Three Principles for Math Teachers

  1. Know the Big Ideas of Mathematics that are in your Curriculum

“Teacher, know thy curriculum”. Know it well. Know it backwards and forwards. I mean that literally- know what is “below” your grade, and “above”. Know where the concepts have come from, and where they are going.

If you are teaching grade 3s multiplication, know that they should have “passed through” stages of skip counting, and making equal groups. Actually, make sure you don’t just make them think that multiplication is about “equal groups”. Play with number facts. Link what they have learned about addition. Show them that dividing is the opposite operation, and let them play with that too.

Some things kids know about multiplication (credit: Melissa Pennarun)

Start each new concept with an interesting problem that “opens the field” to kids’ understanding. Don’t ever just stand up and say, “kids, a squared plus b squared is c squared”. Give an interesting problem about a triangle. A formula can be learned later, and when you are first learning a topic, that’s when it’s time to play.

This is a “‘classic” old textbook problem. Is it interesting enough? Could you make it more interesting?

Open kids’ minds. Play, and then practice. (You need to do enough math to be good at math-practice is important). Start wide and zoom in. One really big idea could be, “there are an infinite number of spots on the real number line.” Are you saying you can’t do anything cool with that? Show kids what real numbers are, and play. Zoom in to the curriculum after- see what it has to say about fractions, decimals, and percents.

2. Be More Interesting

This is the pedagogical principle I want to make my number one pedagogical principle for myself. We could all use to be a bit more interesting. Choosing interesting tasks is important. Mathematics is interesting. It doesn’t need to be dressed up in pseudo-context, or problems about cookies, or treated like medicine that needs to be hidden in sugar.

School mathematics is what teachers make it. Don’t make it a dull set of rules to be applied. Don’t assume kids won’t be interested. They will be as interested as you are. If you are not interested, they won’t be.

Why does subtraction of M & Ms “break” at zero?

If the curriculum says, for example, “solve problems involving rate and ratio”, find some interesting rates and ratios. Find a whole bunch of interesting rates and ratios, and bring them into the classroom. See what rates and ratios that kids know. Use those for practice as well. The worst thing you can do here is just break out cross multiplying. There is time for that later. While you’re at it, don’t you dare not show them why cross multiplying works. It’s not a magic trick, after all- it’s mathematics.

Choose interesting problems. Yes, you can have both interesting and uninteresting problems about cookies. Make your problems interesting. Maybe you can do something with a trendy fad like a fidget spinner. Maybe not. Maybe there are other things that are more interesting in your world, or kids’ worlds. Bring them into your classroom’s mathematical world.

3. Listen To and Talk to Kids

Watch them at work. Learn from watching them at work. Take pictures of their work, to use for assessment purposes. If you aren’t sure if they “get it”, don’t wait for the unit test. Ask them. Have conversations about interesting mathematics.

In the moment, could you interpret what this kid was thinking? How would you record their thinking as assessment data?

Let kids to talk to other kids about their ideas. Make talking about interesting mathematics normal. Normalize mathematical discourse. Use the vocabulary of the discipline. Empower kids to talk about the “distributive property” and “equality” and the set model of fractions.

A blank space, ready to be filled with kids’ thinking.

Make your explicit instruction as powerful as you can. Explain in clear terms when kids are puzzled (when productive struggle has tipped over into unproductive frustration).

Focus on a few kids each day very closely, to make sure they “get it”. Don’t think of differentiation as “creating 30 lesson plans”. Let questions lead. Talk to kids. Talk to kids.

Talk to kids, and let kids talk to kids.

3b) Play.

Play with interesting mathematics. No really, play.

Writing about creativity, books, productivity, education, particularly mathematics, music, and whatever else “catches my mind”. ~Thinking about things~