Counting is Serious Business

Counting is Serious Business

“One, two, three, four, five…” I was interested in how quickly Owen and Ravi figured out a way to count the set of 40 yellow hexagons in their Inventory Bag. The boys took turns saying a number as they placed the hexagons in a line which started to snake across the...
What Does It Mean To Be Smart?

What Does It Mean To Be Smart?

“Wow, you’re so smart.” These words drew my attention to a pair of 5th grade girls in a class I was visiting, who I’ll call Cassie and Sophia. They were mid-way through a turn and talk, each sharing her strategy for solving 84 x 59. I casually moved closer, curious...
What Happens When There Are More Than 10?

What Happens When There Are More Than 10?

Imagine you are 6 years old. Or 7. You know you can use your fingers to model subtraction. For example, for a problem where there are 7 grapes and 2 get eaten, you can raise 7 fingers, put down 2, and count how many are left. But what do you do when the problem...
The Lesson? Students Never Cease to Surprise Me

The Lesson? Students Never Cease to Surprise Me

On a recent visit to a school in a small city in the Midwest, Karen and I joined a class of 5th graders as they learned a game in Unit 3 called Roll Around the Clock. In the previous session, students used a clock to find and name fractions and equivalent fractions....
Watch, Notice, and Learn

Watch, Notice, and Learn

Classroom video is a powerful tool for studying and reflecting on mathematics teaching and learning. Unlike in-the-moment interactions with students, watching video enables us to slow down and more closely examine student-to-student exchanges. This affords us a unique...