MidSchoolMath National Conference 2016

This session on mathematical cognition will focus will be on geometry and number concepts that arise with an exploration of circles! We will engage in several activities involving measurement and approximation that relate the area and circumference formulas, to help develop a deep understanding of the formulas as ideal models, and see how algebraic manipulation links to seeing physical models from different viewpoints.

We will highlight some historical developments about circles that link circles area and length parameters to rational and irrational numbers, polygons and similarity. After engaging in hands-on learning activities (using compasses to draw circles, and estimating and measuring areas and diameters, using a rope to wind into a circle and then cutting and rearranging pieces to make a triangle of rope lengths), we will discuss the design of appropriate assessments for each type of learning as presented in the cognition scheme.

At the end of the session we will review student work samples and scoring rubrics to address how rubrics can serve to provide detailed feedback to learners. Hence, we will make a complete circle of cognitively based assessment!

You'll leave this session with advanced organizer for mathematical cognition and assessment item design strategies, as well as multiple examples of activities and assessment items they can use for a unit on circles for 7-8th graders.