Jocelyn Dunnack, Mansfield Middle School, Storrs, CT
CPM problems are ripe for teachers to promote the Standards for Mathematical Practice (SMPs), but as I have been repeatedly reminded this year, SMPs (like a lot of other things) take time, effort, and practice. I have been part of a research collaboration called Bridging Practices among Connecticut Mathematics Educators (BPCME), which brought together UConn researchers, graduate students, and teachers from urban, suburban and rural districts to learn about the third SMP: Students will construct viable arguments and critique the reasoning of others. We have developed resources to support teachers and students in the process of mathematical argumentation. Here
are a few things I have learned:
- Arguments are not describing your steps or showing your work. Arguments consist of claims, warrants, and evidence. You have to state a claim, and provide enough explicit evidence to prove you are right. It is more like those fun problems that have multiple strategies or solutions, the ones where students have to prove their solution was actually mathematically sound. Argument is about why you are right, mathematically speaking.
- At first, students needed to learn how to provide enough evidence. Then, they had to learn how to explain the reasoning as to why their evidence even mattered. That was much harder to do, and much more important.
- The CPM teachers in BPCME had no trouble implementing argumentation (and seeing growth in our students’ work). Great tasks were already part of our lessons! However, we did have to devote extra time for these tasks. By digging into a good argument question and skipping a few of the other questions in the lesson, we found deeper understanding than we previously got. It was definitely worth the investment and the sacrifice.
Our work will be compiled and submitted for publication approval by NCTM this summer. Even though I had already been doing argument tasks that existed in CPM, it was very powerful for me to see what happened when I made a conscious choice to explicitly teach a math practice, rather than just knowing it was embedded. Guess what? My kids could not really do it at first, but now they can! I am sure you are not surprised.