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Spreadsheet Math A Powerful Tool for the Practice of Mathematics

Spreadsheet Math A Powerful Tool for the Practice of Mathematics. NCTM Boston 2015 April 17, 2015 Art Bardige Peter Mili Ryan McQuade. Agenda. Introduction What if… Labs Questions and Comments. To imagine tomorrow we have to understand today.

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Spreadsheet Math A Powerful Tool for the Practice of Mathematics

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  1. Spreadsheet Math A Powerful Tool for the Practice of Mathematics NCTM Boston 2015 April 17, 2015 Art Bardige Peter Mili Ryan McQuade

  2. Agenda • Introduction • What if… • Labs • Questions and Comments To imagine tomorrow we have to understand today

  3. What if… we started from scratch to design a math curriculum for 21st century students using 21st century tools? To imagine tomorrow we have to understand today

  4. Our math curriculum today was designed… To imagine tomorrow we have to understand today

  5. In the year 1202when Leonardo of Pisa… Leonardo of Pisa (c.1170-1250)

  6. Reinvented the mathematics used by merchants with this book Liber abbaci The Book of Calculation Liber abbaci (1202)

  7. He was born in Pisa

  8. At the same time as the Leaning Tower

  9. When Pisa was a great trading city

  10. As a boy Leonardo followed his father, a “public official” and trader to Algeria

  11. Where he was tutored in Arabic arithmetic and algebra The Compendious Book on Calculation by Completion and Balancing al Khwarizmi

  12. Both academic subjects… Scholars at an Abbasid library, Baghdad (1237)

  13. …not used by medieval merchants

  14. Who computed in Roman math on an abacus

  15. Good enough for the Roman Empire • “None of the cities should beallowed to have its own separate coinageor a system of weights and measures; • they should all be required to useours.” • Dio Cassius 235AD

  16. But not for trade between Medieval city-states, each with its own…

  17. …weights, measures, and money

  18. Requiring multiplication, division and the solving of complex ratio and proportion problems Roman multiplication by Doubling (167 x 9 = )

  19. Leonardo returned to Pisa to write “arithmetic necessary to merchants” Liber abbaci

  20. Based on Indian numerals, place value and…

  21. al Khwarizmi's “algorithmic” procedures in arithmetic and algebra al Khwarizmi (c780-c850)

  22. Using the new technology… paper Paper introduced to Europe c. 1100

  23. Leonardo’s (algorist)math gradually become symbolic and made Algorist vs. Abacist (woodcut 1504)

  24. Leonardo’s (algorist)math gradually become symbolic and made Roman (abacist) math... Obsolete Algorist vs. Abacist (woodcut 1504)

  25. On the recognition of the nine Indian figures and how all numbers are written with them. (place value) • On the multiplication of whole numbers • On the addition of them, one to another • On the subtraction of lesser numbers from greater numbers • On the division of integral numbers • On the multiplication of integral numbers with fractions • On the addition and subtraction and division of numbers and fractions and the reduction of parts to a single part • On the buying and selling of commercial things (ratio&proportion) • On the barter of commercial things (rate) • On companies made among parties (percents) • On the alloying of money (mixture problems) • On the solutions of many problems (Fibonacci sequence) • On the rule of elchataym by which problems of false position are solved. (solving linear equations) • On the finding of square and cube roots, on binomials and their roots. • On the pertinent rules of geometricproportions By the 17th century Leonardo’s table of contents… The Chapters in Liber abbaci (1202)

  26. 2013 This became the curriculum staircase we all know so well Video on Common Core Math Standards

  27. 234381 x 74 Defined by the difficulty level of the algorithms - 49

  28. Every student must climb today!

  29. Yet, so many “fall behind” and fail

  30. To understand what we should do about this great problem We must know what students need in the 21st century

  31. To understand what we should do about this we must first know what 21stcentury students need

  32. For in 1979 a new technology reinvented the mathematics of business VisiCalc on an Apple II

  33. Dan Bricklin Dan Bricklin & Bob Frankston

  34. A Harvard Business School student

  35. Working on case studies

  36. Wanted technology to enable him to ask “What if…”

  37. So he and Bob Frankston invented the spreadsheet VisiCalc 1979 VisiCalc the Visible Calculator

  38. Mitch Kapor added graphs VisiPlot 1980 VisiPlot

  39. And then a database Mitch and Lotus 123

  40. Putting a PC on every business desk with…

  41. …a spreadsheet inside

  42. To enable business people to now ask…

  43. To enable business people to now ask… What if…

  44. What if… Not only what is

  45. *44 Making Leonardo’s math… )

  46. *44 Making Leonardo’s math… Obsolete )

  47. What if we designed our math curriculum around spreadsheets and…

  48. fx And functional thinking

  49. Perhaps the most important concept of mathematics is that of function, which provides us with the means to study dependence and change. • Professor Peter Kronheimer, Director of Undergraduate Studies (2013-14) Functions are…

  50. Spreadsheets are function machines with Inputs Outputs Rules

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