More on Math Tools

I get so many questions on how to use math manipulatives when I do professional development on teaching math. I wrote about many of the logistics in this last post, but really, I'm sure I will continue to write about in various forms and contexts. It's that interesting, I promise! ;)

I started out explaining that I present the groups with a tray of a certain tool, and they are given free exploration time. When I was a math coach/specialist for my district, I actually had this process written into the pacing guides. So the first five days of every school year are about introducing tools and procedures, including number talks.

Because I have an abundance of tools (largely scavenged from hallways and supply rooms where they were discarded) I just give everybody the same tools. If I were short of supplies, I would fill each tray with something different and rotate them over the five days. That's still legit for many reasons, actually, but I choose to do it this way because they also learn about the tools by watching each other use them, and talking to each other about what they see happening in different groups.

While they are working with the tools, I am circulating and learning a lot. I make notes on conversations I hear, math I see, and procedures I may (will) need to reteach. You can learn a lot about who your kids are in math class by watching them work in free exploration.

Who are your sorters...

Your artists...

Your pattern seekers...

Your hard core playahs...

Your spatial geniuses...

Your future engineers....

and, of course, Your Mopers

 I'm always surprised at how much math surfaces during these play exploration sessions. And if it looks like play? So be it.

Since they have their tool bags (these are last seasons bags, and the new ones are much roomier for the same number of tools), they are in charge of deciding which tools to use, to solve which problems, and in which way. I'm not going to lie to you...the first year I implemented this, and I saw what they did, I thought I'd made a HUGE mistake.

For example? Do you see the 18?

No? Me either. Until he explained: 1, 2, 3, 4 cubes...2 green tiles...1 yellow cube...2 sticks...1 red counter. (4 and 2 and 1 and 2 and 1 is 10). Now look at the dice....one says 3 and one says 5. 10 + 3 + 5 = 18.  This is certainly not what I envisioned!

But we pushed through this part, and it has become easily one of the most powerful, sense-making policies of our math period. It took some time, but we always highlight strategic use of tools. I'll often ask students doing something efficient and/or interesting to tell us a little bit more about why they did it that way. "Why did you use a 10 stick instead of the red counters?" Or, for a problem involving regrouping for subtraction: "I see you used a stack of 10 unifix cubes...how did that help you do the subtraction?"

It also takes offering an invitation to experiment. "What if you used _____? Would you get the same answer?" The more students used the tools as part of their daily practice, and the more invitations I offered to do the same problems using multiple tools, the more the kids made sense of the tools and they began to actually use them strategically. (Standards for Math Practice #5, CCSS)