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square roots
Posted:
Apr 24, 2000 1:33 PM
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Wayne Bishop wrote:
My thoughts follow this part of his message:
>
> The following exercises related to this skill are:
>
> 8. Estimate. Then use the square root table in Appendix B to
approximate:
> sqrt(0.003266 x 10^-18)
>
> 16. Simplify: 4sqrt(20,000)
>
> In Lesson 108, #6 emulates #8 above and #14 emulates #16.
>
> Et cetera until the ideas are cinched. Thank you, but I consider this
> to be primarily *conceptual* and exactly the level of conceptual and
> computational competence that I expect students to have coming into
the
> university. Do you disagree?
>
> Wayne.
I think I would agree that the students would achieve a level of
computational competence. But I would appreciate it if you could
clarify some things for me. You must have a copy of Saxon's book (or
your memory is way better than mine). Here's what I remember from the
lesson I alluded to in my earlier post: the discussion did start with
square roots of two and three digit numbers, but when numbers with more
digits were introduced, I recall the instruction went along these lines
(again, please correct me if I am mis-remembering).
To find, say, sqrt(500000000), the student was instructed to count the
number of zeros (in this case there are 8). So the square root will
have have 1 appended with half that number as a factor (i.e., 10000).
the other factor will be sqrt(5), so the sqrt(500000000) =
10000*sqrt(5). If the number of zeros is odd, say, sqrt(700000), then
take half of the largest even number of zeros (2 in this case is half of
4)) and append 1 with that number of zeros and multilply by the other
factor still in under the radical. So, sqrt(700000) = 100*sqrt(7).
I don't remember the book providing any rationale for taking half the
number of zeros to find a square root. If what I remember is correct, I
cannot call this a conceptual development - the book is simply providing
the student with a set of rules to be memorized and remembered.
Now, if I had been teaching this lesson (with or without a calculator),
I would've made darn sure the students understood where these rules were
coming from - maybe lots of teachers would. If that happened, then I
think I'd feel more comfortable with the "conceptual competenece" part
of your sentence. The teacher I observed that day back in 1985 shed no
light on it. She simply read the rules from the book. Given the "warm
body" criteria some school districts are forced to employ when it comes
to hiring math teachers, I wonder how many of those would be able to
fill in the gap left by the author.
--
Mark Klespis, PhD
Associate Professor of Mathematics
Sam Houston State University
Huntsville, TX 77341-2206
936.294.1577 - office
936.294.1882 - fax
http://www.shsu.edu/~mth_mlk
"Everyone has a photographic memory. Some don't have film."
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