Math 8 Intervention – aka ‘Boosters’ – is on my teaching schedule for the 2nd year in a row. The class is a math elective (although not really), and the students in it are hand-selected in conjunction with their counselor, math teachers (current and previous) using a variety of testing, grades, and behavior data of both the qualitative and quantitative kind.
I have 10 students in Boosters so far and I have them during 1st period and advisory. Math skills are very much lacking, and my job is to bring them up to speed enough so that they can be independently successful on their own.
I use a pre-teach model for intervention. Meaning 60% of the time, I teach them that week’s most essential lesson(s) a couple days prior to when they’ll see it in their regular math class. We get to go slowly, since its such a small group.
30% of the remaining time, I do things that boost (get it? harharhar!) students’ basic number sense skills and reteach concepts they should have seen in previous grade levels. I got around to starting dot talks last week, and we do the routine a few times a week.
Here’s a slideshow of the first two times we did dot talks:
I came across students double counting the dots for the first time ever. It was so interesting to me, that I just kinda let it happen during the first time with dot talks.
The second time with dot talks, we focused on just one set of dots and wrote numerical expressions to represent each.
The third time with dot talks (not shown), most students got the idea that you shouldn’t double count the dots by making more than one endpoint or vertex on each dot. But one girl just kept going with it, making more and more complicated shapes and seeing all sorts of things in the dots, double and triple counting everything.
In the end, I had to just tell her point blank that even though her shapes were fantastic, it was making the numerical expression very complicated. We needed to simplify the shapes so that the double/triple counting doesn’t happen and so we don’t need to adjust for it in the numerical expression by subtracting.
I’m not sure if that’s what the original dot talk people would have done, but I did convince the student to keep it simple. And thereafter, her number sense during regular math class has become much more clear and concise. Is there a connection? I don’t know. But dot talks are pretty awesome.
What are your experiences with dot talks? Do your students double count dots like mine did? How did you deal with that?