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Re: math (in)competence



Tina Fanetti wrote:
....
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?

Interesting. Very interesting.
A surprising message was received.
Surprising messages are the most informative:
-- when all the data is as expected, it confirms what you
already know
-- when unexpected data arrives, you have an opportunity to
learn something new.
(You can quantify this in terms of Shannon entropy: a symbol
with _a priori_ probability P conveys -log(P) bits of
information, so the unexpected ones are the most informative.)

She is like you are working out problems, but that is not
showing us how to do it.

There's a message in there. Possibly a very important message.
The message is, alas, somewhat impressionistic, not 100% explicit.
So the question remains, exactly what is this student expecting that
she's not getting? There is a golden opportunity to make progress
here, by following up on this. (There's also a big opportunity
to mess up, for instance by getting defensive or combative, which
would silence the student and shut down a very valuable communication
channel.....)

Also remember that for every student who speaks up, there may
be 10 students who feel the same way but don't speak up.


================================================

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.

I don't know what this means without more context.
*) This is an algebra class, right?
*) What makes you think they _should_ know such things?
(They weren't born knowing it all.)
-- Do you consider those items prerequisites for the class?
-- When the students signed up, did they _know_ those were the
prerequisites?
-- And/or were those items covered in class?
*) How do we reconcile this with the "when do you start teaching"
question?

I suspect only 10% of the students get fractions before the course.

If 90% of those who sign up for the class don't have the
prerequisites, there is something desperately wrong with the
enrollment process. People who need remedial arithmetic should
sign up for remedial arithmetic. People who are ready for 2nd-year
algebra should sign up for 2nd-year algebra.

I have nurses to be, electricians to be, contractors to be, police
to be amoungst others. They frighten me. Really bad.

Get over it. Now. Students can smell fear.
They can also smell disrespect.