Teaching

At the end of the term I ask students to write simple reflections on their experiences from the year:  what they learned about math, about the world, about themselves.  It’s one of the many ways I get students writing in math class.

It’s a great way to model reflection as part of the learning process, and it’s also a good way for me to get feedback about the student experience.

Mostly, it’s fun!  I love sharing and discussing the reflections with students, and it always results in great end-of-year conversations.

Here are some of my favorites.

After learning a little more about math, I think math is created rather than discovered.  This makes mathematicians and scientists the creators, not merely the seekers.

I learned a lot of things from my classmates that I wouldn’t have learned if I were to just study on my own.

I have learned that I still have very much to learn about myself.

Mathematics is magical; it can lead you to a dead end, but then it can miraculously open up an exit.

Learning how to think of things in three dimensions completely changed the way I saw math.

By seeing algebraic and geometric interpretations, I learned how to communicate math in more ways.

The process which turns a difficult problem into a relatively easy problem is the beauty of math.

One of the best parts of reflection is how much it gets you thinking about the future.  Plenty of food for thought here.

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

Related Posts

• Writing in Math Class
• Writing in Math Class: Peer Review
• Why Write in Math Class?

Here is the video of my talk at this year’s TEDxNYED conference.  My talk was on Creativity and Mathematics.

Mathematics is an inherently creative activity.  Students and teachers alike often fail to appreciate just how creative math really is, so I wanted to share some of the simple ways that students and I create with mathematics in our classroom.

Speaking at this year’s TEDxNYED conference was a professional highlight for me.  Getting to share ideas with so many interesting and passionate people was an honor, and the unique experience created by the speakers, attendees, and conference organizers was a true inspiration.

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!