
Re: Essay: The Future of High School Math
Posted:
Dec 12, 2013 5:46 PM



On 12/12/2013 10:53 AM, Robert Hansen wrote: > On Dec 12, 2013, at 12:58 PM, Gary Tupper <gtupper@peda.com > <mailto:gtupper@peda.com>> wrote: > >> If we limit a math education to mastery of various algorithms, then I >> believe we seriously shortchange students. If math is reduced to >> training & memorization, then what advantage is there to learning >> math versus Biology or History. I don't claim that other subjects are >> bereft of analysis, but math has the advantage that such "figuring" >> can take place at a much earlier age. Rather than present a class >> with a 12 X 12 table to memorize  even speedtest, why not provide >> an environment where many students could 'discover' that an even X an >> integer is even; that an odd X odd is odd; that numbers can be >> multiplied in any order etc  leading into the table memorization. > > Show me a text book, just one, that limits math education to mastery > of various algorithms. The problem lies in the old adage "Teach them what we test them on". Not texts. > > And ?analysis? doesn?t take place at an early age. The kid grows into > it, as they acquire the necessary substance along the way to support > analysis. You mean well, but you need to teach kids all the way > through. Odd and even mean nothing if you don?t also know how to multiply. I was thinking simply of rearranging a 3 X 4 set of tiles to 4 X 3 and noting that there is no need to add or subtract tiles. (Of course I mean well!  as do you yourself;) > There isn?t any frame of reference. How are kids supposed to > experience that multiplication is commutative if they can?t multiply > in the first place? Can a 5X7 set of tiles be rearranged to a 7Xn set? Can rows and columns always be switched? > And you don?t want the dialog to stop dead in its tracks because the > student has to stop the precious *thinking* you are after and fumble > with a simple multiplication fact. I guess I believe that multiplication can be understood prior to knowledge of specific products. Or, put another way, 7X3 is the same as 3X7 since multiplication is commutative. (Rather than say, since 3X7 and 7X3 are both 21, then multiplication is commutative) > > Take reading for example. In the beginning it is all phonics and > decoding. The brain is completely occupied with decoding. Only and > until that becomes a background task, entirely without conscious > thought, does the child actually read. It?s the same with mathematics. It's rarely necessary in a discussion of this sort to use analogies. Tends to muddy the waters. > > There is no philosopher?s stone. And that isn?t a bad thing. Figuring > that out is actually a very good thing. Profound! > > Bob Hansen Gary Tupper

