So I was walking in the class one day. Looking at how students are making progress in their work when I see this bright student, hunched down, trying to evade thinking about the work at hand and distract themselves and their group with other trivia. I stand beside them, pick up the knitting which is their constant companion and possibly a selected stress buster activity, discuss the piece with them, appreciate it, linger a little more and ask, “Is Mathematica behaving ?” They seem to de-stress a bit, the problem is with Mathematica not them. It is the software that is being dumb, not them.
I had asked this question because I had seen them previously put mathematical as the lowest point (way down below the white-board, somewhere near the ground) in the previous project. We look at the code together, they appear to have done everything right. The answer from Mathematica is {}, Instead of a list of two functions. I am fond of this student, they understand math well and love working with whacky symbols. In an earlier interaction they had come up with a nice visualization of a mathematical system. I also remember that they with a friend had invented a bunch of novel symbols with which they had programmed Mathematica in the previous project (which was the major reason for Mathematica confusion and their pain). I try to rewrite some of the Greek symbols as alphanumeric and arrange brackets, run a simple test. The test gives correct result, the problem at hand still outputs {}. Then they remember that they have seen two theta symbols behave differently, we replace one of the symbols and voila, the solution appears.
The group chimes together, Mathematica just tells you, you are wrong but not where you went wrong, that is so annoying. I tell them we should shoot a mail to Wolfram, and request them to update Mathematica so that it gives feedback.
This
exchange is particularly interesting and amusing to me because during the
previous project, the group leader had to make an impassioned appeal to the
class to provide feedback on the course so that required course correction can
be made. Feedbacks are important, from
the coding platform or from the class. They play a very useful role in course
correction.
This particular group had been struggling
before too. They had written an equation
.
I
asked them how can a vector be equal to a number ? so they corrected it to
,
I again point out that magnitudes of both
sides do not equal, so they write the correct standard formula for rotation of
basis but say they are not sure how to verify it, I show them two ways of doing
it “either put various angle values to check that the equality makes sense, or
use geometry”. They seem to be satisfied with it and start working in the right
direction.
My Teaching-Learning 