Wednesday, October 03, 2007

Better Understanding VS. Stupid GPA

Say, you want your children to learn about nature, mathematics and sciences and to create new things. Traditional schools in Thailand won't allow calculators, computers, or the Internet during exams. However, using a computer with appropriate programs such as Mathematica is much better for actual understanding and experimentation. What should you do? (Hint: Creativity and understanding is intrinsically precious, GPA is much, much, less so.)

In this excellent essay, Theodore Gray and Jerry Glynn pointed out why automating mathematical manipulations using tools such as Mathematica would allow civilization to go forward. The lists of things that become less important and more important with such tools are instructive:

Less Important
  • Guessing factors for polynomials
  • Knowing many tricks for integration
  • Being careful when copying over expressions many times
  • Finding roots of complex equations
  • Knowing how to do matrix row operations
  • Knowing how to avoid dropping minus signs
  • Memorizing specific rules for derivatives of such functions as tangent and secant
  • Memorizing multiple angle formulas for trig functions

More Important

  • Translating statements about problems in natural language into statements in mathematical or procedural language
  • Learning how to experiment with math
  • Knowing which integrals should best be done numerically
  • Knowing how to work backwards or to use numerical methods to check symbolic results for plausibility
  • Knowing how to use techniques from programming
  • Understanding recursion and how to use it practically
  • Knowing which functions are discontinuous and where they are discontinuous
  • Knowing how to mix math and programming

Another important passage is:

Children need to know certain facts, but acquiring them is not the main point of learning, especially not in the earlier grades. Mainly children need to have effective habits of mind and an ability to think analytically. They also need to be self-motivated, because in real life there isn't always someone there to provide external motivation (unless they join the army).

The hardest things to teach are the skill of solving problems with incomplete information, the skill of figuring out which problems need solving in the first place, and the skill of finding and bringing together the resources needed to solve a problem.

Children are primed to want to learn. They start out valuing learning and accomplishment above anything else in the world. If you see a child uninterested in learning, it is overwhelmingly likely that the child was made that way by something in the child's world: Children do not start out that way. (Of course there are always exceptions, but they are just that: exceptions.)

--- - ---- - ----- ---------
1. แนะนำการใช้ Mathematica ภาษาไทย
2. ถามตอบการใช้ Mathematica
3. Understanding the birthday paradox and hash collision using Mathematica

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