Chad Clark's Open Journal : 2008-04-28

1) Teach math using symbols.  Later apply it to real life.

I thought the point of word problems in math class was to practice
determining what information about a problem is needed and how to use that
information with math to solve the problem.

There is one study with a bit of evidence that many students understand how
to apply math to problems better if they learn the math concepts using
symbols instead of word problems.

Maybe this research does not devalue word problems but indicates that word
problems should not be used until after the math concepts are understood.

This Scientific American article reads:

  New research published in Science suggests that attempts by math teachers
  to make the subject easier to grasp by providing such practical examples
  may actually have made it tougher to learn.
  
  ...
  
  "The primary goal of learning math is this ability to transfer that
  mathematical knowledge," says study co-author Jennifer Kaminski, a
  researcher at O.S.U.'s Center for Cognitive Science. "Concrete examples
  might not be the best to promote transfer; they present a lot of
  extraneous information."
  
  For their study, Kaminski and her colleagues taught 80 students
  undergraduatesplit into four groups 20-persona new mathematical system
  (based on several simple arithmetic concepts) in different ways.
  
  ...
  
  The researchers then tested their grasp of the concept by seeing how well
  they could apply it to an unrelated situation, in this case a children's
  game. The results: students who learned using symbols on average scored
  80 percent; the others scored between 40 and 50 percent, according to
  Kaminski.
  
  ...
  
  Keith Holyoak, a psychologist at the University of California, Los
  Angeles, says, however, that the findings are not that black and white,
  noting that in some instances the students who learned by example scored
  as high or better than the symbols-only bunch. "If they're trying to make
  the conclusion that abstract is always better than concrete training, I
  would disagree," he says. "Good problem solvers or better abstracters are
  better at dropping away what is superficial."

2) Growth in PhD program enrollment in Canada.

The Canadian Press article reads:

  ... enrolment in doctoral programs grew by about seven per cent a year
  between 2000 and 2004
  
  ... over three-quarters of the 2004-05 graduates completed studies in a
  science or engineering field; the most popular was biological sciences.
  
  Survey data also shows a more equitable distribution between the sexes
  among doctoral grads that year with 46 per cent of the degrees going to
  women, up from 43 per cent the previous year.