[Thanks to Sam Shah and *The Virtual Conference of Mathematical Flavors* (https://samjshah.com/mathematical-flavors-convention-center/) for challenging me to reflect on the flavor of my teaching.]

Today was the first day of school. We are a faith-based school, and in order for the school to have a special Mass today, our classes were only 30 minutes long … that’s not a lot of time. At all. Especially when it’s the first time you are meeting your students.

So, I gave my PreCalc classes the 4-Square problem:

Working together in their groups of 4/table, using only straight lines (but as many as they need), divide the unshaded area in Square A into 2 equal parts. There’s an obvious answer, and I praise the beauty of the simplicity.

Next, they are to divide Square B into 3 equal parts. Most kids see that they can divide the square into quarters. But, then we discuss other methods and how can we tell if they are correct.

Then, Square C has to be divided into 4 equal parts. This isn’t as obvious. Working together, students come up with answers – some are correct; some that are on the right track, but need a little assistance. So we work together as a class figure out how to make those ideas into solutions.

Finally, Square D is to be divided into 7 equal parts. The obvious solution is to divide the square with 6 equally spaced vertical or horizontal lines – but most students try to find a complex solution. And that led to a great discussion about trusting ourselves and appreciating the beauty of a problem – even the “simple” ones.

I concluded the class by telling the students that our class is collaborative, we become better thinkers by making mistakes and learning from them, and I can’t wait to work as a team to help each other learn and grow.

I wrapped up class, and honestly – I moved on. I was already thinking about tomorrow.

Until – out of the blue and unsolicited – I received this email from one of my students.

Damn.

Three things jump out:

- This kid may or may not have previously experienced the type of class he’s describing – but is desperate to experience it now.
- My students aren’t just “students” – they are individuals. And are worthy.
- I cannot underestimate the importance of relationship and trust within my class.

And, that the flavor I work so hard to create in my class – relationship and trust.

My main purpose of my class isn’t to teach math. My goal is to help students become better thinkers, better learners, better people – and math is one of the tools I use toward those goals. I know I’m not going to be able to reach every student, but I need to have an environment in place for those who are ready.

This is precisely why I loved having my students write – they share with me things they would never / could never tell me to my face. They gift me (and themselves) with a glimpse into their true thoughts and reflections.

At the end of last year, a student wrote this as part of his year-end reflection. I save it so I can read it after those long, hard days that we all inevitably will face during the year. This, this will remind me of the importance of the flavor of my class:

Hey Cindy – your classroom and your school must be a very special place. I can’t imagine get notes like this from boys at the 2 coed schools at which I have worked. I love how they are so open, in touch with themselves and able to relate to you and the class. So wonderful! although – I know how special you are, so I’m not surprised!!

LikeLiked by 1 person

Thanks for your post, Cindy. The student writing is AMAZING and I like the problem. I have to admit, though, that the effect of your use of the word “obvious” when describing solutions to squares A an D was that I stopped engaging in the math. I took a giant step back.

I’m really curious about language like that, words and phrases that can either invite people into math, or invite people out of math. Some of math teachers’ and mathematicians’ favorite words and phrases are like that for me:

…simple, it’s easy to see that, obvious(ly), clearly, fast, trivial…

I wondered if I should say something, but your example of listening to your students made me think you are an amazing listener, and would want to know!

Thanks again for your post.

Best,

Tracy

LikeLike

Tracy –

Thanks so much for your comment. You are so right about the language choices we use.

In the classroom, I wouldn’t refer to the solution in question as “obvious.” I was writing my own thoughts – BUT…even at that, it’s dangerous! I coached tennis for years and would always tell my players to “practice like you play.” By using the word “obvious” in a dialogue with other math teachers, or even in my own thoughts, I was violating that principle.

Thank you for catching that – and for reminding me!

I hope we can have other conversations again soon –

Cindy

LikeLike