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Anecdote time: I was a late bloomer in math too. From about 6th to 10th grade, I was terrible at math. I think it was because of inapplication problems.

Yes, you get a word problem about Jack and Kwanzeeah trying to fill up a pail or something, it was nonsense to me. Why are they filling up a pail? Why are they using a bucket that is 173/9th's the size of the hose? Why do they have to not let it overflow? Why do I have to decipher this inanity, why can't they just ask me to do this stupid problem of stupid fractions? Why the cloak and dagger?

Then you get to 'real' algebra and you start to find roots of quadratic equations and other useless information. Dear Lord! When has anyone ever done this for any reason? Yes, something something eigenvalues something something computational modeling something runge-kutte. But for real though, quadratic equations are just nonsense gibberish to weed out the poor kids from the rich ones. Trig, yes, it's useful when you are building a shed that has to be totally perfect and crisp otherwise the rich white lady will not pay you. Geometry was a bit 'fun' actually, but in the same way that learning that Custer's Men took a poop at this road-side stop on the way to Little-Big Horn.

It wasn't until Chem in my 10th grade year that I actually 'got' algebra. We were doing moles to molarity calculations to get the solution to the right pH and make it all turn pink or something. It was then that I realized that all this mathy stuff was actually useful to me, that I could use it to make things easier and better for myself and my family. Like, I could 'know' what to do then. Before that it was just drill and kill and bad grades and shame. I remember staying after class and into the next one in the room, just sitting in the back doing these calculations over and over. I got kicked out for doing math! It was such a relief! I finally 'got it' when I needed it for something real to me personally.

For me, it was the issue of 'math' being this blunt-shame-thing that made no sense to use ever. But once I needed to use math, it was trivially easy. Learning math for each of us is individual, we each have our own motivations that are unique that need to be met. I know that is not easy to institutionalize, but if you want to do it, you have to find the 'correct motivation for each kid.

I'd agree with this completely. It's less about teaching what, how and when than it is teaching WHY you need to know this.

In high school, if you can convince a single person that they need to know calculus, more power to you. 99% of people don't and it's literally a waste of time. Teach people finance though...suddenly we have math that people will know is important.

I think motivation is key. That said, I think that the engagement in the 'personal finance' section of a HS class would also be low, maybe not for graduating seniors, but definitely for freshmen. Teaching is tricky, my SO is in education and it's not easy. Kids don't tell you things like their hunger issues, romantic issues, home life, etc. They may not even know they are having an issue, young as they are. Hormones are never going to stop making them nuts. Top that all off with budget problems (most US districts have not increased funding since 2008, pop. growth and inflation be damned) and other bureaucratic stuff, and you get a heck of a mess. Staying motivated as an educator is pretty tough, let along inspiring them to be motivated. At the end of the day, the kids are responsible for themselves largely, just like most humans have always been.

I was so pissed in college when I found out that all of those equations we had to memorize in physics were just the integrals.

Why did I have to memorize all that shit if there's a simple way to derive the formula? Jesus.

At my college, there were "calculus based" and "non calculus based" physics classes. It seemed like the calculus based class was a lot easier for just the reason that you state.

I remember the day in my last year in high school, when my physics teacher looked at us with a frustrated face and asked:

"So, you still didn't have derivation in math class?"

We explained, that we will have it in the final month of the school year, if we are lucky. Her reaction was:

"But we kinda need it already. But I should be able to teach you that in 20 minutes."

And she did. And then she spent the rest of the lesson going through some old equations that she might have spent hours explaining: "Remember how long it took us to get to i.e: equation relating gass pressure and temperature? We always used that finicky helper variable. I think I even named it delta. In reality, you just derive this base form, and do a simple substitution."

Ok, my memory is a bit hazy. But she went on and on, through stuff we have been ehm, deriving without calculus for hours, that took with calculus around 3-4 steps.

Coming up with actual uses would have been enormously helpful to me when I was younger. All I was literally ever told was "you need this to pass the exam"

The one thing I really wished I'd have learned more of, younger, is stats. Knowing how basic probability works would have been fantastic - it took a lot of poker theory to really understand it in my bones.

Doesn't Randall xkcd assert that the paramount math problem that most people need to do is how to split the bill fairly when you take your friend out for their birthday?

If you're splitting the tip and the tax, and everyone is pitching in $3 to cover the Birthday Girl, that's more complicated than a lot of those problems they use that nobody cares about.

(In fact, I think if you put all of those math problems in terms of fairness, you'd get more kids to pay attention. Nobody wants to get cheated, and that's what happens when you're bad at math and/or finance).

> I think if you put all of those math problems in terms of fairness, you'd get more kids to pay attention. Nobody wants to get cheated

That's quite insightful! I can think of a few related approaches that could round it out, like frugality (eg. only buy the paint/bugspray/lumber/etc. you actually need for your project), and laziness (do the least amount of work possible that still gets the job done).

Possibly more important is why logically you're not wise to gamble, work out odds and compare them to every day occurrences.

I often think that kid psychology is probably extremely well suited to kinetic problems. Things that involve their own natural desires, all kids want to move, jump, interact with the world. Connect their eagered mind with a way to denote the world and let them abuse math to communicate and reason their own desires.

A kinetic/kinesthetic approach probably would have worked well for quite a few classmates of mine, but definitely not for me. In fact, the only approach that would have appealed to me even less would be musical.

All I ever learned in high school math was isolated "number tricks" that had to be memorized and then performed on que.

Parrots have deeper understanding than was required of us.

I didn't even get a cracker.

But once I needed to use math, it was trivially easy.

This is close to my experience as well. Math, for me, wasn't super difficult, but it didn't necessarily come naturally either, and I got really bored with the tedious, mechanical aspects of it in algebra, college algebra, trig, etc. Geometry and Calc I were mildly interesting, but I was handicapped a bit in Calc I because my basic algebra skills weren't as strong as they needed to be... because I found basic algebra to be mind-numbingly boring.

Fast forward 20+ years and I'm not working on re-learning some lower level math + leveling up on higher level calculus and linear algebra. This time, it seems easier (although I might not go so far as to say "trivial") and I attribute that largely to the fact that I'm much more motivated now. Now I have specific reasons for wanting to learn this math (mostly to do with machine learning and AI) and that seems to make all the difference in the world.

I am in kind of a similar situation. Was never really good or into math during school, been a software developer for 10+ years (mostly backend and web stuff) and at 34 am now working on my calculus and linear algebra after spending some months brushing up my basic algebra skills (which i still do on the side to keep "fit"). I am actually toying with the idea of going back to college to do a Masters in Data Science because i got so fascinated with Machine Learning and AI as well. Soo, you rock, keep it up!

Pro-tip: Make sure to talk to current student outside of the lab space and without the PI around to get the real deal on how useful the classes are.

Seems like both of you are doing what I plan to do once I finish my Udacity SDC Nanodegree course. I've known for a while (ever since AI Class and ML Class in 2011) that I need a refresher and more on math, because ML. This Udacity course just drove it home.

I'm tired of hearing about "take the derivative" and "perform the integral" (or whatever), and not quite understanding it. Heck, just what I wrote probably indicates I don't quite get it!

Also, my intuition on probabilities and statistics isn't there either, so I want to do something to fix that as well. So, when I finally get done - that's my next goal (after a bit of a break).

It isn't that I'm terrible at math, I just never used much beyond basic linear algebra after leaving high school. I never went much beyond high school: I got an associates from a tech school (worthless, since the school is long defunct), and I've taken a few community college courses, plus my online MOOC stuff that's more recent.

I'm not hurting career-wise; in fact, that's never been an issue as a software engineer (started when I was 18, and just kept going, earning more over time and having fun). I'm not doing bad right now, living in Phoenix. It ain't SV - but then again, it doesn't have the downsides of it, either (not that there aren't certain downsides).

Now - after having done MOOCs in ML/AI - I am finding that I need more understanding and intuition about calculus and other mathematical subjects, so I can really apply what I have learned, and understand it at a deeper level, and perhaps do more with it. I've given thought to going back for a BS and maybe an MS (not that I need it - I just want to do it).

Good luck to both of you; I hope it all works out great!

Best of luck to you too! Try taking some community college (CC) courses too. Calc. is not fun or easy, and having a professor to help 'keep you honest' may be very useful in the long term. CCs are very useful for these things, cheap, good schedule for working people, and an attitude of 'here to learn, not to degree'.

I'm not working

should read

I'm now working...

Trig and Simultaneous equations are probably the two parts of high school maths that I actually use on a regular basis.

I don't think it matters what ethnicity or race you are, it's good to be able to actually get things the right length. And it's a lot easier to do it on paper than run around for half a day with a tape measure.

Where do you use simultaneous equations on a regular basis?

Last I used one was for mixing paint. I will admit it's not super regular, but I use them once or twice a year.

I'm an engineer at an industrial plant simultaneous equations are very common in engineering problems. Just about any "optimization" problem can be represented as a system of simultaneous equations even very complex non-linear dependencies are modeled like this.

i.e a common problem such as calculating the optimal blend of fuel in a reactor is done based on solving a system of linear equations with constraints such as Loss on ignition, maximum allowable ash content, minimum specific energy etc.

Industrial design as well uses simultaneous equations extensively. Do you want to build your aircraft wing out of CFRP or a titanium alloy? One way is to use a constraint based selection method something like strength to weight ratio vs cost.

edit: I should add 99% of the time these are solved programmatically with the aid of a computer. You do not solve these problems "high school math style".

Hi Balgair, your comment made my day, i was feeling the same as you at that age.

Glad to have done so!

Word problems: Designed to see if you can recognize numbers in a contrived short story and plug them into the rote-learned algorithm that the teacher just covered. Fun. It seems like if we taught the application alongside the math, it'd be easier to "get" what the math is supposed to represent.

I've been playing with computer graphics recently; I've understood trig for a long time, but this is the first time I've actually felt a need to understand matrices. Exploring applications on my own is the only way that I've really felt connected to math since maybe late grade school or early high school.

First, 16 is still pretty young. Second, just because you didn't have STEM hobbies when you were young doesn't mean you weren't given the framework to excel at STEM. It's not "you learn math or you don't", rather the argument is "you develop the framework for mathematical thinking or you don't".

For what it's worth I also did better with literature and history than math when I was young. Also, I struggled to pass Calculus 2 but breezed through upper level CS courses. It's a very fuzzy thing.

> First, 16 is still pretty young.

Depends on what we are talking about. The post I was responding to was talking about "the first years of education" and with 16, we are way past that.

Nice to hear some sense, I'm surrounded by tiger parents sending their kids to STEM summer camps & after school classes because it'll help them get into MIT or whatever. Its pretty sad as most of them would be much better off if they had some fun and had some friends.

So basically you're saying that it is a preferred solution to teach kids math poorly, let them develop insecurity and aversion towards it and then spent a lot of money to let them overcome it than just do it right in the first place?

Yeah, I know that's not what you mean, but you're missing a point. The premise of the article is that US has a STEM problem. I merely suggested that they're allocating resources wrong to fix it. I didn't mean they should introduce rigor and discipline or increase hours - I said that the best way to achieve results in teaching math is to fix it early, when it's most commonly broken (in my experience).

It actually helps you if you decide to switch interests, because you got the basics right, which in this case is the ability to think in an abstract way.

If you don't agree with me, you should have provided arguments that math problems do not arise early in education system, but they are introduced later.

One last thought - timing _does_ matter. That's why almost every professional athlete starts as a child. The question is how much you gain for starting early and I agree, that it is usually unreasonable to put too much pressure on kids. Pressure is not necessary to fix the system as far as I see it, though.

> So basically you're saying that it is a preferred solution to teach kids math poorly, let them develop insecurity and aversion towards it and then spent a lot of money to let them overcome it than just do it right in the first place? Yeah, I know that's not what you mean, but you're missing a point.

If you knew it's not what they meant then why did you start off saying that's what they meant? If you thought they were missing the point why didn't you just say that?

To better illustrate the point. I actually started with that, decided that it sounds too aggressive and added that paragraph to make that clear.

Went to college with a guy. Freshman year calculus. He was really slow with it. I helped him, and we did homework together. Now he's a math major. Totally surprised me, but he's now majoring in a subject that he wasn't super good at.

People need good teachers at all ages. I'm glad his college professors helped him out enough to lead him to major in math.

Mind and persons are complex, they can shift entirely. I've seen a girl that sucked at math she had to take lessons in HS. In college she flipped around and got a Master in Math.

On my side I was good at math but crashed in college, so much I avoided it, it's the reason I went into programming. Until 2 or 3 years ago I clicked again, I started to see through abstract math and now I'm back to math/phys because it's beautiful again.

If your buddy finds pleasure and can walk the path I'm not surprised he's still walking :)

>That's why almost every professional athlete starts as a child.

Professional athletes are highly competitive. People don't hire basketball players to throw balls into hoops; they hire them to beat other basketball players. Unless you are one of the best humans at basketball, you are worthless as a basketball player.

In almost any profession, you do not need to be the best to have value.

> Honestly, the whole "you need to get them when they are young" idea never convinced me very much. It's never too late to learn a thing and often you need a certain age to actually appreciate something. You don't have to be a childhood prodigy to be good at something.

While starting early is neither necessary nor sufficient for success, the question should be: do the benefits of starting early outweigh risks? Like the parent comment, I think they do, if done correctly and gently, but it should be decided case-by-case for each child. The only risk I can think of is: if you push too hard, it can have the opposite effect of making the child hate it. So, one has to do it with utmost sensitivity and by responding to cues and feedback from the pupil.

I find that a pretty strange approach to parenting. IMO you should optimize for happiness of your child, not for carefully manipulating them into the path you laid out for them. My perception of a good parent is to encourage your child to discover and pursue their own passions, even if they contradict yours. You can open doors, but they need to walk through it by themselves. YMMV.

Huh? Learning can be fun, last I heard. In any case, that's what I meant when I said 'feedback'. Further, there are some skills that are absolutely necessary to learn to function in society, basic math, basic language skills, etc. More important are skills like perseverance, managing one's own emotional well-being, self-control, delaying gratification, etc. It is one's responsibility to at least attempt to teach these to their children.

I was referring to this sentence:

> The only risk I can think of is: if you push too hard, it can have the opposite effect of making the child hate it.

That seems like a weird "risk".

You say you weren't interested in maths when you were young, but were you bad at maths when you were young?

Not being particularly interested and not being taught math is not the same. You probably had normal math just like anybody else and was not behind other people all that much.

But I agree that the tendency of programmers and public to assume that if you already don't know a lot about computers, you are lost case and stand no chance is harmful. There is strong tendency to overstate how difficult things are and that makes people look elsewhere.

Are you also suggesting that we shouldn't teach kids to read until they are in high school and decide they are interested?

No, I'm suggesting that we shouldn't push for kindergarten kids to read and analyze Shakespeare, because reading is so important (and in the process de-emphasize other subjects). I'm saying that the level of math education happening early (though I can only speak for my home country) is fine, just like the level of reading education happening in the early years is fine. It is completely okay to only reach Calculus and math as a structural science in your late teens and believing that you can teach that widely to kindergarten kids just doesn't work out particularly well for anyone.

For me, at least, understanding math was all about understanding how to translate symbols to concepts.

Seeing an integral sign and understanding what it means, for example, can help simplify seemingly complicated mathematical expressions and make them easy to understand.

way I see it, the comment is in writing and at least a bit creative. Its hard to separate language from math and higher learning. Now, psychology is even mor important with regards to learning. In that sense, keep a positive attitude ;)