Math writing is dull when it neglects the human dimension

Haven't thought is for decades, but was my environments favourite math tutor, because I managed to ground everything in people's reality and rell them a compelling fiction in which knowing how to do the thing was actually a super-power.

You know like the survival tricks certain preppers learn and never use — that, but with math. Even if the examples were sometimes over the top, involved flaming moats and other xkcd-like freakiness I got students where their teachers told me it is hopeless sitting there participating with glowing eyes.

Meanwhile in my own math education I had a teacher who made us do integrals for what felt like a year without telling us once what the hell it is needed for. I had to figure that out on my own.

My colleagues who didn't care just learned it by hard and forgot it immediately after. But I guess they got thought all the material and got ok grades so their education was a success.

What bullshit. Now, 15 years later I relearn a lot of those thinga because school made it sound boring only for me to later discover it is one of the most exiting things your brain can do. But that is about thinking on solutions to actual things not learning steps and doing them and getting punished for making one mistep.

As someone who routinely teaches (Non-STEM) university students practical applications of math I can assure you that none of the students that told me "I am bad at maths" went out of my class without an understanding of the topics we talked about.

Yet I routinely hear a: "Wow, if they told it to me this way during school I might have cared!" or "It really made my head smoke, but it felt good."

Step 1 is believing that every person that doesn't have cognitive problems can understand an abstract concept if it is explained well and they got the motivation to understand it. Then you need to create a situation which motivates them to understand it and now you only need to explain it well.

Many math teachers fail already at step 1. They believe 90% of their students are too stupid to understand things, while this is just a convinient explaination for their own failures. I once was convinced of being that student.

I met one kid that I couldn't teach anything because he would forget things I told him 15 minutes befoee. He was a refugee from Afghanistan and severely traumatized.

The truth is that we should look to the best when teaching and we would be stupid if we didn't. And the best are people like 3blue1brown. If your class falls significantly below such a level of clarity and engagement it will suck. During my own math education I had teachers that left out the most fundamental applications. E.g. something like an integral has clear applications, it is a new super power with which you can solve new problems — yet all we did was learning a receipe and solving abstract problems. The fact that it was a super power was something I had to figure out myself, later.

And this was common. I even was lucky because I had a good physics teacher who managed to being up a lot of what we learned in math and give it a more practical feel, but most of my friends from other schools were not so lucky.

imo this is largely because of the incentives around the game of school and testing.

If you must wait 20yrs before you can do interesting stuff and you’re evaluated primarily on your ability to maximize your grade then anything that gets in the way of that is an annoying distraction for most at best.

Even if you’re a student predisposed to find applications and the narrative of the discovery interesting you still have to focus on guessing what the test questions will be and just doing those, spending mental cycles on other stuff is a “waste” in that environment.

Once you’re finally free of school only then can you actually learn based on where your curiosity takes you, though at that point most choose not to - the curiosity having been driven out of them.

Makes me think a little bit about the movie the lives of others:

> “Did you know that there are just five types of artists Your guy, Dreyman, is a Type 4, a "hysterical anthropocentrist." Can't bear being alone, always talking, needing friends. That type should never be brought to trial. They thrive on that. Temporary detention is the best way to deal with them. Complete isolation and no set release date. No human contact the whole time, not even with the guards. Good treatment, no harassment, no abuse, no scandals, nothing they could write about later. After 10 months, we release. Suddenly, that guy won't cause us any more trouble.

“Know what the best part is? Most type 4s we've processed in this way never write anything again. Or paint anything, or whatever artists do. And that without any use of force. Just like that. Kind of like a present.”

If you look at the comments in khan academy there are tonnes of people asking for real life applications—that said, they’re given in most of the material there.

Inspiring students (and showing the material can help them in their lives additionally) is one of the most important but difficult parts of teaching: good explanations falling on uninspired ears rarely settle.

And I’d argue the onus is on the teacher to inspire but it’s not something I can say is an easy skill to master.

Succinct explanations can be hammered out but fostering inspiration is a soft skill rarely taught—-and rarely deemed important in the already inspired.

> How did folks come up with and it, prove it works and start using it

I mean, anything at the university level should include proofs on why it works. I would go as far as to say you aren't really doing math if there are no proofs.