If I’ve done one thing consistently this year, it has been Number Talks in my Probability and Statistics classes.  I have seen students who, at the beginning of the trimester, told me flat out, “I can’t do math in my head.” Now that Trimester 1 is coming to an end, those same kids are volunteering multiple strategies in these mental math challenges.

During the trimester, we started with the dot image below and have moved through the four operations, onto decimals, and even dabbled in fractions and percents.

How many dots are there?  How did you count them?

What’s important to me with these number talks is the visible improvement I saw in my students’ confidence and flexibility with numbers.

I’ve shared before about my experience with number talks and I plan to continue these throughout the rest of the school year.  But at the NCTM Regional conference in Minneapolis a couple of weeks ago, I had the pleasure of attending Pam Harris’s session on Problem Strings.  I found that problem strings are very useful when wanting to elicit certain strategies or move toward generalization of a strategy.

Here are my notes from a problem string I did recently with the same group of students I have been doing number talks with.

I noticed:

• Many students did not use “17 sticks in a pack” to figure out sticks in 10 packs
• Many more strategies than expected were shared to find the number of sticks in 6 packs of gum.
• Most students were able to generalize about number of sticks in n packs.
• Participation increased with the multiple opportunities to volunteer their strategies.
• Students could see relationships between the numbers and find the solution in multiple ways because of that relationship.
• There are many implications of these problem strings in secondary mathematics. In this example, the slope formula can be easily elicited through further exploration of the table we made.

I’ve read all of Pam’s books, but getting to see her present problem strings in person really illuminated how these can be useful in my classroom. Thanks, Pam, for opening my mind to this and letting me fangirl you.  I’m looking forward to doing more of these, including recording them.  Stay tuned.