
05777692
j
2010e.00422
Abramovich, Sergei
Leonov, Gennady A.
Spreadsheets and the discovery of new knowledge.
Spreadsheets Educ. 3, No. 2, 42p (2009).
2009
Bond University, Faculty of Business, Gold Coast, Queensland
EN
F65
H25
K25
R25
R75
U75
spreadsheets
Fibonacci numbers
Fibonaccilike polynomials
difference equations
cycles
generalized golden ratio
combinatorial identities
Summary: This paper shows how educationoriented spreadsheetbased explorations with Fibonacci numbers can result in the discovery of cycles of different periods formed by the orbits of a twoparametric difference equation of the second order. This equation is motivated through the introduction of the socalled Fibonacci sieve. The occurrence of the cycles is interpreted in terms of Fibonaccilike polynomials brought into being in the context of these explorations. This new class of polynomials possesses a number of interesting properties connected to the notion of a generalized golden ratio and can be used as a background for a spreadsheetenhanced teaching of combinatorial identities and their formal demonstration. The paper reflects on activities designed for a technologyrich mathematics education course for prospective teachers of secondary mathematics. It is argued that an appropriate experience with a mathematical frontier can motivate the teachers to teach through a guided discovery mode.