How do you understand mathematics? I like to connect them to real world situations, real applications, physics, even stories. This helps me not just learning how to use mathematical techniques, but understanding them.
Once an undergrad student who was working on classifying some aerial imagery reached out to me for some help. He wanted to know how he can evaluate his classification. This was a long time ago. Just so that you know how long ago this was: Wikipedia was just recently established, but we hadn’t heard about it yet anyway; so, it might as well not be established at all; Google was established, but Yahoo and Alta Vista were still hopeful and under this false impression that they could win their share of search market back from Google; Python was there but not popular; We were still entertained watching Java and C++ loyal pupils pointlessly fighting which language is the future; and remember this was before social media, so, by watching, I mean really watching; like at the same desk or room that you are sitting, not reading their posts online; C#, standing far in the back of the crowd, who were busy watching Java/C++ wrestling, was jumping up and down and shouting: look at me, look at me, I am here too; VB, believe it or not, was still a thing; and oh!, before I forget, dial-up Internet was still a thing (actually the only thing) in some regions.
So, we had to use the analog version of google search and Wikipedia. And by that, I mean We had to pick up a book, feel the weight of the knowledge in our hand, go to the back of the book for the index section, search for “Confusion Matrix”, and then go to the pages that was listed for it. Good thing about this analog method is that I never remember to get “index out of range” error, although sometimes the index was one or two pages off; it must have something to do with 0 or 1 based indexing. But we were getting “KeyError”, depending on the quality of the index that was created.
Anyway, after going over the material from the book, I could tell that he understood what needs to be done. He knew how to calculate what he needed to calculate and evaluate his model; well, actually models. So, at this point he could complete his assignment and get a full grade. I could have just said all done. Good luck with the assignment; and be done with it.
But, something was not right. I felt like despite seeing the equations and knowing what to do with them, he still doesn’t know what they really mean. All he needed though was a little push. After all, the point of an assignment isn’t just finishing it and getting a high grade. It’s not just a box that you need to check done. It’s a chance to learn.
So, I asked him: ‘Have you heard the story about “the Shepherd who cried wolf”?’. He was, clearly, puzzled and confused at what I just said. Incidentally, his assignment involved detecting and counting animals in the aerial photo, but not wolf. Different Animal. I continued: Well, if you were detecting wolf, and that boy was your wolf detector model, your model would have had high recall, but very low precision. Now, if you can make the connection between that story and why that leads to high-recall/low-precision, you will understand these things better.
It didn’t take him long for a smile starting to appear on his face. That was the moment that I understood my job was done in this case. He was ready to complete the assignment and hand it over.