Teaching Student Centered Mathematics Book Study: Chapter 8

Chapter 8- Early Number Sense
I said it at the end of my last post and I will say it here again. These chapters are SO dense with information that my reflection is really only brushing the tip of the iceberg. If you teach math to primary students you NEED to run out and buy this book TODAY. This chapter was amazing. I felt so confirmed for many of my choices in teaching my students. I learned how to tweak what I am doing to make my instruction even stronger and I have learned about further connections I could be making to build number sense in my students.

So, let's get into it! The chapter began by discussing early counting and the authors defined early counting as an interconnected set of skills including number sequence, one to one correspondence, cardinality, and subitizing. I felt confirmed when the authors talked about how you can not rush these understandings and students need a high number of activities which allow them to build these skills. Thinking back to chapter 1, it's all about building experiences which allow students to build connections from activity to activity in order to construct a strong meaning of numbers and counting. These activities could include rhythmic counting both forward and backward. Building a number path, counting a number of items, gathering a collection of a given number of items, etc.

Next, we moved into the learning trajectory for counting. As I read the 5 steps laid out, I could easily state which of my students fit into each step and having this understanding will help me, in the fall, to take next steps to move them to a more complex understanding of numbers and counting. The five steps here included emergent counter, perceptual counter, figurative counter, counting-on counter and non-count-by-ones counter. Figurative counter was a step I was not formally acquainted with previous to reading this chapter. Figurative counter refers to a student who, given a set of items with a known part of the set covered, would imagine or visualize the hidden items and would still count beginning at 1 while accounting for these items.

We moved from counting into the number relationships which inform number sense. The relationships which we need to help our students to develop include spatial relationships, one more/two more/one less/two less, anchors to 5 and 10 and part-part-whole. Each of these relationships informs the next and activities in each will help students to develop a robust understanding of the relationship between numbers. I have mentioned, more than a few times before, the book "Fluency through Flexibility"   this book is based largely on the research presented in this chapter of the book and relates hands on activities and assessment for developing an understanding of number relationships in our youngest students. I would so highly recommend this book - it's really not very expensive- and you will get so much out of it!

One note in this chapter that I found particularly interesting was the discussion of "calendar time". The authors made the point that using the calendar the promote foundational mathematics because a calendar groups numbers by 7s rather than by 10s. Patterns found in a calendar can be an "in addition to" activity but shouldn't be the basis of a classroom's number relationship discussions.