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Topic: [ap-calculus] new multiplation/division [When to use technology?]
Replies: 1   Last Post: Jan 1, 2008 10:47 AM

 A Cron Posts: 155 From: South Texas Registered: 7/15/07
Re: [ap-calculus] new multiplation/division [When to use technology?]
Posted: Jan 1, 2008 10:47 AM

I have found after 37 years that rote knowledge of the multiplication
tables through the 16s, the first 25 perfect squares, and the first 10
cubes makes much of the so called contrived hand calculations given in
textbooks mental arithmetic especially once a student passes into grades
above the 6th grade. Also, this level of knowledge makes the so called
drudgery of long division not so difficult. The algorithms that the
weather person have valid mathematical reasons for working, but those
textbooks do not teach them. Nor is there significant emphasis in the
teaching of the basic arithmetic properties of commutativity,
associativity, and distributivity. Properties needed in Algebra and
Geometry, this lack of mathematical understanding seems to be the real
problem.

As a student, I was not exposed to the "New Math" of the mid-60's and by
the time I started teaching, it was no longer an emphasis in schools. I
did study it in pedagogy classes in graduate school as I recall there
were two different trends used in the 60s. The methods presented in the
video is just another set of methods that have come from the NCTM
Standards efforts to dumb down the need of rote learning in the
elementary schools. Calculators are a tool to be used once basic skills
are conquered. I tell my students that calculators are for word
problems; problems that are contrived for practice of arithmetic skills
need to be practiced without a calculator. I would not assign columnar
addition of 4-digit numbers of length greater than 3 without a
calculator, multiplication problems with products greater than 1000, and
division with dividends greater that 625. Word problems that are not
contrived to be arithmetic practice and other problems, I have no
problem with a student using a calculator. Some word problems are
contrived to teach how to setup an arithmetic problem to be solved; here
is where a calculator should be used.

The biggest problem that I have is the students that think that every
problem requires a calculator to solve it, but the use of a calculator
is a detriment to solving the problem. Other problems where the
calculator is needed to solve, the student wants to use the calculator
to early in the process and miss the problem completely. There is a
skill need to decide when to use technology. This is one reason that the
AP exam and other College Board exams have a non-calculator sections.

Tony

Jon Stark wrote:
>
> There could be immense value in dropping emphasis on boring
> repetitious hand calculations, and it might well be true that too much
> valuable class time is wasted on such things. The question unanswered
> in the snippets we see is whether what replaces that drudgery really
> contributes to mathematical depth of understanding and/or power to be
> used in application. If students come better prepared to think
> logically, to do reality checks on their work, to see new approaches
> to problem solving, to understand the assumptions behind their work,
> to find interest and utility in mathematics, to show creativity and/or
> courage and/or stamina and/or curiosity, then it could be a good
> trade-off. I haven't yet seen the benefit side in the students who
> come my way, but the loss of computational skill is apparent, so this
> juror is still deliberating.
>

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Course related websites:
http://apcentral.collegeboard.com/calculusab
http://apcentral.collegeboard.com/calculusbc