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Re: Martin Bickman On The Needless War Between Traditionalists And Progressives
Posted:
Sep 1, 2012 5:41 AM
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Robert:
I very much like your time table, and my reasons are below. But first, my response to your request.
>From the time a child leaves the crib, there are many humanly natural paths of personal growth ... depending on the child's environmental experiences. Curricular educators traditionally presume that most children, as they enter kindergarten, are mathematically "about equal" ... (absurd, of course). Curriculum developers do so because of the tradition of trying to educate "classes" of students.
Regardless of what "ground zero" is used as a launch pad (think rockets) the conceivable progress-paths that leave from there constitute a very complex maze of interwoven potential routes. But every one of those progress-paths conforms to the laws of nature. Despite frequent conceptual "leaps, there are no "jump" or "oscillation" or "isolated" or "essential" discontinuities.
So, mathematics instructology looks at the lattice of alternative "conceivable states" (a la the state-transition theory of knowledge-spaces) ... and at the alternative growth paths for climbing that lattice. The search cannot be for which path is "best for all" ... but to discern what works (or works best) for whom.
Traditionally, each curriculum prescribes a single ("linear") path (from a presumed 0-state). Unfortunately, the prevailing curriculum-prescribed paths for "the rockets" to follow so badly ignore the laws of nature that no student comes even close to "following" the prescribed path, as such ... although some manage to "keep up" in some senses (at least for a while). Today, computers are providing some alternative-paths curricula ... which likewise are presently ignoring the natural laws of human psychomathematics.
So, I cannot propose a progress-path that "should" be used, but it is obvious that the present prescriptions are badly failing. What I can proffer, instead, is a growing compendium of Mathematics As Common Sense ^TM improvements over prevailing curricula, some of which might startle conservatives. [For example, normal kindergartners can easily begin to learn about fractions or algebra ... but not the kinds of "fractions" or "algebra" that presently are taught in American schools.]
That brings me back to your time table. Similar "scope and sequence charts" have long been used by authors and publishers of school-mathematics curricula, for designing/describing their respective works. But yours appears to represent the presently "norm" curriculum ... what it actually is, rather than what it "should"/could become. I suspect that some publishers have used such global summaries as basis for composing their own works ... and that the same is true of authors of the "Common Core Standards" in mathematics. But their cross-curricula analyses are not being widely shared.
Bob, you have disclosed the potentials for using such tables as an operations-research tool for discerning the actual "state of the nation" regarding the contents of core-curricular mathematics. Assuming that your table is a roughly accurate description of "the American curriculum", I can conceive of each of your bars becoming a link to another, similar table the airs the underlining details ... some of which would be links to still other ....
Such operations-analytic trees could provide invaluable pictures of "the status quo" and of the CCSS-math ... especially for discerning their flaws and the potentials for improving them.
Of course, I urge you and others to strongly indulge in that kind of research. It could provide much greater service to mankind than do this email-list's persistent debates which serve no purpose.
Cordially,
Clyde
From: Robert Hansen
Sent: Friday, August 31, 2012 8:42 AM
To: Clyde Greeno @ MALEI
Cc: kirby urner ; Richard Hake ; math-teach@mathforum.org
Subject: Re: Martin Bickman On The Needless War Between Traditionalists And Progressives
On Aug 31, 2012, at 4:10 AM, Clyde Greeno @ MALEI <greeno@malei.org> wrote:
When it becomes well known (hopefully very soon) that the prevailing curriculum's "sequence and order" are neither natural nor healthy ... and that the major reason why so few are "good at it" is because of how badly it is sequenced and ordered (it was designed by guesswork) ... and that a drastic reorganization produces dramatically improved productivity ... might we then ask what causes curricular myopia?
Show us the order you think it should be in Clyde. Attached is my rough ordering of K through 6 topics. I am not claiming it to be the bible, just a working document.
Bob Hansen
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