Here are a few simple things that make writing in math class work for me and my students.

Keys to Success

1)  Short and Sweet

Keep the assignments short and well-defined, especially at the beginning.  Don’t ask students to write pages and pages; sometimes a short paragraph or even a thoughtful sentence says it all!  Students may be hesitant to write at first, so making it easy on them can help get the process moving.

2)  Feedback

As with all student work, meaningful feedback goes a long way.  Make sure the students know that you are reading their work, even if you aren’t grading everything.  Correct as much grammar as you are comfortable with, but don’t necessarily feel obligated to grade it like a literature teacher might.  This is likely to be an “extra” assignment anyway, for both the students and you!  Keep it fun.

3)  Shareout and Peer Review

With every assignment, honor those pieces that really moved you by picking a few and sharing them with the class.  Have small groups exchange papers and then share their favorites aloud.  It only takes a few minutes, but sharing rewards students for taking a risk in their writing, and regular peer review helps everyone get better over time.

Get Writing!

There are a lot of ways to get students writing in math class.  It isn’t easy, and it takes time for everyone to get comfortable with it, but it’s an investment worth making.  Establishing a culture of writing has dramatically impacted my classroom:  it gives my students a different way to interact with mathematics, and it gives me a different look into how my students think about math.

For more resources, see my Writing in Math Class page.

A few years ago, I stumbled upon James Propp’s Self-Referential Aptitude Test.  I was immediately hooked, and spent hours navigating the interconnected logic puzzle that posed questions like “The answer to number 8 is ” and “The first question whose answer is C is “.

The experience was so challenging, frustrating, and ultimately rewarding, that it didn’t take long to realize it was a perfect exercise for students.

I ended up creating some simpler examples that gently introduce the student to the idea of a self-referential test, a test where questions and answers refer to other questions and answers.  By playing around with these easier versions, students develop a sense of how to reason their way through using various problem-solving strategies.

After working through the more challenging versions, the final project for students is to create their own self-referential tests, which we then all enjoy solving.  This is the perfect kind of project, in that it allows students to exercise their creativity while pondering substantial and significant mathematical questions like “What constitutes a solution to this test?” and “Are we sure that this puzzle has a solution?”, as well as fundamental mathematical ideas like logical consistency.

To get you started, I offer two simple versions of the test.

Five Question version: Simple Self-Referential Test 1

Ten Question version: Simple Self-Referential Test 2

Enjoy!  And if you do, try making your own!  It’s great fun, and a great student project.  And keep in mind, questions like “Does this test have a solution?” and “Does this test have a unique solution?” are always interesting to consider.

And you can find James Propp’s original Self-Referential Aptitude Test here.  Be warned:  you might find it very frustrating!

Finding ways to get students to write about mathematics has played a pivotal role in my development and growth as a math teacher.  Mathematical writing challenges students to express their ideas clearly and efficiently; it forces students to stop thinking of mathematics as merely equations and answers; and it opens up a new and unexpected dialogue between math teacher and student.

I have always found great value and pleasure in writing.  It is a valuable skill, a necessary tool of scholarship, and a powerful creative outlet.  And now I see its value as a math teacher.  The more my students write, the more useful and interesting we all find it.

In this post, I’ll discuss some strategies for getting students writing in math class.

How to Get Students Writing in Math Class

1)  One-page solutions

Have students choose a good math problem they like and write up a solution in one page.  Have them narrate their process and explain the choices they make.  They can also write about mistakes someone else might make, or offer an alternate solution if possible, or suggest a new problem that’s related but slightly harder.  Problems from math competitions (like the New York Math League or the American Mathematics Competition) are usually great places to start.

2)  Create New Questions

Have students choose a good math question and write up three new questions based on the original.  If the original problem asks to find the sum of consecutive integers from 1 to 10, some new questions might be “What is the sum of the consecutive integers from 1 to 100?”, “What is the sum of consecutive integers from 1 to n?”, and “What is the sum of the squares of the integers from 1 to 100?”  Make sure that the students understand that the assignment is to create the question, not answer it; not being required to answer the question takes the pressure off, and it frees them to be more creative.  Again, math contest questions are great places to start.

3)  Mathematical Poetry

Have students write short mathematical poems, like haikus, quatrains, limericks, or even sonnets.  Ask them to explain a math concept, pose a math problem, or describe a geometric object in verse.  And keep it short!  Insisting that the students only use 17 syllables or four lines to describe their mathematical topic not only forces them to refine their thoughts, but it also makes the assignment so easy that it’s nearly impossible not to do it!

4)   Writing Prompts

Have students respond to prompts like:  “What is your favorite number?”; “What’s the best shape?”; “Describe a mathematical epiphany you’ve had”; “Write an original math joke”; or “Write a mathematical aphorism”.  Create your own prompts, or better yet, have students suggest them!

For more resources, see my Writing in Math Class page.