It’s More Than Math

[Thanks to Sam Shah and The Virtual Conference of Mathematical Flavors ( 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:

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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.

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Three things jump out:

  1. This kid may or may not have previously experienced the type of class he’s describing – but is desperate to experience it now.
  2. My students aren’t just “students” – they are individuals. And are worthy.
  3. 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:

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Teaching “Reflection”

When I was doing my talk on Writing in the Math Classroom at TMC18, I was asked if I provide a model of a reflection statement, or give an example.

I don’t – at least not a mathematical one.

As I’ve played with different ways to get students to learn about reflection, tried to sneak more and more writing and meta-cognition into my classroom, I’ve had lots of failures  — giving an example of a reflection statement was one of my biggest.

Why? Because I ended up with ~120 journals with reflections that sounded remarkably similar to my example. And it was a lot of (unnecessary) work to break them from that pattern.

Instead, I tell them a “story.”

I am a tennis player. I’m very competitive and can be a little aggressive at times. I love to play at the net, when the play is very fast and unforgiving. However, sometimes I forget that aggressive play is only going to win games when I play smart and stick with my strategy.

But, in the heat of the game, it’s really easy to just go all out and play emotionally – it feels great to beat the heck out of the ball or hit a hard volley!  … But if I’m not hitting the ball to the right spot, I put myself and my partner at a huge disadvantage. I lose when I play with the heart, and forget the brain. I am most successful when I play with both.

Then I ask a series of questions:

  1. What type of player am I?  (competitive and aggressive)
  2. At the beginning, did I have a game plan? (yes: aggressive, play smart, stick with strategy)
  3. What happens sometimes during the game? (play emotionally)
  4. Why does this happen? (it’s easy and feels good)
  5. What’s the result of that? (at a big disadvantage and typically lose)
  6. What did I learn? (most successful when I play aggressively – and stick with the strategy)

Then I challenge them to take see how they can reflect about their learning and habits of mind. For some students, this is enough; for others, you might need a have a few more stories handy.

I am a thief.

First: I am not an expert.

Second: I steal materials from the best – all of you – and then adapt to my classroom. If you see material that is familiar, or is your’s, please know I am using it with gratitude.

“Write Like Nobody’s Watching”

I was at TMC18 this past week, and was honored to be able to give a presentation on Writing in the Math Class. I loved the discussion and interaction with the people who came to my session, but I quickly realized I didn’t do a very good job talking about the “how”s. Several people asked if I would write up some “Pro-Tips.”

Then, Chris Luzniak (@cluzniak) threw out the dare-of-all-dares: “Why don’t you blog about it?”

My instinctual reaction about blogging, which I have listened to for the past several years, was to blow it off.

I got thinking about the “Pro-Tips”, the “hows”, the “ideas”, the “prompts”, the “rubrics”, all the things I wanted to share with those in my session. I then got thinking how it would be great to have a central place to store all these ideas – and encourage others to share their ideas with me … and then it hit me … I was thinking about a blog.

Naturally, I was flooded with all sorts of insecurities and middle-school-level anxieties.

In researching blogging – to find reasons to convince myself NOT to blog – I found a blog written by Kate Nowak (@k8nowak) and Sam Shah (@samjshah2). And I came across this line written by Sam, “Write like nobody’s watching.”

“Write like nobody’s watching.” I can’t explain why that phrase did it. Maybe it was because I could imagine Sam saying it, his hand gestures, the excitement in his voice. Or maybe it was just time. If you feel inclined, please join.

Let’s go –