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Re: 4 function calculators
Posted:
Feb 9, 2013 1:38 AM
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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 math-distress ... 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 self-images, their scholastic
self-confidence, and their personal self-esteem. They have been led to
believe that they have "non-mathematical minds" and could not survive
math-dependent college curricula.
One remedy begins with providing them with blank table-templates ... and
challenging them to *conclude* and *publish* all of those theorems into the
tables.
Their rewards are receipts of pocket-size, laminated cards with the tables
pre-printed,
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
math-distress ... 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
long-division algorithm ... as a personally concluded, common-sensible
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 self-assessment. 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 core-curricular
mathematics fully common-sensible to their students. Unfortunately, few
school/college teachers have been educated in the common-sensibility of
core-curricular 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
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