My project started out with examining high school students who, when the new graduation requirements are put in place, would be in danger of not receiving a regular diploma… I interviewed two 9th graders and two 10th graders to get an idea of where their number sense was. I found out that they were largely operating by ones. They didn’t decompose or chunk numbers when performing simple arithmetic tasks. More specifically, they didn’t compose and decompose 10. Moving through decades, whether adding or subtracting was consequently difficult and cumbersome – they often resorted to counting up or down by ones.

I decided to continue my interviews, this time with fourth through … eighth graders. The results and issues were pretty much the same. So, I continued the research down through … 2nd grade. At each level, I found the same deficiencies regarding the composition and decomposition of 10 and in moving through decades while adding or subtracting. I should note that none of these students were special ed students. I asked the teachers to (send me) their lowest, non-special ed kids.

I shared these findings with our curriculum director and our 3 elementary principals, and convinced them to pilot a unit of the new Marilyn Burns materials [Teaching Number Sense by Scharton] for one month with some of these [low math] students. We used the 2nd level of the series, which focuses on moving through decades while subtracting. If necessary, we did a little prerequisite work with composing and decomposing 10 before starting the unit. The pilot was conducted in 3 schools. One school worked with 3rd graders, one with 4th graders, and one with 5th graders. All of the students had similar number sense issues as I described earlier. This was a brief pilot, but we were encouraged with the results. The students made good gains in the areas we were targeting, increased in confidence, and became more active participants in their math classes. Most of them met standard on the state test.

I’m convinced that this issue surrounding “10″ is an indicator of future success, or trouble, in math. These students needed a direct intervention that provided them with good conceptually-based strategies and a greatly increased number of opportunities to work with these strategies.

They may need other interventions in the future, but participating in just this one intervention allowed them far better access to the math they were currently studying. As a case-in-point, I had an opportunity to work with two 4th graders who were struggling with learning multiplication combinations. I worked for about an hour with each student, using techniques and strategies from Van de Walle’s book [Teaching Student-Centered Mathematics: Grades K-3]. The boy I was working with had good number sense, especially around decomposing 10 to move through decades. He made remarkable gains in just that hour. I came back a week later he still had it. On the other hand, the young lady I worked with did not have a good sense of how to decompose 10 to move through decades. Given the same access to the same multiplication strategies, her gains were far less.