Letting Math Teachers Steer: Keeping Grounded with the Empirical Trajectories

August 26, 2016

In the last 3 posts we talked about our different approaches to building learning trajectories (LTs). This third and final approach acknowledges the work being done by dedicated teachers in mathematics classrooms all over the country. For many early adopters, anxious to find a way to include Computer Science or computational thinking (CT) in their students’ day, the mathematics classroom seemed the path of least resistance. This trajectory approach allows us to use their work to find “waypoints” which would “form the backbone for curriculum and instructionally meaningful assessments and performance standards”¹ but still hold onto the joy of exploration. The LTEC project includes several teacher collaborators who have been performing this CT-Math balancing act in their classrooms.

Groups of teachers met to create lessons that were directly connected to lessons in the Everyday Math (EM4) curriculum, but included concepts in computational thinking and coding. While the implementation is far from perfect, we have learned valuable lessons along the way in balancing math and CT. By starting with the classroom, we have found some key topics for mathematics that could more easily lend themselves to exploration with computers. The teachers bring their deep understanding of their district-mandated curricula and a growing number of online resources to help with decisions related to curricular integration. One possible set of waypoints involves polygons and their properties.

Through the work of our teacher collaborators, we have watched second graders walk a polygon using posters to help with the turns. They then use laminated tiles to plan the program that will move their Scratch sprite. Finally, in pairs, they program the computer to draw the figures. Teachers wrote this unit, piloted it, and shared it with colleagues, who naturally brought their own approach to it. Some teachers spend more time with the group exploration and allowing students to tutor each other on computing skills that new classmates might lack.

Looking at polygons from the perspective of physical motion adds to the mathematics by presenting the exterior angle as a turn and getting back to the starting place. Whereas the regular math curriculum introduces polygons through their properties of interior angles and numbers of sides. So, here is an additional experience, a physical experience of walking, a logical experience of designing the similar motion for a sprite, and the coding experience of putting the algorithm into the computer. What does this imply for the learning of the math concept of polygons and the computational thinking process of forming an abstraction for polygon? This question is one of many we explore as we go forward.

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