[agumonkey]

I often wonder about this. I also believe that mathematical pedagogy strive to attract people that are very smart and think in the abstract like euler, and not operationally, meaning they will get it intuitively.

For other people, you need to swim in the original problem for a while to see the light.

[II2II]

I think it is a combination of factors. Mathematical pedagogy is legitimate if the end goal is to train mathematicians, so yes it is geared towards those who think in the abstract. (I'm going to ignore the comment about very smart, since I don't think mathematical ability should be used as a proxy for intelligence.)

On the other side, I don't think those who are involved in curriculum development are very skilled in the applications of mathematics. I am often reminded of an old FoxTrot comic where Jason calculated the area of a farmer's field using calculus.

[melagonster]

Mathematicians also hate the current version of math education.

[BobaFloutist]

Frankly I wish I had known integral calculus going into geometry, I could tell there was a pattern behind formulas for areas and volumes but I couldn't for the life of me figure it out. There are worse ways to remember the formula for the volume of a sphere than banging out a quick integral!

[ForOldHack]

I had known it. Thanks Dr Steven Giavat. The geometric shapes gave the patterns meaning. I read 'mathematics and the imagination' and mathematics a human endever' while I was starting algebra. Also the time-life book on math. All very brilliant because they used the methods that were used to investigate it, to show how it was discovered. These allowed me to fly ahead in math until I got to trig. Which took a long year to get facile, until I was able to finish my degree.

I had brilliant teachers.

Napier's bones, were for adding exponents, hense multiplication. Brilliant and nessary for the development of the slide rule, and the foundation of modern engineering, until the pocket calculator.

[BobbyTables2]

Math is rarely taught with practical problems in mind — that’s engineering !

[smitty1e]

Therein lies the rub. Treating abstract and the concrete in isolation was always tough sledding for me.

Bouncing between the two is where the action is.

And units: if I had it all to do over, I would pore over the units sooner rather than later.

[pbronez]

Absolutely. Units are such a useful idea.

I was recently struggling to model a financial process and solved it with Units. Once I started talking about colors of money as units, it became much easier to reason about which operations were valid.

[kqr]

Strictly speaking this is about dimensional analysis, not units. (When discussing curricula we should be precise!)

[mrcsd]

I really disagree with the straightforward reduction of engineering to 'math but practical', but I'm finding it hard to express exactly why I feel this way.

The history of mathmatical advancement is full of very grounded and practical motivations, and I don't believe that math can be separated from these motivations. That is because math itself is "just" a language for precise description, and it is made and used exactly to fit our descriptive needs.

Yes, there is the study of math for its own sake, seemingly detached from some practical concern. But even then, the relationships that comprise this study are still those that came about because we needed to describe something practical.

So I suppose my feeling is that, teaching math without a use case is like teaching english by only teaching sentence construction rules. It's not that there's nothing to glean from that, but it is very divorced from its real use.

[seanhunter]

As someone who is studying maths at the moment I don’t recognise this picture at all. Every resource I learn from stresses the practical motivation for things. My book of odes is full of problems involving liquids mixing, pollution dispersing through lakes, etc, my analysis book has a whole big thing about heat diffusion to justify Fourier analysis, the course I’m following online uses differential equations in population dynamics to justify eigenvalues etc.

[fenomas]

Agreed, and it's such a shame! A kid goes to math class and learns, say, derivatives as this weird set of transformations that have to be memorized, and it's only later in in physics class that they start to see why the transformations are useful.

I mean, imagine a programming course where students spend the whole first year studying OpenGL, and then in the second year they learn that those APIs they've been memorizing can be used to draw pictures :D

[meindnoch]

I've never seen an introductory math textbook that didn't point out how position, velocity and acceleration are related by the derivative.

[DrFalkyn]

Rules for derivatives require the least memorization

[agumonkey]

Well, logarithms were made from physical entities (celestial bodies) but not on engineering per se.

I think this is already enough context to root the mental effort deeper.