Spreadsheets and the discovery of new knowledge

Abstract

The paper introduces a new class of polynomials discovered as an extended inquiry into a two-parametric difference equation using a spreadsheet. These polynomials possess a number of interesting properties connected to the notion of a generalized golden ratio and can be used as a background for a spreadsheet-enhanced teaching of mathematics. The paper reflects on activities designed for a technology-rich mathematics education course for prospective teachers of secondary mathematics.