My students have found the following concepts/habits difficult:

–Modeling/showing their thinking consistently.

–Explain your work or explain the pattern.

–Discussing their strategies.

–Modeling/showing their thinking consistently.

In order to prevent “answer-getting,” I encourage students to always “show their work” and add a component that makes their thinking transparent. When I grade work, I always attribute points to the transparent thinking whether or not it leads to the right answer, because at least I can see and respond to what they tried. I also encourage students to cross out rather than erase things that don’t work so that I and they can see what they tried and address misconceptions. I also don’t introduce calculators until the first 2 chapters are complete, so students know they have to use a number line, an addition or multiplication table, a graph, etc. to justify their answer. Students also need to be regularly introduced to different ways to model the algebra as well as be mindful that they should model/show their thinking whether or not is is explicitly asked for in the problem or question.

–Explain your work or explain the pattern.

The first thing I do is make sure students have probelms that use or create patterns. Then I explicitly ask them to notice and explain it algebraically or in writing. The goal is for students to begin to intrinsically look for and notice patterns, but it is quite a daunting task at first. Most student skip that part or write ," IDK." So, when I see a pattern in students opting out, I bring the problem sup during math talk so we can attempt explanations and pattens as a group. I also start the year by looking for patterns in the addition and multiplication tables and by identifying and exploring the basic properties.

–Discussing their strategies.

When students respond to problems, they have opportunities to dicuss what they tried with a peer or peers in the groups they choose to work with. However, sometime the conversation turns into, “Here’s what I got. What did you get? Why’d you get that?” After circulating the room and hearing rather limited discussion, I realize that students need discussion modelled by my own consistent questioning when we share our work. Questions like, “How do you know? What do you mean? Why does that make sense? Can you show me in another way? How do we know that works too?” help because then I start to hear students pushing each other with those same types of questions. We also read/act out scripts of student dialogue in our CME curriculum that reflect student discourse over a problem. We initially do the problem as a class without reading the script and then the script acts almost as a summary. The script of student dialogue also models precise language and what we would ideally like hear from students discussing the problem (not the answers, but the different things they tried and how they figure out what strategy is the most efficient or how to self-correct a misconception).