Chapter 5 Discussion Prompt

A key take-away for me in this chapter was reflected in the title: equivalence. The notion that an equals sign isn't just followed by "the answer" really hit home for me. As I've been introducing pre-algebra to my struggling 7th graders, it's been mind-boggling to me to unearth so many of their misconceptions. For example, when asking them to define "sum," many of them said "the answer," without any comment related to the total, the operation of addition, missing addends, etc. And exploring the idea of compensation is difficult for them because of their lack of confidence in mental math. How could we be more intentional about developing an understanding of equivalence and compensation in our students from the primary years into Upper School?

Chapter 4 Discussion Prompt

On page 67, the authors points out that explorations such as those described in Chapter 4 help students develop, "big ideas that in later years can be represented algebraically." How can we be more intentional about "linking the thinking" in later years, so rules and symbols are connected to these big ideas?

Chapter 3 Discussion Prompt

The students in Madeline's class developed understanding through modeling and questioning. In working with our 4th grade video problem solving group (Channel 4-VPS), I'm learning a great deal about students' thinking as I guide their problem solving discussions with questioning. Model drawing and the questions I've been pairing with the models are (hopefully!) starting to build pre-algebra concepts in my 7th grade students too. How can carefully crafted questions support students in generalizing mathematical ideas? What questions have worked well with your students? What new questioning strategies do you plan to try?