Re: Multiple-Choice Exams in Math? Good Idea?

Dave L. Renfro wrote (in part):

The kind of explanation you got in music is what everyone
got over and over again when I was in high school (at least,
at my high school). In fact, now that I think about it, we
had to write some short papers in middle school English and
history classes as well (approx. ages 12 to 14), [...]

Tim Woodall wrote:

I got nothing of this. I have _never_ had any guidance on
"minimum number of references, format for footnotes, minimum
number of typed pages." That's starting fulltime education
at 6 through completing a first degree at 22 and subsequently
doing (part of) a masters degree part time. (It is, perhaps,
telling that when doing the Masters, other students were
asking to copy my work (after it was marked) for guidance
because I was getting so much better results than anyone else)

This may be an endemic problem at UK schools. Certainly my
A'level music teacher didn't spot I had a problem with essay
writing and then sit down with me. My lessons started with
"Nobody ever teaches you how to write an essay properly so ..."

I'm pretty sure our teachers were specific about this because
if they didn't say we needed a certain number of references,
most students wouldn't give any (or maybe just give one or two;
plus, the whole point of references was that it was what we were
supposed to be looking for when our class went to the library,
this being many years before the internet), or if they didn't
say we needed at least 5 pages, then most students would only
turn in a few paragraphs. In effect, it was a kind of spoon-feeding,
but it was high school after all (approx. ages 14 to 18).
Also, we were always being told horror stories about how
hard it would be when we got to college -- more than two
misspelled words and your grade would go down by a letter
grade and similar things. When I actually got to college
I found it overall much easier than it was made out to be,
but this was my experience. I've certainly taught quite
a few college students over the years who seemed quite
surprised to get a C or a D on a test that they actually
studied for. In fact, although I got B's all throughout
high school in English (I think I got an A only once in
the 16 high school grading periods), I got A's in both
of my college English classes (each grade was an A-,
I believe), which curiously put me in the top 3 or 4 out
of about 20 students in each class, whereas among my peers
in high school who went to college (most of whom attended
attended colleges much less selective than I attended),
I was usually near the bottom in English class.

In my case what made college English easier was the low
emphasis on "memorized knowledge", which I have always
had trouble with. Our college English grades were
based almost entirely on out-of-class papers, and thus
I could spend as much time as I wanted and look up
whatever I needed, rather than be stuck with trying
to write an in-class essay about a book character and
being unable to remember certain facts that I knew would
support an argument I was making in my essay but which
I just couldn't remember. One of the reasons I liked
math and did well in math was that there are so many
ways to get around forgetting some specific fact.
You can derive the result yourself, test out special
cases you know the answer for in order to eliminate
the incorrect versions of what you're trying to decide
among, and all sorts of similar methods. In my case, this
inability to do well on "fill in the blank" tests led
me to select electives where much of the grade was based
writing essays and papers that dealt with putting forth
a good argument rather than with writing essays and papers
where you were supposed to display lots of facts that
you were supposed to know (e.g. philosophy, rather than
history, classics, literature, etc.).

Dave L. Renfro wrote:

Then there's college. I don't know about others in here,
but in my two first year English classes (required of
everyone; this was at UNC-Chapel Hill, if anyone's interested)
we had to write 8 to 10 papers in each of the classes.

Tim Woodall wrote:

What age does college correspond to? For me college means
undergraduate (particularly as I went to a collegiate university)
but we also have sixth form college which would be 16-18 (A'level
or equivalent)

Not sure I ever did any essay writing at university at all.
(I did physics rather than maths if that makes any difference)

In the U.S., college corresponds to approximately ages 18 to 22.
In math, the first two years are typically spent taking the
3- to 4-semester sequence in elementary calculus, along with
linear algebra, differential equations (or maybe a discrete
math or a "methods of proof" class) along with a lot of required
electives (English, history, science + lab, etc.), and it's
only in your last two years that you have a formally declared
math major (at least, where I went to college), and in those last
two years you take courses in advanced calculus, abstract
algebra, real analysis, and the like. I wound up taking a lot
of physics also (several advanced undergraduate courses in classical
and quantum mechanics, as well as electromagnetic theory), but
almost all math majors only took the minimum physics required,
which was a 1-year sequence of "physics with calculus" (at the
time, Halliday & Resnick's text was used for this).

Tim Woodall wrote (in part):

I needed that dissection of an example when it came to essay
writing. It's no good saying "You need an introduction, a body
and a conclusion" and give me an example essay. I needed someone
to go through that example with me to point out all the different
parts, why they were there, how they related to other parts etc.
It might all be there in front of me, it might even be "obvious"
to you.

I think these kinds of things were a large part of our (U.S.)
middle school and early high school (approx. ages 12 to 16)
English classes. Our textbooks talked about it, the teacher
usually had at least one bulletin board that dealt with
these kinds of things, etc. Of course, seeing this doesn't
mean you can do it yourself. Going over your writing with
a teacher is best, but I think this doesn't happen all
that often because teachers have too many students and
many of the students have much greater needs than developing
their essay writing skills (for example, some students could
hardly read, let alone write essays . . .).

Something I _didn't_ have much experience with until much
later was writing mathematics. I've had a handful of math
teachers over the years who did a very good job of this,
and the experience was very helpful to me. I'm talking about
someone who, when grading your proofs, actually points out
grammar, poorly worded and ambiguous sentences, etc. in what
you write. My Ph.D. advisor was very good with this, especially
when I was submitting "proof write-ups" of things for my
Dissertation. Another person who did a bang-up job of this
was a topology professor I had for a couple of courses in the
late 1980s. However, based on the math papers that I've refereed
over the years, I suspect many people get can their Ph.D.'s in math
without ever having someone carefully and for a sustained period
of time critique their writing. This is after I take into account
possible ESL issues, by the way. (On the very off-chance that
someone I just turned in a referee report to sees this post,
that particular paper is not an example of what I'm talking
about, despite all the editorial changes I suggested.)

Dave L. Renfro
.

Relevant Pages

  • Re: lousy High School education
    ... college, according to a new study of last year's high school graduates ... I think math teachers, for example, should be able to answer any math ... I think high school math has boundaries. ...
    (rec.sport.football.college)
  • Re: Recording Classical music
    ... I have to disagree with this statement, at least in regard to math. ... calculus was a sophomore-level college course. ... high school; colleges expect students in scientific and technical fields ... which used to start at the junior level in college. ...
    (rec.music.classical.recordings)
  • Re: Are there any non-gifted scientists?!?!?
    ... More recently I've picked up math as a hobby ... I got A's abd B's in high school. ... Got to college, took more math and lots of physics and some comp sci. ...
    (comp.programming)
  • Re: Going back to School
    ... Mike is also enrolled at the same college, and we will be car pooling. ... Now, what worked for me may not work for others, but while I did poorly in high school math, my major self-study breakthrough came when I dug into what math majors call "Foundations of Mathematics", confused educational reformers usually scrambled into "New Math", and is actually set theory and mathematical logic. ...
    (rec.pets.cats.anecdotes)
  • Re: This is sooo stupid
    ... Onideus Mad Hatter wrote: ... like high school and college. ... you want to be spoon fed go the fuck back to college, ... LOL, unlike you I actually finished high school, have an AA, ...
    (alt.2600)