Twenty-fifth International Conference on Learning

Abstract

Multi-digit subtraction is difficult for students to learn. This study explores how second-grade students communicate their understanding of double-digit subtraction through the use of manipulatives. Using clinical interview and a variety of manipulatives, we created a venue to help us elicit student’s understanding of double-digit subtraction. Through qualitative analysis we were able to identify differences in students’ understanding that were not apparent from the typical assessments administered in the classroom. Findings suggest that manipulatives helped reveal cognitive constructs and difficulties that the handwritten algorithms were not conveying. For example, students who exhibited an understanding of the subtraction process had not yet developed an understanding of ten and 10 ones interchangeability. These results highlight the role of manipulatives as communication tools that help reveal students’ actual cognitive development. This suggests another approach to teaching: questioning from the perspective of just understanding what students are thinking and not teaching. Recognizing learning differences can come from creating a space to allow students to articulate their understanding. We offer suggestions to assist teachers in recognizing learner differences and use them as a productive resource in lesson planning.