Outline Aim and Summary The new history The new philosophy The experiment Results Presented at the 2nd People's Education Congress, Homi Bhabha Centre for Science Education, Mumbai, 5-9 Oct 2009, in both panels on (a) Mathematics Education and (b) History and Philosophy of Science in Science Education. Calculus Without Limits: Report of an Experiment C. K. Raju Centre for Studies in Civilizations, New Delhi and Inmantec, Ghaziabad, ckr@ckraju.net,c.k.raju@inmantec.edu web: ckraju.net C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Aim and Summary 1 The new history 2 The new philosophy 3 The experiment 4 Results 5 C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Aim To report on a new system of teaching mathematics, and some recently conducted experiments on it. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Outline of the new system Q. Why is math difficult? C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Outline of the new system Q. Why is math difficult? A. Because theology has got mixed up with it. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Outline of the new system Q. Why is math difficult? A. Because theology has got mixed up with it. Q. How to make math easy? C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Outline of the new system Q. Why is math difficult? A. Because theology has got mixed up with it. Q. How to make math easy? A. Eliminate the theology from mathematics. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results The basis of the new system Involves new history (“theology has got mixed with math”). C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results The basis of the new system Involves new history (“theology has got mixed with math”). and new philosophy of math (“Eliminate theology from math”). C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results The new history Calculus developed in India in response to needs of monsoon-driven agriculture and navigation, C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results The new history Calculus developed in India in response to needs of monsoon-driven agriculture and navigation, as a means of calculating accurate trigonometric values required for the calendar. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results The new history Calculus developed in India in response to needs of monsoon-driven agriculture and navigation, as a means of calculating accurate trigonometric values required for the calendar. Calculus was transmitted to Europe in the 16th c. in response to needs of European navigation C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results The new history Calculus developed in India in response to needs of monsoon-driven agriculture and navigation, as a means of calculating accurate trigonometric values required for the calendar. Calculus was transmitted to Europe in the 16th c. in response to needs of European navigation which required a table of secants (for Mercator chart) and a precise calendar (for latitude determination; hence calendar reform of 1582). C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Reception of calculus in Europe Trigonometric values used for Mercator chart. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Reception of calculus in Europe Trigonometric values used for Mercator chart. Beyond the capabilities of Tycho Brahe, Kepler. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Reception of calculus in Europe Trigonometric values used for Mercator chart. Beyond the capabilities of Tycho Brahe, Kepler. Rejected as disreputable by Galileo. Accepted by his student Cavalieri. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Reception of calculus in Europe Trigonometric values used for Mercator chart. Beyond the capabilities of Tycho Brahe, Kepler. Rejected as disreputable by Galileo. Accepted by his student Cavalieri. Accepted by Fermat and Pascal. Rejected as “beyond the capacity of the human mind” by Descartes. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Reception of calculus in Europe Trigonometric values used for Mercator chart. Beyond the capabilities of Tycho Brahe, Kepler. Rejected as disreputable by Galileo. Accepted by his student Cavalieri. Accepted by Fermat and Pascal. Rejected as “beyond the capacity of the human mind” by Descartes. Accepted by Newton and Leibniz whose work was torn to bits by Berkeley. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Lesson Reception of the calculus in Europe involved difficulties. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Lesson Reception of the calculus in Europe involved difficulties. These difficulties persisted until formal real numbers by Dedekind. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Lesson Reception of the calculus in Europe involved difficulties. These difficulties persisted until formal real numbers by Dedekind. Which used Cantor’s set theory, formalised in the 1930’s. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Lesson Reception of the calculus in Europe involved difficulties. These difficulties persisted until formal real numbers by Dedekind. Which used Cantor’s set theory, formalised in the 1930’s. Leads to present-day teaching of calculus with limits as in current school texts. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Phylogeny is Ontogeny Math is difficult because this historical trajectory is replayed in the classroom. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Phylogeny is Ontogeny Math is difficult because this historical trajectory is replayed in the classroom. in fast forward mode. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Lesson These difficulties arose because Indian gan . ita different from mathematics. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Lesson These difficulties arose because Indian gan . ita different from mathematics. The calculus developed in one cultural context and was absorbed in another. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Lesson These difficulties arose because Indian gan . ita different from mathematics. The calculus developed in one cultural context and was absorbed in another. Calculus arose as gan . ita and was sought to be absorbed within the religious tradition of mathematics (as science of the soul) C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Philosophical objections Current notion of mathematical proof not rigorous. C. K. Raju Calculus Without Limits: Report of an Experiment
Outline Aim and Summary The new history The new philosophy The experiment Results Philosophical objections Current notion of mathematical proof not rigorous. Why? C. K. Raju Calculus Without Limits: Report of an Experiment
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