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I am teaching a first-linear-algebra course for mostly undergraduate Computer Science and Data Science students. Occasionally, I tried to do a bit computer experiments in class and ask students to guess what a theorem should be. But I noticed that students do not seem to be very engaged in the experiments. I guess the problems may be

  • I am the one doing the experiment. So they cannot do much but just look.
  • The experiments I am doing are numeric. So they do not look very interesting visually.

I wonder if anyone of you have tried similar things, and if you have learned how to make such experiments work better.

One example of such experiments would be that I compute eigenvalues of a random diagonal matrix with computer, and asks students to guess the answer from observing such computations.

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    $\begingroup$ Does DS = Data Science? They’re QS at my institution. $\endgroup$
    – Raciquel
    Feb 26, 2022 at 1:20
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    $\begingroup$ Yes DS is data science. $\endgroup$
    – user11702
    Feb 26, 2022 at 1:33
  • $\begingroup$ Can you give us examples of these experiments? What do they involve? $\endgroup$
    – Adam Rubinson
    Feb 28, 2022 at 11:18
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    $\begingroup$ A nice thing about Sage Math (in addition to it having pretty much every part of our mathematics) is that it is written in Python, essentially, meaning using things like pandas and numpy from within Sage is easy. Or you could just set up a Jupyter notebook and try all of the languages you like! $\endgroup$
    – kcrisman
    Mar 4, 2022 at 13:05
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    $\begingroup$ Here is a LA text with a very large amount of Sage: linear.ups.edu $\endgroup$
    – kcrisman
    Mar 4, 2022 at 13:05

1 Answer 1

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One of many possible suggestions: make it interactive!

As one example, see this activity from David Austin's linear algebra text. You could make it a game of sorts for choosing a matrix, and then sliding the vector around to see where it needs to go to be an eigenvector. Try a few, and then start messing with the students by purposely going a direction that is less like an eigenvector. Or do a bunch that have obvious ones, and then pick a matrix with no (real) eigenvectors (like a rotation matrix) and see how frustrated they get.

This may sound corny or naive, but it really can work. My favorite such activity in linear algebra is shamelessly borrowed/stolen from some colleagues at Stephen F. Austin State University, and the students love it. Especially when I choose a singular matrix ... some of them then "improve" on the code.

Obviously this is not a cure-all by any means. But even engaging a third of the class highly, and another third passively, makes the remaining third much less influential in making a bad classroom vibe when you are trying your experiments. And they may be more willing to "sit through" ones that are difficult to make interactive if you have a few that are.

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