We went through our curriculum with 6th-grade students for ten weeks. We are by no means experts, but we developed the following practices from our work with the students: - Many of the tutorials review operations that the students are already familiar with. For example, most students going through this book will already know how to add. However, it has been shown that solidifying concepts with numbers before moving to variables helps students see the relationships between the two. Thus, as an instructor, we suggest you acknowledge their past knowledge, as well as explain the motivation behind practicing what they already know.
- Although this book is designed so that a student can work through it independently, we have found that students would pay more attention to our tutorials when they were placed in pairs. When we had pairs read tutorials aloud to each other, switching off every other paragraph, many were able to resist the temptation to skip ahead to the picture examples as they might otherwise have done. In addition to these benefits, group work made our lessons fun!
- For tutorials that do not have practice problems, we had students gather for group discussion to help solidify the concepts.
- Students will likely initially need explicit instruction to jump from doing arithmetic with the bars to setting up and solving equations.
- Though some students may have been exposed to some (or even many) of these ideas before, these tutorials teach through the lens of bar modeling, and will thus be new to everyone. Encourage all students to participate, even if they have already learned a different way! Research shows that seeing a concept in different ways helps improve problem solving (from Shanta Hattikudur, Pooja G. Sidney, and Martha W. Alibi, “Does Comparing Informal and Formal Procedures Promote Mathematics Learning? The Benefits of Bridging Depend on Attitudes Toward Mathematics," in The Journal of Problem Solving 9, no. 1 (2016), doi:10.7771/1932-6246.1180).
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