A Multi-Representational Approach to Teaching Number Sequences: Making Sense of Recursive and Explicit Formulas via Spreadsheets

Abstract

This article offers innovative and original mathematical vignettes in the treatment of number sequences along with recursive and explicit formulas in a technology-supported multi-representational pedagogical context. Multiple representations are used to explain (i) how to help students understand summation identities of the form “Left-Hand-Side (LHS) equals Right-Hand-Side (RHS)” and (ii) how to use spreadsheet activities to lead to a better understanding of how to develop proofs for these formulas. LHS and RHS can at times be thought of as the recursive and explicit forms, of the number sequence under consideration, respectively. Such a multi-representational pedagogy comprises (but is not limited to) physical manipulatives, diagrams or drawn representations, visual proofs, algebraic representations, formal proofs, and spreadsheets. The article concludes by emphasizing the fundamental role of spreadsheets for a thorough understanding of summation formulas or identities of the form LHS = RHS and the transition from numerical evidence to formal mathematical proof.