On Fri, Oct 5, 2012 at 9:39 AM, Haim <email@example.com> wrote: > Discussing your formula method for adding fractions with someone who mainly fears and loathes mathematics (a good characterization of most elementary school teachers) strikes me as the height of futility. >
Every adult that fears mathematics that I've shown the method to likes the method - it made things at least a little easier for them. One adult in particular, a sub with no more that college algebra level training, after I showed the method and its proof to her (the proof simply involves the identity x = (xm)/m with x being the written sum of the fractions and then distributing the top m and then recombining each addend term) told me that it was the first time in her life that she actually understood fraction addition explained to her and was amazed at how easy it could be going to to a single fraction from all those fractions to be added/subtracted. (As I said before, because it really does make it easy to go straight to one fraction from all those fractions to be added/subtracted, I like to introduce the method on three or more fractions to be added/subtracted, not just two. And this extra point: These elementary school teachers who fear mathematics are perfectly capable of following the steps of a simple proof when the steps are using what they already have shown they are capable to using - they like everyone who gets a degree in anything had to get though at least a college algebra course to get their undergraduate degrees.)
The non-adult students I've shown the method to - to the degree that they care enough to give an opinion - usually liked the method for the same reason - it makes going from a sum of fractions to a single fraction (after getting the LCD) easier.
That is, what I mean is that the more people have had problems in the past with fraction addition/subtraction and the more they cared enough to be willing to learn a new way of doing things to make things easier, the more they liked it once they learned it. This was especially true for those in algebra and above settings who wanted to make it easier when they had to add/subtract rational functions - or fractional forms in general in algebra.
But when I briefly taught middle school (teaching high school is much to be preferred) I was severely pressured by the principal to stop using the method and to use the usual way. Never mind the positive reaction I got from so many of my students who offered an opinion to me on the matter. I went to the union, showed the method - including proving it, but although they knew the method was utterly valid, they "suggested" to me that I should teach the usual way. This was because the union there was NEA - meaning that the union represented not just teachers but also people in administration including that principal. (How many times have I told you that in so many places these teacher unions are not true unions truly representing the grievances of labor - that they cannot be when they also represent management?)
And so here is my followup question:
Why are so many people - including such principals and including such as you - seem to have no interest at all in making skill performance easier and perhaps making things more understandable as well for those who need to have things made easier and more understandable?
Is it simply that they and you simply fear change?
Is it something else?
Yes, you will say that I ran into someone with power in what you call a mafia as evidence of its existence, that someone entrenched in ways of doing things was not going to allow anything beyond those entrenched ways of doing things, but I note that you in at least one sense are on the same side as this mafia you claim to be against: You both seem to have no interest at all in seeing those who need more help getting more help - you both seem to fear change or care more about something else than the welfare of the students or both.