On Thu, Sep 27, 2012 at 9:49 PM, Wayne Bishop <email@example.com> wrote: > So far, we have 3 people with posts strongly supporting Haim's long-standing > challenge >
There are many others who do and who would have a different take on things with respect to whether a pedagogical question is open or whether it is an interesting question.
I would say that many would disagree with you on the point I made once the associated points would be actually brought to their attention.
We teach teachers to teach the adding and subtracting of fractions (and this includes rational functions in algebra) using the least common denominator with a method so clunky, long, and complicated that it cannot be written elegantly and concisely as a single equation. We do not do this with respect to the teaching of the multiplying and dividing of fractions - they are taught with methods that are elegant and concise enough to be written as single equations. Imagine how much worse the outcome would be compared to the present situation if we taught students the multiplying or dividing of fractions with methods that are so clunky, long, and complicated that they cannot be written elegantly and concisely as a single equation.
And here's another question that many would find to be an open and interesting one: Why do we teach algebra teachers to teach solving for an unknown *only* with a method that is long and complicated when we could teach students a method that makes things so much quicker and easier for them to solve for an unknown. An example of what I'm talking about is that we could teach them to view equalities a certain way such that they can solve for x in the equality ab/(cd) = ef/(gx) in just one step or the equality ab/(cd) = ef/(g[x-h]) in just two steps, but we don't - we instead teach them to use methods that take many steps.
One wonders why you seem to be in favor of teaching *only* methods on the topics of fractions and algebra that make things much harder for students when we could be teaching them methods that would make things so much easier for so many of them.
Your attitude as a teacher of teachers-to-be is precisely the attitude of resistance to change - even change for the better - I have run into from some of those you would call part of what you call the education mafia. That would make you part of this mafia you criticize, no?