TITLE: Typos and Uncertainty
AUTHOR: Eugene Wallingford
DATE: February 21, 2010  7:32 PM
DESC: 
-----
BODY:
Last week, a student asked me why one of my examples in
the programming assignment said this:
<PRE>
     <B>&gt;</B> (insertion-sort &gt; '(1 4 2 5 3 6 4 7))
     <B>(1 2 3 4 4 5 6 7)</B>
</PRE>

Shouldn't the answer be <TT>(7 6 5 4 4 3 2 1)</TT>?  Or
was there something that he didn't understand?

At first, I thought his question was a polite way of
pointing out my typo, but as we talked it became clear
that he felt some real uncertainty about the answer.

How?  Surely it was obvious that sorting the list in
descending order should produce the second list.  This
seemed all the more obvious because the previous
example on the same page sorted the same input with
<TT>&lt;</TT> and had the correct output!  What could
he be thinking?

Sometimes, I ask myself such things rhetorically, out
of wonder or frustration.  Over the years, though, I
have learned to take these questions seriously, because
they are the key to understanding what's going on with
my students.

In the Case of the Backward Bracket, I recognize a
lesson I have learned before: <B>Even the smallest
error or inconsistency can create major doubt in the
mind of a novice</B>.  Originally, I wrote "fragile
novice", and it's true that some novices are more
fragile than others.  But to be a beginner is by its
nature to be fragile.  Our minds are still learning
to see, so when they see something that is wrong we
are willing to believe that something is wrong with
with us.

Learning functional programming and Scheme puts my
students in the position of facing problems they
feel confident solving -- if only they could use their
favorite programming style and language.  Right now,
though, they struggle with a new way of seeing, and
this creates uncertainty for them.  It makes them
tentative, maybe even scared.  They see my typo and
wonder what it is they don't get.

This lesson means at least two things to me as a
teacher.  First, I need to be extra careful to weed
out mistakes in what I tell, show, and ask them.  I
want them to be able to focus as much as possible on
the necessary complexity in the problems, not on
distractions that result from my <I>fingerfehlers</I>.
Second, I need to keep my eyes open for moments when
this kind of uncertainty and fear begin to dominate my
students' minds, whether in class  or working on their
own.  By recognizing the situation early enough and
intervening, carefully, I may be able to help them
stay on a productive path toward understanding.
-----