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Re: [Phys-L] problems with the teaching of algebra

Anyone with good reasoning can easily figure this out without algebra, and
this is precisely the sort of thing that Benezit would have had students do.
And yes there are methods that can be used such as bars, but a little
proportional reasoning and picturing the situation it is a reasonable
problem than any middle school student should be able to do. I suspect that
CIMM would also promote being able to solve this type of problem.

Elementary teachers do not need full algebra, but they do need to able to
use proportional reasoning. Beginning at 5th grade, age 10+ is when
proportional reasoning can be developed fully. Shayer & Adey propose
starting with reasoning tasks in K and 2st grade as there is a window of
opportunity of rapid brain growth at that point.

First students need to develop proportional reasoning, and then algebra
becomes obvious and transparent. Most pre-service elementary teachers do
not use proportional reasoning, so teaching them algebra and requiring a
stiff course is useless.

John M. Clement
Houston, TX


Is this example meant to be ironic? Which of these kids is
going to learn fractions today? :)

More seriously, though: if you believe that it is important
that elementary school teachers can do a little algebra,
putting one or two items on a multiple choice test is not
going to make that happen. You'd be better off requiring
that they have one college level course in a subject that
uses algebra, one that they'd be unlikely to pass without
that minimal level you were hoping to see.


On 10/12/2014 2:30 AM, Ze'ev Wurman wrote:
On 10/11/2014 8:43 PM, Bernard Cleyet wrote:


Aaaagh!

You’re correct, however, this practice exam. includes one,
I think —
at least I used algebra , #22

‎www.ctcexams.nesinc.com/pdf/cbest_opt_math.pdf
<http://www.ctcexams.nesinc.com/pdf/cbest_opt_math.pdf>

The problem is:

At the beginning of a class period, half of the students
in a class
go to the library. Later in the period, half of the remaining
students go to the computer lab. If there are 8 students
remaining
in the class, how many students were originally in the class?


It is interesting to note that Singapore students are expected to
solve such problems in the third grade with their bar models.

Ze'ev
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Forum for Physics Educators
Phys-l@www.phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l