I love incorporating children’s books into math lessons. Since most of my teaching focuses on math, it’s a treat for me to read a book aloud to a class. After the students have a chance to enjoy the story and respond to the illustrations, then I use the book as a springboard for a math lesson.

Over the years, I’ve collaborated with Lynne Zolli and Patty Clark on a variety of math education projects. For this blog, we worked together to share our thinking about how Listening to Learn math interviews can serve teachers and students.

David Brooks wrote an opinion column in The New York Times on November 19, 2020, “Nine Nonobvious Ways to Have Deeper Conversations.” K–5 math wasn’t his focus or even hinted at in his message, but his suggestions jumped out at me as useful and important for connecting with students.

Yes, that’s a photo of me, taken about 30 years ago when I was conducting my first ever math interview. That was an extraordinary experience. It dramatically shifted my professional focus and, after all these years, has finally resulted in Listening to Learn, a digital interview tool to help K–5 teachers learn about how their students reason.

On Wednesday, May 5, 2021, I posted the sixth in my Wednesday Twitter series of video clips from Listening to Learn math interviews. The response to this Tweet amazed me―it received over 100,000 impressions! I was appreciative of the many supportive and insightful replies. Read more.

Asking students to solve problems mentally, without paper and pencil, is always revealing and often surprising. I thought that asking students to solve 100 ÷ 3 would be sort of a slam dunk. My, was I wrong!

Tic-tac-toe is a game that has some advantages―it’s easy to learn, requires only paper and a pencil, and doesn’t take long to play. But the game has the disadvantage of getting boring pretty fast. Don’t give up on it. Try these variations, all of which give kids (even adults) a chance to think strategically in new ways.

I just learned about Factors and Multiples, a shelter-at-home game that’s engaging as solitaire and can be played as a two-person game either cooperatively or competitively. (I’ve played it both ways.) It’s intriguing for both adults and kids (as long as players know about factors and multiples of numbers up to 100). It’s a keeper.

Looking for an easy-to-play game that requires only the ability to count to 20, but has a real mathematical kick? Here it is. Teach it to your kids at home or to your students online to play with someone at home. Read on for the rules and some tips, including how to tweak the game to keep kids interested and challenged.

Riddles are usually a hit with kids, and with many at home and sheltering in place (as I am), diversions can be helpful. When rummaging through my book shelves, I found a book that I wrote in 1981―The Hink Pink Book. I wrote it shortly after I first learned about Hink Pink riddles, and also about Hinky Pinky and Hinkety Pinkety riddles. I think these riddles are good for some language play for kids at home, with a little math thrown in.

Good Questions for Math Teaching is a Math Solutions book that has long been one of my favorites. It’s a resource that I dip into when I feel the need for something fresh. And it speaks directly to our current shelter-in-place coronavirus crisis as many of us look for ways to mathematically engage students online, children at home, or both. Here are samples to get you started. I’ll continue to post more ideas on Twitter (@mburnsmath).

I’m often surprised by what I learn when I interview students. Watch this 46-second video clip of Jonah solving 100 ÷ 3. Then read how I used the clip in a lesson with a class of fifth graders, and also read the letters the students wrote to Jonah.

I’m a huge fan of math games, especially when they involve both strategic thinking and luck. And I’m always on the search for games that work with a span of grade levels. The Two-Dice Sums Game fits both. Learn about the game and read the letters of advice that 7th graders wrote to 2nd graders.

What am I doing on the floor? Teaching angles to fourth graders. Read about how instruction using Pattern Blocks and hinged mirrors, along with supporting number talks, can help students learn to understand and measure angles. Here I present a (sort of) photo essay to describe what actually occurred over the first three days of instruction. Ideas for continuing the instruction follow.

Fourth graders solve the problem 5 ÷ 4 in the context of sharing cookies, figuring out how to share five cookies equally with four people. The students came up with six different solutions―all of them correct! (Try and think of what they might be before continuing to read.)

Last year, I agreed to meet with a friend’s sixth-grade son. Oscar’s math teacher had raised an alarm for my friend and her husband about Oscar’s math progress. They were shocked. Oscar did his homework and was proficient with paper-and-pencil math. What was the problem?

Have you ever asked students to solve 12.6 x 10, and they respond that the answer is 12.60? I have, many times. Students who do this apply a pattern that works when they multiply whole numbers by 10—they tack on a zero to the end of the number they’re multiplying. But then they apply the same pattern when working with decimals. What can we do?

I thought I was on the right teaching track using real-world contexts to talk about fractions with a class of fourth and fifth graders. Then a surprise occurred! I’m still mulling over what I could have done. I’d love your thoughts.

I believe strongly that mistakes are learning opportunities. At least that’s what I regularly tell students. But it sometimes feels different when the mistakes are mine . . . and especially when they are pedagogical mistakes that I make while teaching. That happened to me recently when teaching a lesson to fourth graders.

A friend and I were talking recently about how much work we put into planning lessons. Even after all these years of teaching, I have to think through lessons as carefully as possible, both about the logistics and about the mathematical thinking I want to keep in mind and support. Here’s an example.