Math Blasters as a tool for Modeling

Over the past two years, my colleague, Irene Witt, and I have received feedback from our 8th grade colleagues that they struggle with how little material it appears students have retained from years prior.  Even in 7th grade, we see students losing content within months of learning it.

The Original “Math Blaster”

Our first attempt at addressing this issue came in the form of implementing a program we called “Math Blasters” two years ago.  To develop the weekly assignments, we either identified key skills that were critical for success in the current material or identified skills from recent grade-level material that we wanted to have the students continue reviewing/practicing.  We created documents with practice problems, worked examples, answers, and links to other practice.

Math Blasters were assigned on a Tuesday and assessed the following Tuesday with no option for retakes.

Making a Shift

We had mixed results with the Math Blasters.  Many kids forgot to study.  Others told us in surveys that they didn’t like having only online options for review.  Others just racked up failing grade after failing grade.  Worst of all, we had limited evidence that the Math Blasters were leading to increased retention.

Irene started advocating for a change in structure and, at the start of 4th quarter in the 2017-2018 school year, we shifted to a take-home model.  Students received the assignment on Monday and it was due on Friday.  As with the original, the revised version still had skills, questions, worked examples, and links.  As with the original, the revised version still had issues, largely with students forgetting to complete it or to bring it in on Friday.  But there was one really important shift that came out of the revision:  moving to using information.

From regurgitating information to using information

One theme for our work this year has been to ask our students to use information, rather than to memorize and spit it back.  Although this is not a new pedagogical shift, Irene and I have been pushing ourselves to expand our comfort zone with this approach.  Kids don’t know their multiplication facts?  Give them a multiplication chart.  Kids can’t perform operations with fractions?  Give them a notes sheet.

When we give students resources, we can raise our expectations for students to use that information.  Once they have everything they need and are not dependent on their memories, our work shifts to demanding that students correctly and accurately use the information.  If we relieve the cognitive demand of memorizing and remembering material, then we can realistically demand that students can use the information and apply it correctly.

Extrapolating from an Example

In practice, the revised version of Math Blasters has given me opportunities to have students really engage with the idea of following a model or a sample problem and extrapolating from that example.  Sometimes, students think that following a sample problem means copying the steps exactly, such as always dividing by two when simplifying a fraction because that’s what we did in the sample we provided, rather than understanding that is an example, not an “every time.”

The revised version of the Math Blaster also allowed me to spend time with students as they generated the rules for themselves while working through applying the examples.  It’s important to keep in mind that Math Blasters are always review material, either from earlier years or earlier in the same year.  Most of the students learn the material as and when presented, but there are always a few students who need something different or extra.  Having the Math Blasters as a long-term homework assignment allowed me to work in class with students.

I had great conversations with students where they ended generating the rules for distributive property out of looking at the problems and discussing the patterns they saw.  One day, towards the end of the year, I had a student who was struggling with distribution especially with a fraction.  To his mind, the fact that there was a 1/3 to be distributed explained why there was a one and a three in the answer…rather than that one third of nine is three and 1/3 of three is one.  He wasn’t seeing the multiplicative relationship of distributive property.  I asked him to look at a different problem where there were no fractions; without the complication of the fraction, he was able to identify the multiplication and to apply it correctly to problems with fractions.  Although distributive property is not new (sixth grade) and distributive property with fractions is not new (early seventh grade), I don’t think it started to click for him until he was asked to look for the pattern in the underlying work.