carl bogardus

The message below is being cross-posted from LogoForum.

Hi Brian,
*
I appreciate your comments -- often I bounce ideas off this board, its
the only place I know that where most people think before posting.
*
Actually, I don't mean using a pencil and paper -- I meant mentally.
Basic operations should be mental to a large extent. Unfortunately,
most students have so little experience with estimation using mental
math that they cannot determine if an answer is close or not -- they
could get it wrong no matter what method they used to calculate.
*
What I meant by the "sorta" quote is that the question is more
important than the answer -- If one cannot determine the question,
(mathematically), how do you figure the answer?
*
For example, I am covering a surface w/fabric, the process I am using
requires one inch of overlap of the glue joint. If the bottom surface
wraps around a tube 5/8"*OD, how far do I have to overlap the top*to
make sure I get the 1" overlap. So I have to figure that the fabric of
the top surface will wrap 1/2 the circumference of the tubing -- is
that enough to make the 1" overlap? Then I can develop the math problem
and either figure it on calculator or paper, (yes, I know there is an
easier way of approximating the answer).
*
IMHO, I don't think kids learn much by memorizing basic facts if they
do not understand the background of the math processes. I was taught
these so long ago I barely remember anything about it.
*
No, I don't want to go back to DOS, neither do I want to learn more
Unix commands, (learned using email and surfing the Internet using my
C64).
*
Carl

The message below is being cross-posted from comp.lang.logo.* Please
reply to LogoForum@yahoogroups.com or (Brian Harvey)
<bh@cs.berkeley.edu>.
Carl Bogardus <Use-Author-Address-Header@[127.1]> writes:

Eh?

Pencil and paper arithmetic *also* only gives you the answer.* The only
difference is that it takes longer, often it gives you the *wrong*
answer[*], and it frustrates kids.

I especially don't see how you can use the phrase "frees a person from
these basic operations" about pencil and paper!* It is precisely the
calculator that frees us from arithmetic operations.

The higher level reasoning -- *no matter how you do the arithmetic* --
is
in knowing what arithmetic to do.* And in understanding what the
operators
actually mean.

I think people get confused about this because the same teachers teach
both
pencil-and-paper arithmetic and what-the-operators-mean, and they think
those
are the same activity.* (Whereas, with a calculator, there's hardly
anything
to *teach* about how to do the arithmetic.[**]) But this is a fallacy.
Teaching pencil-and-paper algorithms has nothing whatever to do with
teaching
what the operators mean.* The latter is taught, for example, by doing
word
problems, by drawing rectangles representing multiplications and
turning
them
90 degrees to illustrate why multiplication is commutative, by using
blocks to
illustrate place value, and so on.
[*]:* People who believe in torturing kids with arithmetic like to tell
horror
stories about kids getting ridiculous answers by asking a calculator
the
wrong
question.* But this is unfair; I have just as many horror stories about
kids
getting ridiculous answers doing pencil-and-paper arithmetic because
they ask
the same wrong question.* There is nothing about calculators or about
pencil
and paper that encourages a kid to ask the right or the wrong question.*
The
only difference is that with pencil and paper, you're quite likely to
get the
wrong answer *even if* you ask the right question, whereas that never
happens
with a calculator.

[**]:* Interestingly, I've never heard anyone argue that modern
computer
graphical interfaces prevent kids from understanding how to use
computers, and
that instead kids should use DOS commands to get a better
understanding.*
Yet
that argument is exactly analogous to the one about calculators versus
pencil
and paper -- the argument is that having a hard-to-learn interface
increases
understanding.

bh

Carl Bogardus <Use-Author-Address-Header@[127.1]> writes:


I agree about the question being more important than the answer. (Remember
Tom Lehrer being sarcastic about that in his "new math" song? "... five.
Well, six, actually, but the idea's the important thing.")

And I agree that making a rough ballpark mental estimate is a good habit to
get into. This requires understanding place value. Recently in my fifth
grade, the teacher read the kids a book about large numbers that included the
remark that it would take 23 days to count out loud to a million. Then she
asked the class how long to count to a billion, and sure enough, one of the
kids said 46 days.

But my point is that this kid, like the rest of the class, has been through
five years of arithmetic instruction, without demolishing that wrong idea.
If she'd had a calculator, and those five years had been spent on ideas
instead of mechanisms, would she be better off? I don't know, but it seems
likely to me.

mike_doyle_(mícheál_Ó_dúill)

The message below is being cross-posted from LogoForum.

Please allow me to add another angle to Brian's comments on mental
arithmetic. We are a technological species - but not the only species
that
ever used language. We use technology to do mundane tasks so our brains
can
do more important things. Arithmetical computation is a mundane task.
Estimation, on the other hand, is often mission-critical. Many
engineering
innovators, e.g. Richard Trevithick, could not do 'school sums' but had
mental techniques to get things right. Now we have the calculator,
please,
let it get the sums correct whilst the kids get round to doing the
thinking.
Mícheál

LogoForum messages are archived at:
http://groups.yahoo.com/group/LogoForum

mike_doyle_(mícheál_Ó_dúill)

The message below is being cross-posted from LogoForum.

Brian
I think you missed a trick on
Carl Bogardus' comments:
"For example, I am covering a surface w/fabric, the process I am using
requires one inch of overlap of the glue joint. If the bottom surface
wraps
around a tube 5/8" OD, how far do I have to overlap the top to make
sure I
get the 1" overlap. So I have to figure that the fabric of the top
surface
will wrap 1/2 the circumference of the tubing -- is that enough to make
the
1" overlap? Then I can develop the math problem and either figure it on
calculator or paper, (yes, I know there is an easier way of
approximating
the answer)."

This looks like Papert's kitchen maths to me where, of course, you need
no
standard metric like 'inches' etc. The overlap is 'just the right
amount,'
which is about what wraps round the pipe? You estimate according to
properties. I do this all the time at home and in the garden. This is
thinking without numbers, even!

Mícheál