As a teacher, I want to know what I can do to support my students’ mathematical development. One of the new “teacher moves” I have learned from our research into Student Adaptive Pedagogy is giving a child a “recent experience of counting.” Today I want you to watch a video of me interviewing Eden. She solves the following three problems: 6 + 3, 7 + 4, and 8 + 5. Let’s think about the same questions we did in my last blog on a Counting All student:
- Did she solve each problem in the same way?
- Was one problem more challenging than another?
- If so, what did you notice that led you to that conclusion?
Eden needed to count an item for each of the addends before she could create material to use to solve the problem. Hiding the blocks after she counted them engaged her need to retrieve a mental image of the blocks and her counting experience. This teacher move supports her development in the abstraction of number. Allowing a child to count something and then hiding it before solving the problem is critical to their development. Before engaging in this area research, I hadn’t realized I should hide material for students. Now I know that hiding material and giving students a recent experience of counting can support their mathematical development.
You may be wondering why we should hide the blocks after a student counts them. The developmental progression we have studied found that as students develop their concepts of number, they move through levels of working with perceptual material (anything visible or tactile, including a drawing), figurative material (mental images of material), and abstract material. If I let her only count the visible blocks, I am not encouraging her growth toward the abstract. Although it is not explicitly stated in common core standards, developing an abstract concept of number is foundational for a student’s mathematical development. Try giving your students a recent experience of counting and let me know how it goes?