Digging Deep into Proportional Reasoning
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...