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Re: weight vs. mass (was: Units and Conversions)



Unfortunately, these students did have arithmetic and fractions and ratios
in school even though they act as if they did not. This problem is not
quite unique to the community colleges. A quote from "Hispanic and Anglo
Students' Misconceptions in Mathematics. ERIC Digest."
Mestre, Jose (1989) http://ericae.net/edo/ED313192.HTM might be revealing.

-------------------------
Write an equation using the variables S and P to represent the following
statement: "There are six times as many students as professors at a certain
university." Use "S" for the number of students and "P" for the number of
professors.

The most common error in this problem (committed by about 35% of college
engineering majors ) is to write "6S = P." (The correct equation, of course,
is "S = 6P.")
-------------------------

Most engineering students enter the program with at least precal under their
belts, yet they have difficulty writing simple equations. Essentially math
and science teaching is failing to properly prepare students no matter what
level they are at. It really is irrelevant how knowing how many roots an
equation has if you can not write a correct equation to begin with. Some of
the examples Tina cites are the same as the ones in the short article by
Jose Mestre. Jose also provides some references to papers on effective
methods to overcome these problems.

There is evidence that part of the problem stems from teaching memorized
algorithms before students are ready to comprehend the operations. This is
the important idea behind the Benezit experiment that Richard Hake has
referenced many times. Physics education research has shown that exactly
the same problem exists in teaching physics. Students memorize equations
without comprehending them. F=ma is one of the best examples of this. Most
books start by stating NTN2 as an equation or an equation paired with NTNs
classic statement which is sometimes rephrased. Then various examples
follow this. Students latch onto the equation and then just go uh-huh with
the examples. The sequence which is more productive is to have them
experience the examples first in labs where they have to predict results
before seeing them. Then present the law. Finally have them do some
applications.

Math instruction makes the same mistake. It presents memorized rules first
and examples second. Often word problems are completely omitted. I think
the majority of math teachers use no manipulatives, and geometry is hardly
ever taught with any drawing and measurement. The 4 items for $10 is a good
example. Students should be dealing with numbers first by using familiar
examples. The most familiar one is money. They can readily say that 4
items for $1 means each item is a quarter, so 3 items is 3 quarters or $.75.
These sorts of rules of thumb should be generalized and students should be
pushed for more such rules before they memorize general rules such as long
division. Fractions should be first taught using divisible objects so that
students can readily see that 2/3 + 2/3 = 1 1/3. Cheap items would be cut
up paper circles. Then a few rules can be generated by the students, and
finally a general rule generated by the teacher only if necessary. These
same techniques should work with college students, and are very similar to
the methods of PER. When my own children demonstrated they did not
understand decimal numbers, I had them cut up a sheet of paper into tenths,
one tenth into hundredths ... Then I would ask them to give me .356 sheets
of paper or 2.712 sheets or .015 sheets ... And then do the reverse where I
gave them the pieces and they had to figure out how to write it down. It
worked beautifully.

When a math teacher tells me, "I don't understand why they don't get it. I
told them clearly many times.", I feel like replying "They don't get it
because you told them." Renner, Karplus, and Lawson have all done research
into these problems. Renner found that it is imperative that concrete
operational thinkers (Tina's students) use manipulatives, and that concept
introduction must come before term introduction (formal rules).

This problem has been around for a long time. In previous eras many jobs
such as policeman required no math or writing skills. Often police attended
a short police academy after HS, and teachers were trained in normal school.
In the 1950s my mother was shocked when she tried to buy 10 items at 23
cents each and the store clerk laboriously wrote out the math as a long
division on paper. My mother said "It's $ 2.30". The clerk looked up, then
continued to do the multiplication. Finally the clerk said "You're right.
How did you know that?". Now the schools are doing training that was
formerly done by the companies. Assembly line workers were trained on the
job and needed no academic skills.

The current political reaction to this problem is to test students for the
presence of these memorized algorithms, and to require teachers to have more
training in the subject material. The first practice reinforces the wrong
methods of teaching, because principals mandate review books rather than
good content teaching. The second practice is drying up the supply of
qualified teachers rather than increasing the qualifications of teachers,
because math majors can find better jobs elsewhere which do not require
combat training without the combat pay. Incidentally Tina might get better
pay and better students if she were teaching HS. At least she would not get
just the lowest students.

Unfortunately most university teachers never encounter these lower students,
so they really have no concept of what is going on. The little frustrations
in stores seem minor until one realizes that some of these same products of
our educational system might be caring for you in the hospital.

John M. Clement
Houston, TX




Some of them do. By far the majority of them do.
They weren't born knowing it, but they figure it out.
This thread started out referring to a college class.<<

Yes and it still is. Let me describe this class for you. I
start out teaching the students how to add, subtract, multiply
and divide whole numbers. About 1/3 of the class can't do that.
Then we move to decimals, which most can do via calculators.
Then comes positive and negative numbers. 3/4 or more of the
class can't get that. Eventually they get it via the calculator.
Then we do fractions. I suspect only 10% of the students get
fractions before the course. Then come percents. Few students
can do this. I love it. I love taking them for a ride because
we all know that if something costs $100 and it is on sale for
20% off that means it should ring up $120 right? (believe me
they think it does) Or it should ring up $20. After that it is
unit conversions.
Then onto what perimeter, area and volume are. They think it is
the same. Love to be a contractor here. Then we do incredibly
simple algebra. Then they learn how to plug numbers into formulas.

Okay I went to a not so good private school. I learned how to do
this in grade school. For about half my students this is the
first time they have seen this material at all.

Most just don't get it. I have nurses to be, electricians to be,
contractors to be, police to be amongst others. They frighten
me. Really bad.

If you have ever tried teaching at this level it is frightening
that they just dont get it.

Today one asked me when I was going to start teaching. This is
only the 5 week of the semester. I was like what do you think I
am doing up here? She is like you are working out problems, but
that is not showing us how to do it. It is not like i work the
problems out in silence. I tell them what steps I am doing....

Tina Fanetti
Math at WIT
a^2 + b^2 = (a+b)^2
x+y=xy
4^5/4^3=1
(mistakes my elementary students made on the last test)
I could go on but it gives me nightmares.

Tina Fanetti
Physics Instructor
Western Iowa Technical Community College
4647 Stone Ave
Sioux City IA 51102
712-274-8733 ext 1429