Responding to the first sentence of Professor Wayne Bishop's rejoinder to James Elander: QUOTE > Elander's response represents (one of) the problems > associated with > the New New Math focus on mathematics through > applications rather > than traditional (cookbook if you like) applications > of mathematics > having been developed (lots more of mixed variety are > usually needed > - - see Singapore or Saxon) with the emphasis on the > general > applicability of the mathematics having been > presented. UNQUOTE (The whole of Wayne Bishop's post is pasted below my signature, for ready reference).
I do gather that Professor Bishop disapproves of James Elander's approach, but that's about it.
After having struggled with (and having failed to understand) that astounding first sentence quoted above, I decided it would be more profitable for me to try to re-read "Finnegan's Wake", by James Joyce, as representing something more readily accessible, and certainly more enjoyable. (I have not tried to read anything beyond that first sentence).
Suggestion: BEFORE we do any math (or criticisms of math approaches), we should try to learn to write clearly and understandably.
GSC Wayne Bishop posted Feb 27, 2013 12:51 PM: > Elander's response represents (one of) the problems > associated with > the New New Math focus on mathematics through > applications rather > than traditional (cookbook if you like) applications > of mathematics > having been developed (lots more of mixed variety are > usually needed > - - see Singapore or Saxon) with the emphasis on the > general > applicability of the mathematics having been > presented. Often, they > are ill-posed, a no-no in mathematics. In the real > world, > applications are usually such that at least 3/4 of > the problem is > getting enough communication out of those with the > problem to > formulate some kind of mathematical model that > approximates being > good enough but that is an inappropriate setting for > the learning of > mathematics. In fact, coming to such problems with a > broad knowledge > of mathematics (not necessarily deep; if one knows > where to look, > that part is not hard) is necessary to be a real > world mathematics > problem solver. Since school is a zero-sum game, > learning the > appropriate mathematics to be prepared to learn > enough more > mathematics to have that broad knowledge is essential > for being a > good real-world problem solver and there is not > enough time to waste > on the "real world" problems done there. Not nearly > enough > mathematics is known to address anything but the most > mathematically > trivial of problems; a common one is: > "You have n-dollars to spend. Plan a > . Plan a three-week trip to Europe." > "Your group" is supposed to find routes, use the > Internet to locate > and price places to stay, not-to-miss restaurants, > and the > like. Lots of time wasted on 5th or 6th grade > mathematics at the > expense of moving forward competently. It is a time > trade-off from > which only students with exceptional mathematics > potential will ever > escape and even most of them never do. > > Wayne > > At 10:10 AM 2/25/2013, James Elander wrote: > >Depends on how you define winners, could be 5 races > and top three times > >Yes to the assumption stated. > >On Sun, Feb 24, 2013 at 7:46 PM, Richard Strausz > ><Richard.Strausz@farmington.k12.mi.us> wrote: > > >> There are 25 bicyclists and just 5 bicycles. Of > all > > >> these we need to find best 3 cyclists. How many > races > > >> should be held to determine top three winners > and > > >> why? > > >> http://www.basiccalculator.org > > > > > > Do we assume that all the bicycles are > equivalent? > > > > > > > >- -- > >Jim > > > >Jim has 5 new CDs on the market. > > CD1:TGIF MATH (A 100+ activities to make a hectic > math > > period on days like prior to homecoming > into an rewarding > > learning day.) > > CD2: EVERYDAY DECISION MAKING VIA GEOMETRY > > ESSENTIALS (A Logical development of > the essentials > > of PL. & Solid Geometry and applying it > to decision > > making.) > > CD3: EVERYDAY DECISION MAKING VIA MATHEMATICAL > > BRIDGES FOR A BETTER FUTURE (Liberal Art > > "bridges" emphasizing critical > thinking.) > > CD4: EVERYDAY DECISION MAKING FOR A BETTER > > CAREER (Mathematical topics needed for > skills and for > > better decisions) > > CD5: BASIC HIGH SCHOOL MATH REVIEW (Review for > SAT, > > ACT or other tests with Dec ision > Making skills) > > For more info: > > > > > > > > > > > > > http://sites.google.com/site/mathfordecisionmaking/