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f(x)

what if math. f(x). Functional Thinking. 11.5.13 Art Bardige. Perhaps the most important concept of mathematics is that of function , which provides us with the means to study dependence and change. Mathematics Professor Peter Kronheimer , Director of Undergraduate Studies.

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f(x)

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  1. what if math f(x) Functional Thinking 11.5.13 Art Bardige

  2. Perhaps the most important concept of mathematics is that of function, which provides us with the means to study dependence and change. Mathematics Professor Peter Kronheimer, Director of Undergraduate Studies

  3. We think functionally when we use the scientific method…

  4. And when we use spreadsheets for business.

  5. Functional thinking can change the way students learning problem solving. Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet?

  6. To understand this revolutionary pedagogy let us see “from whence we came.” Copernicus – On the Revolutions 1543

  7. In 1202 Leonardo of Pisa introduced algorithmic thinking as “arithmetic necessary to merchants.”

  8. Enabled by a new technology -- paper

  9. Algorithmic thinking replaced abacist thinking Algorist vs. abacist 1507

  10. In 1637 Rene Descartes invented a new concept.

  11. In 1673 Gottfried Leibniz named it “function.”

  12. In 1686 Isaac Newton based science on cause and effect -- functional thinking.

  13. In 1734 Leonard Euler gave us the symbol for function -- f(x).

  14. In the 19th and 20th centuries functions became transformations M. C. Escher

  15. In 1979 Bob Frankston and Dan Bricklin revolutionized business math with spreadsheets

  16. Enabled by a new technology

  17. Replacing algorithmic thinking with functional thinking in business

  18. Yet in classrooms we rarely if ever learn to think functionally

  19. We still concentrate on algorithmic thinking to solve exercises.

  20. What if… ...students learned to use…

  21. functional thinking organizes problem solving into: • Inputs • Rules • Outputs

  22. Functional Thinking is analytic

  23. Functional Thinking is dynamic

  24. Spreadsheets make functional thinking:

  25. Where we focus on patterns: Science April ‘88

  26. Tables Visual Graphs and Charts Formulas

  27. Concrete

  28. Flexible

  29. Start with a problem and a conjecture to answer it. 29

  30. Represent the function with… ...a table with inputs and outputs 30

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