Model the Learning

This morning, as I try to get back into a routine ahead of Monday's return to work from March Break, I started reading Kathy Richardson's How Children Learn Number Concepts - A Guide to the Critical Learning Phases . This was a book that was given to me earlier this year after my role was expanded from working with grade 7-12 mathematics teachers to a full K-12 mathematics co-ordinator role. With only a background in intermediate & senior math, I've learned so much from primary and junior math teachers this year, and I'm eager to learn more about how students acquire concepts of number, relation, and computation. In her introduction, Richards describes what she calls Critical Learning Phases - "crucial mathematical ideas that students must understand if they are to find meaning in the mathematics they are expected to learn." These crucial ideas are "insights, rather than facts or procedures," meant to be carried forward as students engage in ...

This past fall, we continued a series of cross-panel co-teaching days with some of our grade 7/8/9 math teachers. In addition to co-designing and co-teaching a lesson in a grade 9 classroom, we also spent part of the day dedicated to digging a little deeper into a continuum of concept development for proportional reasoning. Ahead of time, we asked each teacher to give the following task to their students. Calculators and manipulatives were allowed, and the question could be read to the students, but no instruction or guidance was allocated. The point of the task was two-fold. First, we wanted to introduce teachers to the idea of how students develop proportional thinking. In upper elementary grades and in secondary math courses, we often jump right into the more advanced concepts, without looking back to see how students learned the basics (or even if they have learned the basics). Second, we wanted to give teachers a chance to see how their students would fare on a question...