Math is Bigger than Measuring Cups

On the wall of an apartment hangs a wooden spoon – too large to be used as cutlery, too carefully placed to be a standard kitchen item. Even through the small, grainy rectangle of a computer screen, I can tell this spoon has a story.

The task that day was simple. It was only the second day of school, the sixth month of a pandemic and I was attempting to delicately balance building trust, relationships and interest amongst my new group of virtual students. We were on a math scavenger hunt – finding mathematics in the spaces and objects surrounding each of us – a unique task given that we were starting the school year outside of a traditional classroom.

When it was time to share, the student on whose wall hung the spoon, told about that object – he’d taken a photograph of it as well. The spoon was from his grandmother in Somalia, he said, and he was wondering about the spoon’s length. (What might be the most useful way to discuss or measure the length of a decorative spoon?)

What was a relatively simple beginning of the year exercise took on a whole new meaning in the realm of remote teaching. Despite the challenges and the traumatic circumstances that had necessitated this shift, there was a unique opportunity to bridge the worlds of ‘school’ and ‘home’. A grandmother’s spoon may not have crossed this student’s mind as ‘math’ in a traditional year, as we might have spent our time instead finding the math around us in our classroom or school building. This experience leads me to reflect on what may be gained when we are able to easily apply new learning to our own personal and cultural contexts.

Fast-forward until it’s one week before the last day of school, one year and three months into the pandemic. No longer greeting students through the computer screen but in flesh and blood, I stood in the warm breeze of the doorway between my classroom and the outdoors. Our class had spent the past week exploring the ways that math, art and culture are intertwined – particularly regarding the geometry of shapes and patterns. After studying examples, students were to search for an image that represented their culture or identity in some way, and find the shapes and patterns within it.

One of my students walked up the ramp and tugged on my sleeve. “I have something to show you,” she whispered. She took out a red bracelet with a black and white bead. “It’s a Mexican bracelet,” she explained. She had brought it as a result of our conversations the day before, noticing the patterns the braiding formed and wanting to tell me why it was meaningful for her. As she held it out, I asked her if I could take a photograph.

On a regular day, this student was often quiet, and for a multitude of reasons, teachers worried about her, or saw her as a compilation of the things she couldn’t do or hadn’t yet achieved. However, as we discussed as a class what connections we might find between our own cultures and mathematics, while many students struggled finding these connections, this student immediately gave an example of her family’s sombrero, and asked if she might bring it  to school.

While she ended up bringing the bracelet instead, the significance of the act remains the same. This student was not asked to bring an object from home – she was simply inspired by the conversation we were having in class and wanted to share a personal connection she had made, and in doing so, truly owned the mathematics in that moment.

I think back on the ways the spoon and bracelet are connected. As a teacher, I do not believe it is my job to tell young people the ways mathematics (or any discipline) should connect with their lives, but rather facilitate their ability to foster this for themselves. In many ways, school defines ‘mathematics’ by certain narrow ideas or experiences. The mathematical scenarios teachers present to students often mean little to them, and in turn often end up feeling like a puzzle to solve or a code to crack, rather than something meaningful that applies to their own lives.

As a teacher, there are things we may not be able to easily change – the curricula our school purchases, the expectations for grading student work or the assessments students must take. But what might happen if we, as teachers, recognize the gifts our students offer to us? If we take these gifts and use them to create a culture of mathematical learning that is defined by who we are as individuals and as a collective, rather than in spite of these things?

Written by Janaki Nagarajan (@janaki_aleena)

This piece has been adapted from a blog at StrongerMath.com

Picture a trapezoid. What comes to mind?

That’s what trapezoids looked like to me, anyway. My teacher told me trapezoids have a pair of parallel sides, and every picture I saw in my textbook looked like this. I never really had a reason to question it any further. But one day, I started thinking about it a little more.

After all, we know what this shape is:

A square, of course! But none of us would bat an eyelash if someone called it a rectangle, because it meets all the rules for rectangles. It just has a little something extra.

And speaking of rectangles:

There it is. Two pairs of parallel sides and all. But wait, that means it’s also a parallelogram!

And while we’re on the topic of parallelograms, there’s this little cutie:

Who doesn’t love a rhombus? Or is it a kite? Oh, it’s all three!

We have no trouble accepting these multiple classifications for different quadrilaterals. But suggest that a trapezoid can have at least one pair of parallel sides instead of exactly one pair, and everyone loses their minds!

Unbeknownst to me, I had established what is sure to be a lifelong rivalry with Zak Champagne and wandered into a discussion that had been going on for some time: The Great Trapezoid Debate.

Camps had been established on opposing sides – those who defined trapezoids using an exclusive definition — a trapezoid has exactly one pair of parallel sides —  and those using an inclusive definition — a trapezoid has at least one pair of parallel sides.

Now, you might not particularly have a firm opinion one way or another, and you wouldn’t be alone. And that’s totally okay! But I want to take a moment to talk about why (I think) this matters.

Math has a little bit of a reputation problem. It’s boring, it’s dry, there’s only one right answer or one right way of doing things. Everything is settled and nothing is up for debate. While the tides have started to turn a little bit, by and large this is still what comes to mind when most people think of math because this is what they experienced when they were in school.

Memorize this definition, use this algorithm, don’t ask questions.

The reality, however, is far more intriguing. Many of the things that we accept as fact in mathematics did not start out as universal truths. Equal signs, irrational numbers, negative numbers, even zero itself were up for debate until a collective agreement was reached, for one reason or another. Just recently, a fascinating conversation came up on Twitter about whether 0.999… is equal to one. I’m still not convinced that “convenience” is a good reason for zero to the power of zero to be equal to one instead of being undefined. But, I digress.

If we truly believe that our students are capable of being mathematicians and engaging with math authentically, then we also believe that they are capable of forming their own opinions and setting criteria that make sense to them and to others. Our job isn’t about building everything for students, but handing them the tools they need and offering guidance and encouragement. It’s about showing kids (and adults) that they, too, are able to examine evidence and come to a conclusion. It’s about demystifying a subject that has been exclusionary for far too long.

And that is why the Great Trapezoid Debate matters.

Written by Shelby Strong (@Sneffleupagus)