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Re: 4 function calculators
Posted:
Feb 9, 2013 1:38 AM


Why teach arithmetic tables and algorithms to college students??? Certainly inexcusable on the basis of *scholastic* reasons ... but beneficial because that is the humane thing to do (if done in healthy ways). Done right, it is powerful *therapy* for mathdistress ... and is preparatory for effective mathematical parenting.
College students who do not already own "the tables" ... or the algorithms that apply those tables ... typically have floundered with arithmetic, for years. It has hurt their academic selfimages, their scholastic selfconfidence, and their personal selfesteem. They have been led to believe that they have "nonmathematical minds" and could not survive mathdependent college curricula.
One remedy begins with providing them with blank tabletemplates ... and challenging them to *conclude* and *publish* all of those theorems into the tables.
Their rewards are receipts of pocketsize, laminated cards with the tables preprinted, thereon ... to serve as "memory" cards that they can carry around and use. [For the tables, the cards often are handier to use than are calculators.] Of course, there are advantages to having quick access, mental memories ... but that is mathematically no more essential than is memorizing the full table of integrals.
The psychological impact is that the students then *know* that they created the tables, mathematically ... even if they never use those cards. Thereby, they are led toward perceiving that the doing of mathematics lies in the generation of knowledge ... rather than in memorizing and recalling facts which earlier have been concluded by others.
Even stronger therapy can be achieved by wisely using the algorithms of arithmetic.
The college student who does not already own, say, an algorithm for long division arrives with a history of prior failures to digest whatever algorithm was taught *at* him or her. The aversion already is seated. Any newly encountered difficulties with long division will worsen the mathdistress ... even if the student becomes (temporarily?) well trained to execute a sufficient algorithm, well.
However, it that student is instructively guided to personally *create* a longdivision algorithm ... as a personally concluded, commonsensible theorem ... perhaps the same algorithm that confounded him or her in past years, such a conquest of a longstanding enemy can have very beneficial effects. So resolving several previously confounding algorithms into personal common sense can result in a mathematical metamorphosis ... and in a greatly improved selfassessment. But it only works when the student internally constructs the theorem as personal common sense ... regardless of what instructional mode is used.
All that is needed is for teachers to know how to make corecurricular mathematics fully commonsensible to their students. Unfortunately, few school/college teachers have been educated in the commonsensibility of corecurricular mathematics. Fortunately, a glimmer of hope may be found in forthcoming Forums on the Mathematical Knowledge for Teachers' Education. [Information can be obtained from clinic@malei.org.]
Cordially, Clyde
  From: "Alain Schremmer" <schremmer.alain@gmail.com> Sent: Friday, February 08, 2013 6:04 PM To: <mathedcc@mathforum.org> Subject: Re: 4 function calculators
> > On Feb 8, 2013, at 6:48 PM, Phil Mahler wrote: > >> I don't see why we try to teach the "tables" and algorithms using the >> tables to college students, especially those with diagnosed learning >> disabilities. > > In the latter case, I don't see either. > > In the former case because it is a nice situation in which to see the > innards of an algorithm and their necessity. If I may quote myself, this > is what I did in the first half of > > <http://www.freemathtexts.org/Standalones/RBA/RBApdf/RBAchap18.pdf> > > Regards > schremmer > **************************************************************************** > * To post to the list: email mathedcc@mathforum.org * > * To unsubscribe, email the message "unsubscribe mathedcc" to > majordomo@mathforum.org * > * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * > **************************************************************************** **************************************************************************** * To post to the list: email mathedcc@mathforum.org * * To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.org * * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * ****************************************************************************



