lördag 9 november 2013

Why Calculus Reform Is So Difficult (But So Needed)

              Education of Calculus teachers:  Reading Calculus: A Complete Course.

The computer has given Calculus new meaning, tools and power, but Calculus education is today basically the same as when I studied at Chalmers 50 years ago, which was the same as the Calculus education 100 years ago untouched by the computer, and so on...

Real life experience shows that Calculus education resists all forces of reform. The situation is well described in the Preface to the standard text book Calculus: A Complete Course by Adams and Essex:
  • Calculus is in many respects a classical subject.
  • It is much older than the memories of anyone alive.
  • It is taught in every institution of higher learning in the world.
  • If it is so universal why do we not just reprint old text books from, say, the nineteenth century?
  • The mathematics is the same isn't it?
  • Of course , it is.
  • If your great great grandparents had studied Calcukus in their time, there would be much that they would recognize in modern texts.
  • The text books have grown larger, with many more examples, applications and exercises. Colorful ink and elaborate diagrams burst from the pages.
  • The mathematics is the same but the audience is not.
  • One unprecedented change began to take place more than a decade ago - a mere wink in the of the eye in the history of Calculus.
  • Computer code began to appear in text books to respond to the growing awareness, access, and dependence of the audience on computers. 
But isn't it possible to question the standard dogma that Calculus is the same today as in the 17th-18th century, when it was developed by the great mathematicians of that time? 

No, the Calculus canon represented by Adams cannot be questioned because teachers of Calculus have been thoroughly trained during their studies to believe and confess to the Calculus canon and therefore are unable to go outside the cage and question the canon. And the rest of the world has nothing to say, because the only people who understand Calculus are teachers of Calculus. 

MST/BodyandSoul questions the Calculus canon, not just superficially, but on the fundamental level concerning the basic concepts of real number, continuity, derivative, the Fundamental Theorem of Calculus and more generally about the very meaning and use of Calculus. 

Accordingly, MST/BodyandSoul is banned by KTH, and to get a link put up on a Calculus course web page at Chalmers,  as supplementary material questioning Adams, has shown to be very difficult if not impossible.  

But the "unprecedented change" of the appearance of the computer will eventually push reform...because of "growing dependence of the audience (not teachers) on computers"...    

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