Small Group Work
Consider students sitting in pairs, which may be conducive to small group processing of ideas. In Nancy’s groups, students worked individually applying her rules. Therefore, there was little motivation for group members to share ideas even though the small group size would have made that easy to achieve. Furthermore, it was Nancy, not group members, who judged the correctness of answers. In their report on the need for equal opportunity for students’ acquisition of deeper learning, Noguera et al. (2015) describe key elements for facilitating group work for deeper learning:
The largest positive effects appear when students receive explicit instruction on how to work productively in a group and when the work involves “group-worthy” tasks that require the talents of all participants and call for a significant amount of analysis and discussion. Structured student roles, interdependent group rewards, accountability for both individual and group efforts, and opportunities for groups to reflect regularly on their own process also make group learning more effective. Many studies have found that low-income students, students of color, and urban students tend to see even greater benefits from group work than do other students, making it a crucial strategy for an equity agenda for deeper learning.
If Nancy has English-language learners (ELL), then students with the same first language could be paired in small groups to allow them to brainstorm before having to worry about the translation for sharing with the whole class.
Manipulatives are alternative, concrete representations that are conducive to the discovery of more abstract concepts or algorithms. They are valuable when they are introduced as an integral part of a lesson to challenge student thinking. Nancy’s use of the algebra tiles could have pushed students
thinking, but she presented the tiles in the same algorithmic manner as the distributive property. Yet an application of this tool is in helping students see or discover the algorithm for multiplying binomials and the distributive property.