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Unformatted text preview: From Modeling in Mathematics Education to the Discovery of New Mathematical Knowledge Sergei Abramovich SUNY Potsdam, USA Gennady A. Leonov St Petersburg State University, RUSSIA Abstract This paper highlights the potential of modeling with spreadsheets and computer algebra systems for the discovery of new mathematical knowledge. Reflecting on work done with prospective secondary teachers in a capstone course, the paper demonstrates the didactic significance of the joint use of experiment and theory in exploring mathematical ideas. Conference Board of the Mathematical Sciences. 2001. The Mathematical Education of Teachers . Washington, D. C.: MAA. Mathematics Curriculum and Instruction for Prospective Teachers. Recommendation 1. Prospective teachers need mathematics courses that develop deep understanding of mathematics they will teach (p.7). Hidden mathematics curriculum A didactic space for the learning of mathematics where seemingly unrelated concepts emerge to become intrinsically connected by a common thread. Computational modeling techniques allow for the development of entries into this space for prospective teachers of mathematics Fibonacci numbers Twoparametric difference equation Oscar Perron (1954) f k + 1 = αφ κ + βφ κ1 , φ = φ 1 = 1 a = β = 1 {Φ κ } ∞ 1, 1, 2, 3, 5, 8, ......
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This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.
 Winter '08
 JARVIS
 Algebra

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