Promoting the Aha Experience Using Spreadsheets

The purpose of this paper is to give an example of guided problem solving and using a spreadsheet to help solve a related series of mathematical problems. The context is that of side totals, where the numbers 1 - 2n are arranged three on each side of an n-sided polygon. The context allows for the problem to start small and easily accessible by exploring ways to arrange the numbers 1 - 6 on the sides of a triangle. From that beginning and with support from spreadsheet calculations, the investigation extends to finding arrangements of numbers that form equal side totals on squares and pentagons. From there, a number of patterns emerge that can be applied to polygons with many more sides and students can be guided to engage with the explorations by following patterns that arise in a simple context and applying those patterns to more complext contexts. Discovering the various patterns provides opportunities for students to have the Aha experience that accompanies the discovery of numerical patterns and problem solutions in mathematics. This article is designed to foster that experience amongst secondary students to whom the mathematical content of the problems will be readily accessible.