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 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.
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/