Sentence Frames: I noticed___ so I looked for____/We noticed____ so we____
Summary: Using sentence frames (such as those listed in this title) can help students share their mathematical thinking and make it easier for all students to participate in class discussions and/or reflections.
School Connection: I have used the “notice or wonder” strategy for years and incorporating these sentence frames seemed like a natural next step. That is, the sentence frames present a way for students to take their notices and wonders and use them not only to better understand the problem, but to also develop concrete solution strategies over time. For these reasons, I used the sentence frames in the launch and closing during a 7th grade lesson on integers this week. See the blog post, "Using Sentence Frames to Promote Math Thinking" for more details.
Connection to Equity: “Focusing on student thinking sends the message to students that their ideas have merit, and students start to see themselves as capable mathematicians” (p. 10). This aligns with the equity practice of “challenge spaces of marginality” because the sentence frames “encourage student-to-student interaction and broad-based participation” (from the "Five equity-based practices"). Furthermore, using these sentence frames and ask yourself questions allow students to understand the problem with less teacher support. This aligns with “releasing control” (“R” in the ICUCARE equity framework) which places a focus on student sensemaking as an equitable practice.
Visible Random Groupings: Improving Student Collaboration
Summary: The idea of using "visibly random groups" (VRGs) came from Chapter 2 of Peter Liljedahl's book, Building Thinking Classrooms. In his book, Liljedahl reports that creating random groups of 3 (in grades 3-12) led to the "perfect balance of redundancy and diversity" whereas self-selected groups ended up with "too much redundancy, not enough diversity" (p. 45). The students also needed to see the groups being randomly constructed for the groupings to be effective (p.44).
School Connection: As of February 2023, I have been using VRGs daily with great success. Students work more effectively in these groups (compared to the self-selected groups I used earlier in the year) and I have noticed students are more attentive to each other during whole class discussions. I use the random group generator from the website Flippity to create my random groups. I like this website because you can enter the students' names in a google sheet file and reuse it every class period. This website also lets you temporarily edit the list (e.g., to remove absent students) right from the webpage which makes it very easy to use.
Connection to Equity: Placing students in VRGs aligns with being “Critically Conscious” (the first “C” in the ICUCARE equity framework) because it can erase the effect of negative stereotypes by assigning competence to all students: When all classmates are asked to work together, it provides opportunities for more voices to be heard and appreciated. Additionally VRGs "leverage multiple math competencies" (from the "Five equity-based practices") by structuring activities that promote student collaboration.