We created a PD series that would help teachers understand Kathy Richardson’s work around the Critical Learning Phases of math.  Here is Kathy’s description of the phases:

“For each major mathematical idea, there are certain understandings that must be in place to ensure that children are not just imitating procedures or saying words they don’t really understand. These understandings must be in place, or at least developing, in order for a child to benefit from particular instructional experiences. These mathematical insights are predictable and universal. I have labeled these understandings, Critical Learning Phases.”
– Kathy Richardson

Our project highlights the assessment and instructional strategies that are based on the Critical Learning Phases.  The link to the video below is an example of one of these assessments.  The Hiding Assessment asks students to recall with automaticity the partners of numbers 3-10.  As you watch the video, note what numbers the student can recall automatically, and what numbers causes the student to call upon his strategies.

Kenan Project- Hiding Assessment Video

(Note: At the point of the video the student is automatic with partners of 3-4 , but needs to think about the partners of 5, and needs more time to process partners of 6.   However, upon using the recommended instructional strategies for his learning phase, we recently administered the assessment and he is now within the number ranges of 7-9!).