Students' Engagement in Each Other's Ideas - A Framework

Math PD at my school this year is going to focus on Cognitively Guided Instruction, and I have spent the last couple of days re-reading Carpenter, Fennema, Franke, Levi, and Empson’s Children’s Mathematics. There is so much good stuff in there, but their framework for categorizing students’ engagement in each other’s ideas particularly caught my eye. In the past I have seen and somewhat implemented various student discourse sentence stems. But the categorization and leveling of how one student might respond to another’s strategy seems much more useful. Instead of telling kids what to say it offers them options for what to think about and do. If needed, sentence stems could be added in association with each of the options. My excitement about this matches my current general excitement about frameworks—it helps me (and my students) to know how things are related to each other.

Here’s the framework, basically lifted from the book (pg. 154) and converted from paragraph form into list form. In order to make it to the next level of sophistication, you have to have done or been able  do the thinking required in the previous level. 

Level 1: Comparing an Idea to Another Student’s Idea

This form of engagement asks students to look at another student’s strategy in relation to their own ideas and make a judgment

• determine whether someone else’s strategy is same or different from own strategy
• determine whether someone else’s strategy makes sense and is accurate (agree/disagree)

Level 2: Attending to the Details of Another Student’s Idea

• repeat or explain what they heard someone share
• explain a representation that was displayed by another student
• explain specifically how a strategy they heard is similar to another strategy
• ask a question about an aspect of someone’s strategy

Level 3: Building on or Adding to Another Student’s Idea

• add further detail
• correct a part of the strategy that was inaccurate
• make a strategy more efficient
• propose an alternative strategy
• explain how the alternative strategy was different than the strategy that was shared
• justify why a strategy works
• explain how a strategy could be used on other problems
• co-construct a solution with another student

This framework is something that I’m really excited about using with my students this year—explicitly teaching, reinforcing, and having them self-assess.