A spiral pattern investigation : making mathematical connections

Abstract

Nowadays there is considerable agreement among educators that learning mathematics fundamentally involves making mathematics. Students learn mathematics while working on tasks that they consider meaningful and worthwhile, and their interest is aroused when they can see the point of what they are being asked to do. Given that learning mathematics involves a process of meaning-making – the use of mathematical language, symbols and representations as learners negotiate ideas – activities should provide students with a variety of challenging experiences through which they can actively construct mathematical meanings for themselves. Over the years, task designers have offered a range of mathematical tasks to engage students in doing mathematics by stimulating their curiosity in exploring and explaining mathematical meanings. The spiral pattern investigation is one such task designed to offer secondary school students a mathematical challenge. The challenge presented through this spiral drawing is one intended to encourage students to pose problems and questions and then to investigate them. The robustness of the spiral pattern investigation lies in the range of mathematical topics that can be dealt with, the multiple ways in which conjectures may be tested and the different ways in which students may work through the task.