Friday, November 19, 2010

Whose Computer Can Solve This for Me?

There's an scene in The Simpsons where Edna Krabappel is teaching the students math.  The dialogue is below.
Mrs. Krabappel: Now, whose calculator can tell me what 7 times 8 is?
Milhouse: Oh! Oh! Oh! Low Battery?
Mrs. Krabappel: Whatever.
 I was reminded of this scene when I saw this talk by Conrad Wolfram on the TED website.

I found a link to the talk on this post by Maria Andersen.

The modern version of The Simpsons scene would have Bart's class in a computer lab.  The dialogue would be the following.

Mrs. Krabappel: Whose computer can compute this integral for me?
Milhouse: Oh! Oh! Oh! 404
Mrs. Krabappel: What's the whole answer?
Milhouse: 404 Error: Page not Found
The thesis of the Wolfram's talk is that the mathematics taught in school today does not reflect the real world.  Also, requiring calculations to be done by hand is the bottleneck preventing students working on real world problems.  His solution is to use a program like WolframAlpha, which can solve many mathematics problems automatically, with students.

I do agree with his statement of the problem.  I do have a few points of disagreement with his solution.
  1. Graphing calculator do quite well with teaching mathematics.  At my college, we use graphing calculators at all levels of algebra.  Our College Algebra class is modeling based, so we make heavy use of calculators.  We teach graphing operations, statistical operations, and using the solver application.

    Access to calculators is not a limitation.  The local high schools require the TI-84 calculator, and most of our students still have theirs.  Also, the college has some available for students to borrow.

    The calculators do have limitations, but those are not disadvantages.  The calculator can only process the mathematics that the students put into the calculator.  That means that the students have to develop or find the formula to measure how drunk is someone on their own.  Also, the computers are too fast in presenting the results.  Calculators require the students to slow down and see the fine details.  Finally, calculators cannot get information off of the internet.  Any communication device is also a cheating device.
  2. There is no silver bullet to fix mathematics education.  The problem is that there is a new silver bullet every five years or so.  At some point, people outside of the teaching profession are going to have to realize that people learn in unique ways.  Wolfram is not alone in thinking that he has found the solution.  Some colleges are changing all developmental (below college level) mathematics courses to computer delivered instruction.  This mode of learning only engages two senses.  Three if you count the soreness in your butt from all the sitting.
  3. Computers do not let students feel mathematics instinctively.  Our instincts are not wired for computer simulations or moving sliders with a mouse.  Our instincts are wired for dealing with the tactile world.  To teach surface area, let the students count the tiles on the floor.  Let them see what a square foot looks like.  To teach linear functions, let the students walk down the hallway and make distance and time measurements.  To teach surface area, let the students paint a box and see how much paint they use.
  4. Don't use programming to teach elementary mathematics.  This is adding a layer of difficulty and abstraction on top of a difficult subject.  I know that I would learn well using this technique, but I also know I am rare in this learning style.
  5. It is not true that all calculations have been done by hand except in the last few decades.  My abacus and slide rule want to know what you meant by this, Conrad.
I don't disagree with Wolfram that there is a problem with how mathematics has been taught in the past.  I am concerned by anybody who claims there is a single solution to the problem.  Computers have a part in the mathematics curriculum, but they must not upstage the rest of the valid learning techniques.