Date of Award


Document Type


Degree Name

Doctor of Education (EdD)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Eileen Fernandez

Committee Member

Steven Greenstein

Committee Member

Eileen Murray


Multi-digit subtraction is difficult for students to learn. The purpose of this study is to explore how second-grade students communicate their understanding of double-digit subtraction through the use of manipulatives/tools. This qualitative study reports on six case studies of second-grade students where clinical interviews were the main source of data. Findings suggest that manipulatives/tools 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 potential role of manipulatives/tools as communication tools that help reveal students’ actual cognitive development. Implications to research and practice in relation to students’ learning trajectories are discussed.