[robomartin]

> Maybe the field would benefit to go more towards philosophy and logic, explaining it with words.

Interesting perspective.

I studied Philosophy and Logic in university:

https://en.wikipedia.org/wiki/List_of_logic_symbols

Much of it was familiar to me because, earlier, I took a class my Physics professor insisted we should take, as he put it, "if you want to get out of the dark ages": Programming in APL.

AS it turns out many of the symbols used in APL come from Logic.

To this day I find it disturbing that Python uses "^" for bitwise XOR, because both in Logic and APL, this is the symbol for AND. Anyone who studied Logic instantly recognizes the APL logic operators.

I say "interesting perspective" because the reality of what you are asking is precisely opposite what you think the outcome would be.

[GDC7]

> https://en.wikipedia.org/wiki/List_of_logic_symbols

Among all those symbols only ">" and "<" are somewhat intuitive, all the others you have to learn what they mean.

Even "=" is derivative of "<" and ">" because by reasoning you can understand that you get to it by rotating the 2 lines about 30 degrees after realizing that you are dealing with 2 numbers which are in fact the same and not one being bigger than the other

[robomartin]

Yes, of course. BTW, I don't think my comment covered the fact that I agree with you 100% on the impenetrability of mathematical notation.

That said, all notations --including the written alphabets of many spoken languages-- are impenetrable until you learn them. As a personal example, for me, learning French and German was a million times easier than learning Chinese and Japanese. In the first two cases I could read and write the languages right away. In the case of the latter two the notation imposed both a significant time drain and a cognitive load that got in the way of learning. I did a lot better with Japanese than Chinese. And BTW, I would not dare say I know these two languages. I can rattle off a bunch of phrases in Japanese and understand them if spoken slowly. My brain has yet to synchronize to Chinese.

My point is that specialized notations have been a part of the human experience forever. From cuneiform to modern written languages. Our brains are pretty good at learning notation. I would not fault mathematics for anything other than, perhaps, practitioners assuming everyone reading a math-heavy text understands the notation as they do.

Personal example: One of my kids is going though an MIT CS class on edX. He got scared when he was presented a formula with a huge sigma "Σ" sign in front of it and numbers below and above it.

It took less than a minute to explain that this just means a sequence of sums, maybe ten seconds. I just wrote down something like: "(a0 * b0) + (a1 * b1) + ... + (an * bn)" and said: "This is what it means. Summation". Done.

The point is, notation doesn't have to be hard.

[GDC7]

> It took less than a minute to explain that this just means a sequence of sums, maybe ten seconds. I just wrote down something like: "(a0 * b0) + (a1 * b1) + ... + (an * bn)" and said: "This is what it means. Summation". Done.

I think the real world feedback is quite different, given that math can be explained textually with words , why should we not do it?

The burden of the proof is always on the institution trying to do something. In this case the US government trying to make the US population better at math.

The population is quite okay with the present day situation, it's the government's job to make stuff happen and change things around to obtain the desired result, that is an improvement compared to what we have today.

Math proficiency is in line with new notation foreign languages proficiency from your examples (Chinese, Japanese, Austrian and German to a certain extent), that's because as you said both math and those languages have a different notation.

Given that (unlike foreing languages) math can be explained WITHOUT having to teach a new notation, then why don't we do it?

New notations are necessary for Chinese, but not for math, so why don't we remove this barrier to entry?

New notation is part of the human civilization but it has to be acquired early on to become like a second skin, which is what Latin letters are for us.

One has to be realistic . Mathematical notation will always take the backseat vis-a-vis literal notation. Kids just don't learn (and aren't taught) mathematical notation the same way they learn (and are taught) latin letters.

Instead of fighting against windmills we should take that as a given and try to influence what can be influenced.

As I said the institution trying to make a change in end results, must consider changes in the process...otherwise nothing happens.

[robomartin]

I think the notation is very much needed because it quickly becomes a tool for thought and communication. This is very much the case for every spoken language and other areas, such as music. Your point, which is quite correct, is that the math might not be explained well enough and internalized to the extent where the notation becomes a language for students beyond the simplest levels of mathematics.

A kid can learn the notation for whole, 1/4, 1/8, etc. musical notes and their positions on the staff very easily. An immediate relationship is created to the key on the piano or the fret on the guitar. I have been to math classes where the professor simply vomits formulas on the blackboard for one hour and you are left to figure out what they hell happened. That is a problem. Not the notation. The way math is taught.

[GDC7]

> A kid can learn the notation for whole, 1/4, 1/8, etc. musical notes and their positions on the staff very easily. An immediate relationship is created to the key on the piano or the fret on the guitar

I don't know about that. How many people can read music?

But also music, much like Chinese and Japanese is at a comparative disadvantage compared to math because there are no other tools to explain how high or low a note is.

You can use words to explain math, just like you did with your son.

Internalization is key, if you miss the window as a kid then it's gonna be an uphill battle and life being complicated as it is would mean people giving up on it.

And real world feedback is telling us that such window will be missed, that's why I had thought about math being always explained using the familiar English language which is almost always never missed as a kid.

[Jtsummers]

> Given that (unlike foreing languages) math can be explained WITHOUT having to teach a new notation, then why don't we do it?

Can you explain, say, orbital mechanics, without math notation? In a way where someone can determine where a satellite will be at a particular time given its position and velocity at a prior time taking into account disturbances to the ideal orbit caused by the Moon and Sun (we'll stick with just those 2 and pretend the Earth itself is a perfect sphere).

I don't mean explain in a pop-sci sense. That's actually feasible with very little math (though you will probably want some diagrams), I mean explain in a way that the audience can then apply this math-but-not-in-math-notation to solve real world problems.

[GDC7]

Again, you are assuming that math is only done at the frontier.

I don't care about the frontier, I care about improving standards of living and quality of life, and that you can do by moving the needle in a concrete manner for HS and college math proficiency.

Not to mention that the satellite operations you mention will benefit a lot thanks to a higher standards of living/quality of life which are synthetized in the GDP metric.

One can only imagine the GDP growth that would happen if math proficiency levels were to suddenly become on par with coastal China.

At that point the satellite operations you'd speak of would become much smoother without even needing to move the math frontier forward.

You'd see collapsing costs everywhere ranging from personnel, raw materials, building operations, security and so forth.