Let me make a 'controversial' statement and then ask a question.
What if I said something "We Learn All the Math We Need For Learning Mathematics Beyond Sixth Grade During and Before 6th Grade." It seems to me that if ordinary life beyond 6th grade is relatively math free for many a particular person - say Joe - then Joe has indeed learned, most likely, all the mathematics he needs for the ordinary life. However, if - say Susie - plans on doing a bit of physics that requires a bit of calculus then Susie has some math learning to do after 6th and that math learning has, in some reasonably consequential fashion, some critical groundings in grades 6th and prior.
Okay, here is my question. Forgetting about the silly math wars and sillier politics, and assuming that indeed those sixth years are somewhat critical, why do we as mathematics educators - I'm talking about the research community and us higher education types - focus so much our attention on the secondary years? If I was building a fourteen story highrise and skimped on the first six floors, things would be problematic indeed. Is it because we think secondary teachers can fix students who struggle through those six years? Is it because we don't really care and it is survival of the 'fittest'? Is it because we have, in a sense, dumbed down the elementary school mathematics education curriculum to the extent that elementary school teachers, in their collegiate years, come away unsure and ill prepared and we, in effectively a vicious cycle, write them off?
On Jan 14, 2013, at 12:04 PM, Richard Hake wrote:
> Some subscribers to Math-Learn might be interested in a recent post > "Do We Learn All the Math We Need For Ordinary Life Before 5th > Grade?" [Hake (2013)]. The abstract reads: > > ******************************************* > ABSTRACT: In response to my post "Einstein on Testing" [Hake (2013)] > at <http://bit.ly/UHjqET> the following lively exchange was recorded > on the archives <http://yhoo.it/iNTxrH> of EDDRA2 [non-subscribers > may have to set up a "Yahoo account" as instructed at > <http://yhoo.it/iNTxrH>]: > > a. Literature major and Standardista-basher Susan Ohanian > <http://www.susanohanian.org/> stated that she (paraphrasing) "never > seemed to gain any insight from solving the calculus problems in > Courant's text, which struck her then as plodding and now as without > meaning." > > b. Susan Harman then opined (my CAPS) "WE LEARN ALL THE MATH WE NEED > FOR ORDINARY LIFE BEFORE 5TH GRADE." > > c. Guy Brandenberg countered by calling attention to David > Berlinski's "Tour of the Calculus" <http://amzn.to/11sZIUv> whose > publisher states: "Were it not for the calculus, mathematicians would > have no way to describe the acceleration of a motorcycle or the > effect of gravity on thrown balls and distant planets, or to prove > that a man could cross a room and eventually touch the opposite wall." > > d. And Susan Ramlo made the point that students in her algebra-based > physics class "almost always make a comment about how suddenly . . > .[[after exposure to the *real-world* of physics]]. . . much more of > calculus makes sense." > > With regard to Harman's opinion that "We Learn All the Math We Need > For Ordinary Life Before 5th Grade," basic to "ordinary life" is > motion and change, requiring the rudiments of calculus for proper > understanding (see the Bartlett signature quote). > > And I agree with Ramlo's point about students' better understanding > calculus after exposure to the *real world* of physics. In > "Interactive-engagement methods in introductory mechanics courses" at > <http://bit.ly/aH2JQN> I wrote: "the term 'substantive > non-calculus-based mechanics course' is an oxymoron." > *************************************************** > > To access the complete 13 kB post please click on <http://bit.ly/10sYmKl>. > > Richard Hake, Emeritus Professor of Physics, Indiana University > Links to Articles: <http://bit.ly/a6M5y0> > Links to Socratic Dialogue Inducing (SDI) Labs: <http://bit.ly/9nGd3M> > Academia: <http://bit.ly/a8ixxm> > Blog: <http://bit.ly/9yGsXh> > GooglePlus: <http://bit.ly/KwZ6mE> > > "The greatest shortcoming of the human race is our inability to > understand exponential change." > - Albert Bartlett <http://bit.ly/VpN2pm> [I have taken the > liberty of substituting > "exponential change" for Bartlett's more esoteric "the > exponential function."] > > REFERENCES [URL shortened by <http://bit.ly/> and accessed on 13 Jan 2013.] > Hake, R.R. 2013."Do We Learn All the Math We Need For Ordinary Life > Before 5th Grade?" online on the OPEN! AERA-L archives at > <http://bit.ly/10sYmKl>. Post of 13 Jan 2013 16:52:01-0800 to AERA-L > and Net-Gold. The abstract and link to the complete post are being > transmitted to several discussion lists and are also on my blog > "Hake'sEdStuff" at <http://bit.ly/RQkucu> with a provision for > comments. > > [Non-text portions of this message have been removed] > > > > ------------------------------------ > > Yahoo! Groups Links > > >