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

On Tue, 17 Feb 2009 05:02:44 -0800 (PST),
Dave L. Renfro <renfr1dl@xxxxxxxxx> wrote:
Jonathan Groves wrote (in part):

Excellent point. In fact, that is a big reason many
students can't write decent sentences anymore; schools
don't make them write enough and don't grade their writing
seriously. I have had a lot of students who, when I asked
them on homework or a quiz or an exam to explain a concept
(and all they needed was a sentence or two), can't write
anything beyond meaningless garbledygook.

Tim Woodall wrote (in part):

Perhaps you (someone) needs to teach them how to structure
their writing.

I went though school struggling with "essay" subjects. Never
a failure, I was usually getting B grades, but I was incapable
of getting A grades[1] no matter how much work I did. This
was O'level (exams at 16)

[1] Sometimes I might get an A- and sometimes a C+ but this
was just luck of the draw.

It was frustrating. Not least of which because I'd get as
good marks, and often better, if I dashed something off in
a lunchbreak before it was due than if I spent days researching
the subject first. Especially frustrating because I couldn't
understand why one essay was better than another.

Fortunately, at A level (exams at 18), as well as taking
double maths, physics and chemistry, I took music. At last,
someone sat down with me and explained how an essay needed
to be structured. Suddenly everything started making sense.
If only someone could have sat down with me at 14 and made
the same explanations I might have got As in all my O'levels
instead of just half of them. (I still didn't get an A in
A'level music but that was expected)

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), and much of
the focus with these papers was what was expected of us
(minimum number of references, format for footnotes, minimum
number of typed pages, what the introductory paragraph is
and what the concluding paragraph is, etc.).

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 ..."


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.

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)


This said, I do agree with the general sentiment in this
thread that many people don't write very well when asked
to explain something, but I don't think this is due to
a lack of being taught how or a lack of practice. I think
the situation is similar to that in math literacy. People
are taught arithmetic of whole numbers and decimals in
grade school, fractions and percents and elementary aspects
of geometry in middle school (in the U.S., this is *everyone*,
not just those planning to attend college), and at my high
school those planning to attend college took algebra and
geometry and often a second course in algebra (now I think
it is almost the norm for students to go through these three
courses in high school), and yet many people still struggled
with basic arithmetic and algebra in college (both when I
was in college and now). What I think is at the root of the
problem is that many people never care to learn what is taught
to them, whether it's basic algebra (up to and including
quadratic equations) or basic writing (how to write a paragraph,
an essay, or a term paper) and, in addition to this, many people
do learn these skills but they just don't bother to do what is
asked of them. I suspect quite a few of the students who write
"meaningless garbledygook" do so not because they are unable
to do otherwise, but because they either don't care or they
don't think it really matters in the grading of their work.

Maybe it's the same problem in reverse with mathematics. I was shown one
example once and then I was off, easy. I can remember the very first
time I saw simultaneous equations and solving them via graphing the
functions (I read this in a book rather than being taught) and it was
all completely obvious to me. But others needed it to be explicitly
explained that you can "write down" every possible solution to an
equation by drawing a line on graph paper. All I needed was "just draw
the curves and look where they intersect". Once I'd got that I then went
and asked how you could solve them without drawing a curve - or more
accurately I went and asked how you could get an exact solution other
than looking at the graphs and then guessing the correct numbers and
trying them by substitution.

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. But I lacked whatever
it was that enabled me to see the structure outside of the words until
someone explicitly drew that structure for me and also criticized my own
essays, not just with good/bad or even "it would have been better to put
this paragraph first" but _why_ it would be better to put that paragraph
first.

Of course there are plenty of people who don't seem to care about
getting it right. Maybe the differences between US and UK compulsory
education are so different that we cannot really compare experiences.
But my experience is that if you don't know how to do it but are
sufficiently able that you can get passing marks then you're in a bind.
In my case without even knowing the right questions to ask to make
progress.

Tim.

--
God said, "div D = rho, div B = 0, curl E = - @B/@t, curl H = J + @D/@t,"
and there was light.

http://www.woodall.me.uk/
.

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