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Integrated Spreadsheets as a Paradigm of Type II Technology Applications in Mathematics Teacher Education

This paper explores the use of integrated spreadsheets as a type II technology application in mathematics teacher education. It examines the surface and deep structures of signature pedagogy and discusses the use of spreadsheets in investigating Fibonacci numbers and the golden ratio. The paper concludes that this approach enhances teachers' understanding of content and promotes a better educational experience for students.

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Integrated Spreadsheets as a Paradigm of Type II Technology Applications in Mathematics Teacher Education

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  1. INTEGRATED SPREADSHEETS AS A PARADIGM OF TYPE II TECHNOLOGY APPLICATIONS IN MATHEMATICS TEACHER EDUCATION SERGEI ABRAMOVICH STATE UNIVERSITY OF NEW YORK AT POTSDAM, USA

  2. Geography of SUNY Potsdam

  3. A graduate level secondary mathematics education capstone course or "a capstone course sequence in which conceptual difficulties, fundamental ideas and techniques of high school mathematics are examined from an advanced standpoint" (Conference Board of the Mathematical Sciences, 2001, p. 39)

  4. Two types of technology application: Type I & Type 2(Maddux, 1984) Type I – surface structure of signature pedagogy Type II – requires acting at the deep structure of signature pedagogy dealing with uncertainty, motivating engagement, and enabling formation

  5. Structures and descriptors of signature pedagogy (Shulman, 2005) Surface structure Deep Structure Implicit structure Uncertainty Engagement Formation

  6. FIBONACCI NUMBERS AND THE GOLDEN RATIO 1170-1250 AD 432 BC

  7. FROM THE GOLDEN RATIO TO GENERALIZED GOLDEN RATIOS CYCLE OF LENGTH THREE !!!

  8. FROM THE GOLDEN RATIO TO GENERALIZED GOLDEN RATIOS Spreadsheet-based experiment The Ratios may form cycles of any given length

  9. Capstone course assignment: Consider the equationa modification of the equation Using an integrated spreadsheet (Maple, Wolfram Alpha and the Graphing Calculator), find a and b responsible for the cycles of period seven, that is

  10. Using Maple

  11. Using Maple

  12. Using Maple

  13. Using Wolfram Alpha x = a2/b

  14. From Maple to the Graphing Calculator

  15. Spreadsheet confirms cycle of period seven

  16. From Pascal’s triangle to an open problem in mathematics: Fibonacci-like polynomials don’t have complex roots Maple-based proof for n ≤ 100

  17. Conclusion “This project allows a perspective [sic] math teacher to achieve a deeper understanding of content material which translates to a better educational experience for students in the classroom. Furthermore, the use of technology present in these explorations is stressed as an essential component of education by each of the three groups. It is for these reasons that this project, through its relation to the goals and expectations set forth by these groups, serves as an appropriate capstone experience.”

  18. 2015

  19. THANK YOU abramovs@potsdam.edu http://www2.potsdam.edu

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