I haven't posting recently, but I've been thinking about plenty. One topic is the development of number concepts. Principals are provided an abundance of professional reading material, and one of my recent acquisitions was How Children Learn Number Concepts: A Guide to the Critical Learning Phases by Kathy Richardson. If you're not familiar with her, she's the reigning queen of math instruction.
This book is a sourcebook for elementary educators (and perhaps really motivated lay people) to use to recognize and respond to the math understandings children demonstrate. Richardson describes in detail what we might see a child doing and what it tells us about what that child understands about numbers at that phase. I began reading the book thinking I would learn lots of helpful tips to support teachers in math instruction, but it is really designed for teachers to experience directly. Richardson is so detailed in her approach to the phases that I would expect teachers to have it in hand when analyzing student data or even assessing students. Unless you're Kathy Richardson, it would not be reasonable to expect to remember each aspect of every phase. I could see a teacher noticing a pattern in a student's performance on a math task, needing support to identify how to help the child next, and turning to this book to gain a clearer understanding of what that child's work indicates about his or her understanding at that time.
If you read this book and have other ideas for the best ways to use it, let me know!