The developmental spine: how mathematical understanding builds from counting to fluency to models, operations, and properties. But why is it taught that way? What does it all mean?
It is time to expose the secret double life of subtraction. It all comes down to that foundational number sense we work with students to develop as they grow as elementary school mathematicians. We give students the opportunity to build…
Sometimes the best definition is so brief and obvious…if you were to ask me just yesterday how to define fact fluency I would have given you a mouthful of alphabet soup teacher-ese. This morning, over coffee, shuffling through some of…
If you’ve read the previous post on the fundamentals of counting, then subitizing is not news to you. If you haven’t yet, here is a link to that post! Tenzi is one of my favorite at-home-fun-for-everyone games that has a…
Today we briefly talked about something I’m not going to name for the students just yet, because we are still playing! We’re on a cliffhanger until Monday. We left this unresolved for now… What I can tell you is that…
We’ve covered the critical pieces of developing counting with meaning in this post. What happens next? Enter additive thinking! When counting gives way to reasoning, it is the beginning of additive thinking. The journey from “count everything” to “just know…
Dice and dominoes are probably some of the first quantities we consciously subitize and assign a numerical value to as children. (Subitizing, you say? What’s that? Check out this post on the many nuances of counting.) The “pip” or dot…
What would you think if I told you counting was actually not as easy as 1-2-3? I was as surprised as you when I studied the development of numeracy in our youngest mathematicians. What we might consider done and dusted…
When a student is used to scrutinizing the values she is working with, the connections emerge. Often the kids are so excited to share the connections they’ve made that they annotate their math homework or burst into an excited monologue…
How many dots do you see? HOW do you see them? This image appears in our Kindergarten curriculum as part of something called a “dot talk.” This is an opportunity for students to see math as something that is perceived…