On Fri, Jul 4, 2014 at 8:19 AM, Robert Hansen <email@example.com> wrote:
<< SNIP >>
> I am not against the use of activities to help students get it. That is > what the 25% is for. I am against replacing the 75% with those activities > because the 75% is the material we are trying to get. But many teachers > don?t get this and they replace the material with activities and those > students will never get it because they are not even being exposed to what > it is that they are supposed to get in the first place. > > Bob Hansen >
I think we've agreed though that the 25% is not happening. "Activities" such as coloring and roaming about in nature collecting pine cones sounds like watered down 75%, as you suggest, but that doesn't make it part of the 25%.
An appreciation for the role of mathematics in everyday life would require analysis of institutions: how does a supermarket work; a casino; a bank.
What elementary school math class shows depositors putting the cash through window A and getting interest rate y%, while the bank loans that same cash out through window B getting interest rate z% with z% > y%. Lets "do the math" on the bank's balance sheet.
If that's not high level enough, lets talk about the ships bringing ice from North American lakes and Norway, to markets in Britain. Factory ice (swimming pool sized baths of ammonia in which ice slab moldings were submerged) would come later.
Now lets talk about spherical trigonometry and navigation and how those ships got around. Lots of exercises / story problems may be developed around this material, but at least we're (a) talking about institutions and inventions (b) looking at generalized principles re hot, cold, sphere shape (c) investigating the evolution of humans in their ecosystem context.
That's more what I mean by the 25%. Gotta have it. If it's all just exercises, exercises, exercises, then I think the students are just being abused.
The problem is mathematics is safely apolitical and purged of substantive STEM content precisely to keep it a "safe subject". No one wants the hassle of students learning too much, knowing too much, about the so-called "real world".
The more you're into mathematics, the more you might be a threat to the powers that be, and the more you're encouraged to leave the "real world" in favor of this other place called the "Platonic Realm" which you're supposed to love more and express your loyalties toward.
If you're a stereotypical "mathematician" then the "real world" is something to distance oneself from and get snobby about and leave to the low life engineers. These inculcated attitudes I think sicken our civilization. They trace to a weak 25% -- deliberately weak would be my contention.
Math pedagogy has everything to do with instilling compliance and a grin-and-bear-it attitude to assigned work (homework). Math pedagogy is not about informing students about how the world works, even though those workings are intensely mathematical. That kind of knowledge is too dangerous to share widely.