Explore Math with Prompts – Semester 1

A few years ago, I learned about Sam Shah’s wonderful Explore Math project. (Sam wrote a great blog post on it.) The goal was to have students explore some math outside the curriculum so they could begin to see some of what math could be, not just the content standard they have to learn this year. I think it is SO important for students to see that math is more than graphing a line or factoring expressions. Using Sam’s template, my students had a menu of options to choose from (reading an article from the NYTimes about math, exploring Visual Patterns, and many, many more). For each Explore Math assignment, students would choose one option, learn something about math, and then write a paragraph reflection on it.

I wanted to keep it manageable and low-stakes. I had them do about one a month (really about 3 a semester). And most students would get 90% or higher just for writing a decent paragraph. I really liked that it was low-stakes, and because there was not pressure to “perform” in some way, students had fun with it. Many students would talk about it in their end of year surveys as the time when they “actually had fun with math” or learned that “math could be cool.”

While I like the choice option, this year, my goal was to narrow the focus a little for each assignment. I’m so happy with how it went! Below is what I did for Semester 1.

*One caveat: students were able to substitute the focused assignment for anything from the full menu if they really wanted to. So there still was some choice, though nearly every student stuck to the focused assignment.

Assignment #1: Who is a mathematician?

To start the year, I really wanted to challenge students’ pre-conceived notion about who can and does “do math.” Are “math people” only those who make a life-long commitment to the study of math? I think not! We are all mathematicians in our own ways! So inspired by Annie PerkinsMathematician Project (mathematicians are not just old, dead white dudes), I asked students to find a mathematician to learn a little about. Their ultimate task was to write one paragraph about what makes this mathematician interesting and include a picture. I asked about what makes the mathematician interesting specifically to avoid a paragraph of random facts about the date of birth, family facts, etc. I wanted students to get to the heart/excitement of who that person was.

I asked students to get approval from me on the person they chose, so that I could make sure no two students from the same section researched the same mathematician. What I was pleasantly surprised by is that, in addition to many wonderful historical mathematicians to choose from (I shared this website as a resource), students started asking if they could interview a family member (who perhaps worked in a STEM field), a favorite STEM teacher of theirs on campus, or a friend of theirs who they thought was a mathematician (perhaps someone in an AP math class).

What resulted was a wonderful wall display of mathematicians who were female, people of color, currently working in the field, teachers on campus and students. We had this wonderful collection of photos and “interesting paragraphs” on the wall near the pencil sharpener that students could look at anytime they walked by.

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And thus we are able to constantly talk about and remind ourselves that everyone can be a mathematician. That math isn’t mystical. It is something we all do!

 

Assignment #2: What makes math cool?

I wanted student to look around and find a concept (even if they don’t fully understand it) that shows some cool math. My instructions were as follows:

“OK, so you learned about a mathematician. Now what? Now it’s your turn to explore some cool math! What’s a golygon? Have you heard of sexy primes? The Hilbert problems? Fractals? The different sizes of infinity? Or do you have a cool math challenge you want to solve and discuss?

Your second task is to read about some math topic you never heard of before and write a short paragraph about it. Be sure to include visuals/examples! Alternatively, you may solve some math challenge we have introduced in class (or one you find on your own) and write a paragraph about it.”

Again, students submitted a paragraph and included some sort of visual. I was so delighted by what I saw. One student stumbled upon the problem of the Bridges of Königsberg, one of my favorite problems, and she started playing with it for fun. Another student taught herself (and me) what the math was in the movie Good Will Hunting. Being her favorite movie (and to her surprise, one of my favorites too!), she found math in the art world that she latched onto and ran with.

 

Assignment #3: How does your family do math?

For the last assignment of the semester (and I purposely gave this out before the Thanksgiving break in case students wanted to do it then!), I wanted students to bring the ideas that (1) they are mathematicians and (2) math can be cool to their family!  Here were my directions:

“Wow! You’ve explored some cool math! You learned about lots of cool mathematicians. One more thing to go…What is your family’s take on math?

Your third task is to do some math with your family (#FamilyMathNight). You can define your family however you want. You can do any kind of math you want. But you need to be explicit about it and take a photo! Think about all the ways you and your family already do math: calculating costs, counting items, using fractions in cooking, figuring out a percent of a cost (tip or sale), etc. Use something like this or a challenge problem or something original. You get to decide!”

Students again had to write one paragraph and submit a picture with it, but they could interpret the assignment in many ways. Some students chose to do a challenge problem we had done in class or that they found on their own with a sibling or parent. Some tried to teach their family a topic from their current course over Thanksgiving dinner!

This turned out to be my favorite of the three tasks, as I learned so much about students and their families, and I got to laugh and ponder with students as they turned in the assignment. Many students talked about how frustrated their parents got with what they thought was “simple math” and reflected on how they never realized how far they have come in math (these are my Calc and Pre-Calc classes). Some have gone further in math than their parents were ever able to or interested in. Some talked about how their parents seemed to have forgotten everything. I think it was shocking to many students how wide-ranging their parents’ reactions were. It built confidence in students to see how some adults in their lives were so math-averse, while (with a growth mindset and a new idea of who could be a mathematician) they didn’t see math as something to run away from.

Overall, this was a fascinating explore math adventure for me and my students. I’ve learned so much more about them and their families, and I’ve seen them open themselves up to learning math so much more. I’m excited to keep this up and am pondering what to do next semester…any ideas?

3 thoughts on “Explore Math with Prompts – Semester 1

  1. Amy Zimmer January 7, 2020 / 1:45 am

    Such an awesome affirmation of the positive climate and relationships you have built with your students!

    What about math from another land? Something discovered faraway?

    Or math in art

    Or math in a book—Curious Incident of Dog in the Nighttime, or “parabolic rain” from Snow Falling on Cedars, Alice in Wonderland?

    Math and social justice: census, gerrymandering, redlining

    One last one, math around campus: a design? Parallel railings? Alternate interior angles?

    • pispeak January 7, 2020 / 11:52 am

      Ooo, love these ideas! Especially math in another land or math and social justice. I’m going to play around…

  2. Joe January 8, 2020 / 11:47 am

    Great concept, Bill. Thank you for sharing! Seems to me like your project would set up a bunch of candidates for the most recently announced MoMath Prize: Steven H. Strogatz Prize for Math Communication: https://momath.org/the-steven-h-strogatz-prize-for-math-communication/

    Best from The Island, another area that you and Strogatz have in common.

    Joe

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