Why Mathematics is Boring (2007) [pdf]

Following on from my other reply...

When we start teaching math to students, we start with counting blocks: "You have 2 piles of blocks, one pile of 3 and another pile of 2. If you put them together, you get a pile of 5 blocks!"

That stops working as well when you deal with fractions. You can get away with 2.5 blocks, but 2.5 blocks is really 3 blocks, but one is a little smaller than the others. And at some point you can't use blocks to represent 2.3456 blocks. So you need different kinds of "natural" problems to represent those numbers.

But, as you point out. There are some things that aren't really representable as "natural problems". For a long time the idea of 0 wasn't natural. (People were actually killed for talking about the idea of 0) I mean, what does it mean to have 0 chickens? You either have some chickens, and you say "I have N chickens", or you don't have any chickens and you say nothing. Why would you need a number to represent nothing?

Maybe n^2.1 doesn't have a natural explanation. At least, not one you can hold in your hand. Can you imagine a shape with 2.1 dimensions to relate it to geometry? Probably not. But you can use geometry to prove that n^(a+b) = n^a * n^b and then you can apply those rules to "unnatural values" with an understanding of what is happening. The natural explanation of n^2 can be applied to the unnatural idea of n^2.1

Everything in math can't be understood with geometry or "natural examples", lots of math (most of math?) describes things that are not representable within the constraints of our physical world. That's what makes it so powerful!

Also, not everything in math can just be calculated (see: irrational numbers)

To me it was sometime in high school Physics class that math started to have any semblance of utility to solving actual problems. But by that time most students had already been bored to death with years of the most obtuse memorization and test passing behaviors that it was all lost. Even then Physics was mostly a blizzard of formulas with absolutely minimal explanation and application. The exams were basically "cram as many of the formulas in the book as you can onto a single sheet of paper and then plug and play during the exam".

I did not do well in either set of subjects in K-12 -- even to the point that my graduation from high school was threatened. In college I forced by way back through it all by sheer force of will and got my A's.

There's something fundamentally broken in math/science pedagogy as these subjects aren't really all that difficult. There's far too much time spent memorizing things that are trivial to look up and way too little time understanding how to use them.

An analogy might be learning to cook, and spending all of your time remembering precisely how many spoons, bowls, cups, and cloves of garlic or other ingredients you have. And doing that kind of thing for years, and maybe seeing a demo once of pouring water into a cup. And tests might contain problems like "a party of 5 is coming over for dinner, are you able to set places for all attendees for a 7 course meal?"

The real message being sent is this: "Sorry kids, actually cooking from recipes is only for academics, and to get your PhD and be allowed into the hallowed halls of these academic cooks you must come up with one original recipe (edibility will be determined by peer review)".

In college I retook everything from Algebra up and found the math pedagogy focused more on symbolic manipulation and getting used to how that works in each subject rather than drilling arithmetic in various guises. Tests that required various pre-derived formula were usually just an open book problem. And what mattered was how one went about solving the problem, not the rightness or wrongness of it. Calculators were absolutely expected so you didn't waste time fighting with trivial mistakes.

The sciences usually had a mandatory lab portion that forced application of math to the problem space. Because the labs typically had you collecting your own measurements, it forced you to work through the calculations yourself anyways since there was nowhere else to look up the answer. Again the methods and approaches were where the grade came from, not the slavery to memorization.

Still, while I think the approach I encountered in college was much better than grade school, it still wasn't as good as it could be.

I think that's the joke.

Math does not describe reality, Physics does. Math is just pure thought. If anything, Math is an abstraction of how we think about things, but not the things themselves.

>how to spice them up with narrative

Oh, Lord; NO!

I would like see all Human Narratives/Unnecessary frivolities/Assume-reader-is-a-Idiot language banished from the Teaching of ALL Maths/Science.

What we we need is a focus on the direct teaching of Principles along with their Real World Applications.