Re: What's "Developmentally Appropriate"?

[Larry Smith <larry.smith@SNOW.EDU>]

At 5:42 PM -0500 10/14/03, Jack Uretsky wrote:
> Great!  Maybe, Larry, you will consent to continue your G/P role, for a
> bit.  I'd like to know, for starters,
>        1.  How much set theory did you remember when you entered college?
> (that's not a very precise question, but perhaps you can give us a
> flavor).

I remembered the fundamentals I was taught.

I do have another disclaimer: I really doubt I was normal.  One friend that
went through all this new math with me ended up teaching math at a high
school, but most students probably didn't enjoy the "new math" as much as I
did.

I do have another disclaimer: I don't remember much "new math" from
elementary school (I think it may have been standard non-new math).
However, I do still appreciate the emphasis on "solution sets" and place
the same emphasis in the math courses I teach currently.

But in 7th grade (which was actually in the '70's) my class started a 4-yr
course called "Unified Math" by Fehr, Fey, and Hill.

In seventh grade we studied finite number systems such as "clock
arithmetic" (modulo), groups, mappings (I knew the difference between the
range and the co-domain), lattice point graphs, sets (including subsets,
empty set, Venn diagrams, union, etc., all of which I remembered as I
entered college), and symmetries.

In eighth grade we studied coalitions in voting bodies, bi-implication,
inference, groups, fields, affine geometry, and a bit on statistics.

In ninth grade we studied matrices, rings, linear systems, metric geometry,
probability, trig, informal solid geometry, linear independence, and vector
spaces (here's a theorem from my ninth grade book):
Let S be a set and F a field, with mappings
  + : S x S -> S
  . : F x S -> S
Then (S, +, .) is a vector space over F iff
1. (S,+) is a commutative group
2. etc....

In tenth grade we studied programming in BASIC in chapter 1 (this was in
the mid '70's), sequences and series, mathematical models, complex numbers,
more trig (DeMoivre), conditional probability, and more on vector spaces
and the inner product.

Then I took calculus in 11th grade and linear algebra in 12th (neither a
part of the Unified Math series).

>        2.  Have you ever had a course in: set theory, number theory,
> probability theory or real analysis?  If so, can you estimate how much you
> were helped by your early exposure to set theory.

Yes, as a math major I had those courses.  I think I could probably have
done as well in those classes without early exposure to set theory, but I
can say that my junior high and high school math classes were anything but
boring and may have kept my math fire alive long enough to even major in it
in the first place.  I think I remembered enough set theory and other
things listed above to have helped slightly...maybe not directly, but
indirectly by giving me an early exposure to some of the breadth of
mathematics.  I think it helped develop my mathematical maturity.  I can't
say I really remembered all of it in detail, but then again I don't
remember all of any class I took in junior high.

>        3.  Are you presently fluent in Boolean operations?  Can you
> analyze logic circuits, for example?

Yes, I've taught Intro to Computer Science.  It is a GenEd class so I'm not
a great expert, but I can do simple circuits.

> If so, when you learned these skills
> did you have a sense of deja vu going back to your elementary school days.

Not deja vu per se, but a bit of familiarity, and increased confidence when
I saw this stuff in college.

>        4.  What do you consider is the highest level math text that you
> can read casually (like a novel)?

I don't know of any math texts that read like a novel.  But I enjoy
reading/perusing all lower division math texts (I teach at a 2-yr college)
up to Diffy Q and Discrete Math.

>        You will not be graded on this exam!

Thank goodness!

I don't know if I helped prove your point or not, but either way, I'm only
one data point.

Cheers,
Larry