Use Your Imagination

Do you remember ever being asked to use your imagination in math class? Turns out, this is exactly what we do when we think about extending patterns.

Last week, I kicked off my final summer of coursework for my Master’s in Teaching Mathematics. The course—Patterns, Functions, and Change—brought together educators from around the country who work with students across the Pre-K through high school grade span.

I timed how long it took for someone to say their mind was blown—about 30 minutes into the first day of a week-long seminar. One of the joys of these courses is the chance to fully step into learner mode and deepen our own understanding of mathematics. It’s hard to describe, and wonderful to experience.

In one of my small discussion groups—made up of a great balance of one early elementary, one upper elementary, and two middle school educators—we discussed a shared reading about how kindergarten and first grade students work with patterns. We quickly connected the dots between their early thinking and one of the major topics in 8th grade math and Algebra I: linear functions.

Here are a couple of glimpses into what we were discussing:

• Kindergarten children worked to predict what came next in each of these animal track patterns (image from Patterns, Functions, and Change Casebook published by NCTM).

• First grade students were thinking about a “cube train” like the one pictured below, figuring out what colors would appear in different positions by exploring the structure of the pattern.

Patterns are Mental Constructs

You may remember that patterns are one of the major math building blocks for children, starting as early as toddlerhood. (If you didn’t get to read my pattern-focused newsletter back in May, you can read it on my blog here). 

This first discussion in my course was a powerful reminder of how easily the seeds for higher-level math learning can be planted—and nurtured—from early childhood. And how critical it is that we do so.

If you have a child in the 18-36 month age range, consider learning more about patterns (and the other foundations for mathematical thinking that are already developing!) in my bite-sized mini-course Before Numbers: Math Building Blocks for Toddlers.

Try it This Week

Extend a patterning activity using materials around your house. You can use a cube train, blocks, or snack items, or just show your child the animal tracks chart from above and ask them to “use their imagination” to make predictions about what would come next! Here are some questions to spark thinking: 

• What will the next box hold? 
• What will the last box in the picture hold?
• Which box in the sequence would hold the 4th dog paw print?
• (And for any of these):  How are you thinking about it?

I’m also posting a series on Instagram with different patterns made of magnet tiles—follow along if you’re looking for more playful patterns prompts of varying challenge levels to explore with your child!