Chapter 6 Discussion Prompt

On p. 104-105, the authors point out that, "... concepts are the results of cognitive processes and not the other way around. Working with diagrams facilitates important cognitive processes." It's so important that students at all levels build conceptual understanding through big ideas such as those outlined in this section. I find, however, that a fair number of students seem to lack confidence in working with visual representations, whether it be an open number line, bar model drawing, or their own diagrams. To what extent do you see this in your students? How could we be more intentional about building persistence, confidence, and accuracy with visual representations to develop those all-important big ideas?

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?

Chapter 2 Discussion Prompt

In the first YMAW blog group, we discussed Models as Tools for Thought (p. 32 in this book). We know that visual models serve as representations of our students' thinking; however, the language associated with those models can give us an even more powerful window into how students use the models as well as their levels of abstraction. At the intermediate level, how can we use visual models + language to help our students build meaning?

Chapter 1 Discussion Prompt

Wow! So many great quotes, points, and food for thought already in this first chapter! Reading about Camille's classroom implementation helped to bring the teachers' workshop principles to life. One idea I've been more conscious of with my students relates to open-ended questioning and waiting until a little later to "fix" the mathematics vocabulary (p. 18). How often might our good intentions to quickly guide students toward the concepts we want them to develop be interfering with their own long-term understanding? (See also Camille's comment on p. 16, "They're just doing it because I asked them to. But what are they really learning.?") In what ways could we more carefully construct learning experiences and use questioning so students develop concepts that will last and transfer over time?

Welcome to our FHCDS Algebra book study blog!!

Thank you for joining the study group for the book, Young Mathematicians at Work: Constructing Algebra. We hope this format will be one that you'll find user-friendly and a fun way to share perspectives and reflections about the book with colleagues. Stay tuned for the first set of prompts/questions about Chapters 1 and 2!!