Subject: Re: [MATHEDCC] Assessment
From: Martha Haehl (haehl@kcmetro.cc.mo.us)
Date: Sat Feb 12 2000 - 19:08:17 EST
By the way, to get the idea why the decimal is moved and how far, I have
students round to one or two significant digits then multiply to estimate
the result. When the first significant digit is left of the decimal place,
such estimation really helps a student understand decimal placement.
For example, do the following WITHOUT A CALCULATOR.
1. 3.57 x 2.89 = ____ Round each factor and calculate the estimated
product_____
2. 78.03 x 1.004 = ___ Round each factor and calculate the estimated
product_____
3. 14.93 / 7 = _____ Round the divisor and dividend and estimate the
product_____
4. 14.93 / 0.7 = _____ Round the divisor and dividend and estimate the
product_____
etc.
Then in a follow-up activity, I have them use the calculator as tool to help
develop number sense and the placement of decimals. In each of the
following, I allow one student (the calculator expert for the day) to have a
calculator while the other students put theirs away. The instructions to
the class are to round each of the following to 1 or 2 significant digits to
estimate the product or quotient. I call on students to give me their
estimate which I write on the board or on an transparancy. Then the
calculator expert gives me the exact product (or approximate to x number of
decimal places quotient) and see how close the estimate is to the exact
product.
1. 147.0987 x 3.00987 = _____ Rounded and estimated answer = ______
2. 29.285 / 5.09878 = _____ Rounded and estimated answer =
______
3. 2.705 / 0.0037 = _______ Rounded and estimated answer = ______
etc.
Martha
----- Original Message -----
From: Stefan Baratto <sbaratto@earthlink.net>
To: 'Martha Haehl' <haehl@kcmetro.cc.mo.us>; David Beach
<DavidB@labette.cc.ks.us>; 'Bob Leibman' <bleibman@io.com>
Cc: <mathedcc@archives.math.utk.edu>
Sent: Friday, February 11, 2000 6:57 PM
Subject: RE: [MATHEDCC] Assessment
> Martha has hit the nail on the head.
>
> I'd like to add slightly more to her statement. When asked to multiply
two
> decimal numbers, nearly every student in an Intro to Algebra course can do
> this successfully (as long as the second one has one digit). For example,
> 8.6 * 0.2; they do the multiplication and get 172 and move the decimal two
> places over to get 1.72 nearly every time.
>
> I have yet to meet a (non-math major) college student (through Calculus,
at
> least) who knows, or can think through the question, why do you move the
> decimal over?
>
> The calculator isn't the problem.
>
> Stefan Baratto, Chair/Faculty
> Department of Mathematics & Science
> York County Technical College
>
> sbaratto@yctc.net
> (207) 646-9282 x 214
>
> On Wednesday, February 09, 2000 6:06 PM, Martha Haehl
> [SMTP:haehl@kcmetro.cc.mo.us] wrote:
> > O.K., I just had to jump in. The biggest fraud is not the use of a
> > calculator. It is the failure to teach students to think. Teachers who
> > make students write 1x2=2, 2x2=4, 3x2=6, etc. for 100 times and call
that
> > teaching are just as guilty of dumbing down education as teachers who
> say,
> > "Here's how to multiply 3 times 2. First punch in 3 then the times key
> and
> > the 2 key." Today as well as yesterday, there are teachers who
challenge
> > their students to wrestle with mathematical concepts and real
> applications
> > as well as learn basic skills, and there are those who think the
ultimate
> in
> > education, particularly in the lower levels, is rote memory.
Calculators
> in
> > the lower levels can enhance learning (while students learn to think) or
> > they can be just another rote memory educational tool. The culprit is
> not
> > the calculator, it is the lack of expectation that a student can and
will
> > think, and interpret information and results.
> >
> > I require my Basic Math students to have and use calculators. However,
> last
> > semester, I gave 11 skills tests. On 8 of those students could not use
> > calculators. On the ones where they could use calculators, they were
> > getting a decimal approximation to the hypotenuse of a right triangle,
or
> > the circumference of a circle, or other problems where expressing the
> answer
> > in decimal form makes more visual sense. (What carpenter ever measures
> and
> > cuts a board to the square root of 7 feet?) Their answers had better
> match
> > what they determine makes sense from measurements and drawings.
> >
> > Martha
> > ----- Original Message -----
> > From: David Beach <DavidB@labette.cc.ks.us>
> > To: 'Bob Leibman' <bleibman@io.com>
> > Cc: <mathedcc@archives.math.utk.edu>
> > Sent: Wednesday, February 09, 2000 9:18 AM
> > Subject: RE: [MATHEDCC] Assessment
> >
> >
> > > Bob and Dorrit:
> > >
> > > My thought is that what they (k-12 ed) have accomplished is to help
> create
> > > students who can't think and who believe god is machine and machine is
> > god,
> > > who can't estimate, can't measure, and cannot think abstractly about
> > > mathematics.
> > >
> > > The idea to keep pushing calculators down to lower and lower grades is
> one
> > > of the largest educational frauds ever perpertrated upon the american
> > > public.
> > >
> > > DavidBeach
> > > Labette Community College
> > >
> > > > ----------
> > > > From: Bob Leibman[SMTP:bleibman@io.com]
> > > > Sent: Tuesday, February 08, 2000 9:13 PM
> > > > To: Alton Amidon; mathedcc@archives.math.utk.edu;
> > > > DOhallaron@CHUCK.STCHAS.EDU; castagna_p@hotmail.com
> > > > Subject: Re: [MATHEDCC] Assessment
> > > >
> > > > At 1:06 PM -0500 2/8/00, Alton Amidon wrote:
> > > > >And the problem goes further. Our Community College graduates going
> on
> > to
> > > > >a four-year college or university or often restricted in calculator
> use
> > > > in
> > > > >higher level Mathematics, Science, and Engineering courses.
> > > > >
> > > > >Al
> > > > >
> > > > >Alton Amidon
> > > > >P.O. Box 185
> > > > >5049 Highway 306 South
> > > > >Grantsboro NC 28529
> > > > >252-249-1851
> > > > >FAX 252-249-2377
> > > > >
> > > > >>>> "Paula >>>
> > > > >Dorrit:
> > > > >
> > > > >This is one battle looming that I have not tackled. The high
> schools
> > > > tell
> > > > >us that we are undoing much of what they have accomplished if we do
> not
> > > > allow
> > > > >students to use scientific calculators on our placement tests. I
> > concur,
> > > > but
> > > > >have not mounted the energy to fight this particular battle.
> > > > >
> > > > >Paula
> > > > >
> > > > >
> > > >
> >
> >*************************************************************************
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> > > >
> > > > I know that I am going to sound like a reactionary, but I am
> wondering
> > > > just
> > > > what it is that those who use calculators in their teaching think
> that
> > > > they
> > > > have done and, therefore, what it is the those people at the next
> level
> > > > are
> > > > "undoing."
> > > >
> > > > If the calculator is used to allow the student to learn through
> > > > exploration
> > > > and thus make the concepts being studied "their own" this is great.
> If
> > it
> > > > permits them to handle a greater variety of problems without the
> > > > restrictions of being limited to those which are easily done by
means
> of
> > > > the algebra which we teach, that too is great.
> > > >
> > > > I wonder, however, why, at the end of the course, that same student
> > should
> > > > not be expected to do the simpler problems for which calculators are
> not
> > > > necessary with the same ease as those who did not have the benefit
of
> > > > learning with a calculator.
> > > >
> > > > I just noticed that the original comment was referring to scientific
> > > > calculators rather than graphing calculators, but I think the same
> idea
> > > > holds - the computations involved would presumably be easy enough to
> > > > reasonably expect hand calculation - or the answers would be such
> that a
> > > > reasonable estimate should make the correct answer clear.
> > > >
> > > > I say this on a day in which a reasonably bright student in
> Elementary
> > > > Algebra could not tell me what 6% of $100 is, could not multiply
> > > > 0.06($100)
> > > > because she didn't have her calculator - and wouldn't even try.
> > > >
> > > > Bob Leibman
> > > > Austin Community College
> > > >
> > > >
> > > >
> > > >
> > > >
> >
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