What STEM Students Need to Know | Hacker News Reader

What STEM Students Need to Know

wsj.com

41 pointsjkuria65 comments

As a student currently in "the system," I think the biggest problem with the math curriculum is that unless you're in an accelerated program, math progress stagnates until seventh grade, where they introduce algebra (way too late imo) and then it stagnates again, repeating the same algebra year after year.

I agree. Colleges and Universities end up teaching basic math concepts and playing catch-up instead of being places of higher education. It must be costly to be keeping this up.

It is costly, which is exactly why Universities and Colleges favor it.

That was my experience as well. In 7th grade I did the Saxon Algebra 1 book, then my school changed curriculum and I spent the next four years rehashing what I'd already learned, excruciatingly slowly, until I took Calculus senior year.

There was a lot of dicking around with TI-83 calculators, and drawing graphs to solve equations, which frustrated me since I'd already mastered the symbolic manipulation to do it faster and more easily.

Algebra directly to calculus? No trigonometry, geometry or statistics?

Do you need statistics in order to do calculus? They seem independent. I didn't do much statistics at high school because it didn't interest me as much, but I did calculus.

In fact you'll find more applications of calculus in statistics than statistics in calculus won't you? Seems the wrong way around to do statistics first.

As I recall, my statistics class used calculus, at least for some of the proofs and derivations.

I think they are independent, I never took stats but took calculus in high school :)

Just seemed surprised that OP seemed to imply his high school offered only two courses... Algebra and calculus.

Mine offered algebra 1,2, stats 1,2 geometry, trigonometry, Calc 1 and 2.

Of course also pre algebra if you didnt take that in middle school...

Most of geometry and trig was covered in that algebra textbook. The rest, I picked up more from shop and programming classes than I did from my high school mathematics courses; trig is incredibly useful for e.g. planning out rafter designs for building construction, and when the programming environment you are using for graphics consists primarily of poking pixels, and doing collision tests by hand, you become very familiar with geometric equations.

Stats remained something of a blind spot.

When I went through middle/high school about a decade ago, the curriculum for honors students in Texas was: algebra in 7th/8th grade, geometry/trigonometry in 9th grade, pre-calculus (aka calculus lite) in 10th grade, advanced algebra 11th grade, and in 12th grade you had the option to take calculus or statistics (or both).

From my experience, at least, my math education was astoundingly good. I went to a top 50 US university and immediately went into advanced math classes my freshman year and felt fine. The problem, though, is that I followed the "honors student" curriculum. The "regulars students" curriculum didn't include advanced algebra, calc, or stats, and the quality of geom/trig/algebra education that was included wasn't that great.

Another problem is that this was just my experience in Texas. Other states have different curriculums, which makes the whole exercise of saying "education in the US is ____" very difficult.

I remember I wold finish my 5th and 6th grade math tests in 10-15 minutes out of the allotted 60, because the problems were so easy and challenging myself to go as fast as possible was the only way to not be bored.

I'm grateful of my math teacher for both those years for not reprimanding me for my brashness and encouraging me to solve number puzzles (one of those 0-9 tile sudoku-like things with math equations on laminated paper) for the rest of the period every time. RIP I was lucky to have you.

It's funny because in the real world, if the test was a project and you find is he'd in 25% on schedule. You would keep your job and others get fired. But in school, if you go a 100% in 15 minutes and another kid 90% in 60 minutes... You get the same reward. An A.

In the real world the kid who got 90% in 60 minutes becomes your manager when he realizes he's better off managing people than writing code.

The fundamental problem is that the US teenager has too much homework. You can like cut it in half and it won’t make a difference (look at like Finland). The gained time can be then spent on hacking and exploration.

Hmmh, really? I thought they spend 6 hours on social media and another 4 hours watching TV? :)

or similar hours on games especially for boys. the smart phone is taking a toll on teenage daily.

Without PC gaming and getting into modding as a teenager, I'd have never become a programmer. Not to mention all the experience unborking computers after trying to install something trashed the system. Or the history and geography I picked up by osmosis playing strategy games.

Those hours were much more valuable in the long run than most of the time I spent in the classroom.

Modern mobile/social games and even some PC games are pretty locked down and difficult to mod, which makes them way less educational than the PC games of your time.

I'm sort of glad that my parents never got me and my sister any game consoles; we had the PC for my mother to write test reports, and do the taxes, and type up my father's logging invoices. Consequently, I had the advantage of getting to frig around a lot with getting games to run, and with PC games that had a thriving, if rough-around-the-edges modding scene.

I don't think I would have gotten anything like the same learnings if I'd been playing on a SNES or Genesis, vs a Pentium clone. Not to mention the dramatic skew in the kinds of games that are available on the different platforms.

Yeah so what?

I think there is no standard for amount of homework. Amount of assigned homework mostly depends on the teacher. Students can choose electives which does provide some control over the total amount. From what I can remember amount of homework per-class features heavily on teacher review sites (ratemyproffesor.com).

I was a B student in a Russian school from 1 to 8th grade and started in an American High School in 1999. If you factored in ungodly amount of mandatory summer break reading everyone had to do in Russian schools, you'd probably end up with 3 times the material covered in a span of a year compared to American schools. This basically allowed me to just coast through all 4 years of High School with all kinds of stupid awards and a GPA of 4.0. The same amount of effort would've probably turned me into a dropout back in Russia. Kids here don't learn anything and I think lack of quality material both in and outside of school is to blame. Ironically, I hear they don't learn much in Russian schools either these days.

These anecdotes from smart foreigners contemptuous of Americans never make any sense against the stats. White Americans outperform all of them in the PISA tests. America only performs poorly in the PISA tests when you don't exclude non-whites.

Non-whites are Americans too, and I don't see a reason to exclude them. The fact that non-white students perform so poorly as to drag down the average so much speaks of a massive systematic failure in education.

If whites have high test scores while non-whites don't, it might mean that the system does work for some groups, but not for others. This indicates as problem not with the curriculum, but rather with the way the curriculum is "distributed" (aka: the massive disparity between schools in wealthy areas vs poor urban areas).

This is a pretty important distinction to make, given that this entire discussion is regarding the content of the curriculum.

The system works for all groups. Russian-Americans outperform Russians. Nigerian-Americans outperform Nigerians. And so on.

There is ultimately a problem of the students involved that is not going to change on the scale of a single generation or two. Across multiple generations of concerted effort, who knows. But ignoring what might be 200 years from now the American education system actually works pretty well.

It's not the case. Citation another commenter posted

https://isteve.blogspot.com/2013/12/overall-pisa-rankings-in...

I fail to see how "it's not the case". That link very clearly shows that White Americans and Asian Americans vastly outperform African Americans and Hispanic Americans.

Asian Americans are #4 on that list and White Americans are #16, bested only by a handful of Asian and European countries that are notorious for their stellar education systems. Meanwhile, Hispanic Americans are around #50 and African Americans around #60 on that list.

Your original comment said

"If whites have high test scores while non-whites don't"

Whites do not have the highest test scores. Are you implying Asian Americans live in wealthier areas than whites?

Based on your link, it very clearly shows that some groups in America excel in America's education system while other groups don't. I'm not sure why you're so intent on splitting hairs about that.

By the way, yes, Asian Americans typically do live in higher-income areas when compared to other racial groups in America. Very few Asian Americans live in rural areas or in states that are known to have poor education distributions (eg deep south). Asian Americans overwhelmingly live in LA, NYC, Massachusetts, Dallas, Houston, or the Bay Area, which are certainly more "wealthier area" than places like rural Alabama, West Virginia, or Montana where poorer whites live. Asian Americans have the highest income levels out of any racial group in America.

See: https://en.wikipedia.org/wiki/Demographics_of_Asian_American...

Considering that racial difference in learning outcomes is due to socioeconomic status, if you are going to use socioeconomic status to normalize or filter American results, shouldn't you also do it for the country you are comparing it to? I am sure if you exclude poor people from the results of every country (or use a proxy for poverty like race in America; perhaps religion, ethno-linguistic background, geographical location, etc in other countries) the results for all of them would significantly improve. It's not fair to compare rich people from country A with the average of county B.

> Considering that racial difference in learning outcomes is due to socioeconomic status

Citation required

For what it's worth here's a citation proving counter to the statement...I stole from another commenter.

https://isteve.blogspot.com/2013/12/overall-pisa-rankings-in...

As someone who grew up in a poor immigrant family where the first generation was uneducated and spoke no English...I always find it insulting when low education is attributed to not having money. Not just myself as a counter anecdote, but 10 out of 11 of us second generation have college degrees and doing pretty darn well for ourselves . #11 is still in college.

Just goes to show you that school smarts don't make a successful nation. It takes a cohesive people and cultural heritage. This is why immigration is such a huge problem. I don't care how smart and high earning and proud of themselves the foreigner in question happens to be. These people are a huge problem for our future. We got where we are in substantial part on the basis of our culture and self respect. We can do without the snide foreigners. They should leave.

After all, You're here. I'm not making derogatory and chauvinistic comments in your country.

I gave you the benefit of the doubt for your earlier comment that is now clear was undeserved. So your solution for the failure of the American education system is that non-white people (whom you call "snide foreigners") should leave?

I'm addressing the very, very common phenomenon of post-Soviets, Indians, and East Asians coming here to a country superior to their own in almost every measure and talking smack about how dumb we all are here, with little basis in fact. They should lose the chip on their shoulder, realize they come from flawed countries and flawed cultures, and see the relative superiority of the one they elected to emigrate to. After all, I'm not the emigrant being snide in a foreign land. I've lived overseas extensively and was always respectful and learned a lot. These newcomers should learn to salute Old Glory and cheer or they should go home.

Good luck going to China (where the other fellow apparently ethnically originates) and talking about how dumb they all are online and how much smarter westerners are. They have an insane and violent sense of chauvinism. I merely hope to instill a sane level of chauvinism in Americans who read disparaging foreigners.

Wow that went south fast.

> For what it's worth here's a citation proving counter to the statement.

Does it? It seems to support my view. Your link shows that in PISA rankings by race in America are in this order:

1. Asian Americans

2. White Americans

3. Multiracial Americans

4. Hispanic Americans

5. African Americans

Ignoring the multiracial category, because I couldn't find a source that included this category, that is exactly how median income differs between races in the US, i.e. Asian Americans have a higher median income that White Americans who have a higher median income than Hispanic Americans who have a higher median income than African Americans [1]. How exactly does this disprove my statement? And what exactly is insulting about saying education outcomes are related to socioeconomic status?

[1] https://en.wikipedia.org/wiki/Household_income_in_the_United...

The heresy is probably that the higher median income, which correlates with higher test scores, are both caused by another underlying difference. I really haven't decided whether that is culture or genetics, but there's something there.

Your second sentence is clearly not accurate, especially for math:

https://isteve.blogspot.com/2013/12/overall-pisa-rankings-in...

The Sino nations completely game these tests. Japan is legit. The Baltics are legit. The high entries for China et al are total nonsense and should be struck from the list. They game who takes the test, and it's not tightly observed.

The purpose of the link I think is not about other countries but the subset between Asian Americans, white Americans, multi racial Americans and other races.

White and multi racial are very similar. Asian Americans are much higher. Unless you think the Asians Americans in America somehow game it...

That is often claimed without much evidence. Any citations?

Singapore, Korea, Taiwan, for example are well known for their technical capabilities, which correlate well with the PISA scores.

The link I posted refutes the GGP’s second sentence regardless of which countries have a higher score since there are quite a few of them in several geographic regions.

> White Americans outperform all of them in the PISA tests. America only performs poorly in the PISA tests when you don't exclude non-whites.

I'm not sure that's a good metric of overall literacy levels in the country. Additionally, I think Soviet-era education, which expired around 2002, always stacked up pretty well to other leading countries.

> These anecdotes from smart foreigners contemptuous of Americans never make any sense against the stats.

It doesn't seem unlikely that smart foreigners might be placed in schools with other smart kids in their home country, while getting placed in schools with average kids in the US. As a smart white American who went to an unselective American college, it was certainly easy to learn contempt for the abilities of the students there.

Math in the US needs a revamp. Kids get the notion early on that math is some sort of ominous monster ready to devour their time and grades. It has a bad rap, and this keeps people from getting into it early on.

What we need is someone to "popularize" math in a genuine and non-patronizing way. Say what you will about Bill Nye/Neil DeGrasse Tyson/Carl Sagan/Issac Assimov, but they've been incredibly successful at introducing advanced scientific concepts to a wide audience.

Math needs these same kinds of "popularizers". Not only to introduce interesting topics, but to validate and remove the stigma surrounding math in the US.

I also have noticed that math and language learning are viewed by many people in the US as something that's not even worth trying because it is too hard. Pretty sad and I think this will hurt the country big time later. You can't run a country with only extrovert MBAs and lawyers that manage foreign immigrants.

The grand experiment is in progress.

Vi Hart is an amazing math communicator, and is a model of what teaching math in fun, hands on, intuitive ways looks like.

I’d pay a lot of money to see what she could do with a full television crew to produce a PBS style math show.

https://youtube.com/channel/UCOGeU-1Fig3rrDjhm9Zs_wg

From an early age math was a puzzle and game for me, and it was fun to solve these puzzles. It'd be nice if we can somehow get that perspective into the classroom.

USA had Martin Gardner. Ironically, I got so much of my love for math from reading his books, translated to Russian.

My wife runs an after school learning center. She has had parents withdraw because they would rather their kids spend more time practicing sports. She's also had parents complain that their kids aren't being progressed fast enough or gets too much repetition - then she has to give an analogy that their child understands some of the concepts, but not all. And just like a basketball shot, I think you need to practice till you can do it perfectly, under pressure...not just once in a while during practice. A 70% might be passing in school but not here, and not in the real world.

If only parents made sports as "cool" as sports.

I'm sorry but if parents don't take the responsibility to make education a high priority for their kids then they are failing their kids. Parents are the kids biggest role models and they should be the ones to "popularize" whatever is necessary to change behavior. Whether it's math, or not doing drugs.

observing as a parent, who was educated outside of US, but whose children are attending a well-rated US public school 8th grade:

  (a)  my child is an 'A' student (getting over 92% on most tests)

  (b) the student cannot do basic algebra without help.
  
  For example cannot convert   a^2 + 2ab + b^2 , back into

(a+b)^2

  Does not even know what a geometric proof is.

Eg. proving that 2 triangles are equal when each of their sides is equal, would be way beyond any knowledge that was presented in school.

  (c) Can do many simple problems 'quickly' and efficiently.

  However, cannot even approach a problem that should take say a genuine 1-2 hours. I am not even talking about more complex ones.


  So the whole way of thinking about Math (and science subjects)  -- is targeted towards 'secretarial/data entry' kind of activities.

  Quick tricks, filling in blanks, fitting answers...

  There is a complete lack of homework problems that require a creation of any kind of approach/ thought framework...

(and then testing out that creation).

  Instead, they are overwhelmed with huge number of simple stuff.

  But, as I know form being in the industry, 
  it is that kind of job skills that being replaced by computers, or outsourced...

  (d) Student is trained (or may be brainwashed) to think that material in school and good grades -- is not just necessary, 
  but absolutely sufficient 
  (with exception of social work and leadership skills... always can do more of those...)

So the resulting mind set is:

  If I get good grades, and if I am tired and busy with

all the homework -- then that's a sufficient indicator that I am doing exceptionally well.

This makes it very difficult, almost impossible for a parent to penetrate through this wall, (plus the social media, and peer-pressure cancers that constantly compete with me for influence on the child).

  I feel like my kids are just being treated as 'head count', in some 'feel good' & 'reward for participation' virtual video game,
 whose purpose is to create a fake reality,
 to reduce their chances of being competitive,
 ... and I cannot do anything about it.

Apologies if I sound too frustrated.

Your post reads like notes for a Black Mirror episode. :(

That's super weird. In eighth grade (2013-ish, not long ago) we had an entire course on geometry that was all about proving theorems and turning some given information into "the shape satisfies the definition of a parallelogram because..." The tests were exactly what you described you wanted: hour long journeys where you applied the theorems and postulates we learned up to that point to prove something about a shape. I struggled a lot but ultimately I believe I am better at thinking because of it. If you want some books:

The textbook we used: https://www.amazon.com/Geometry-Ray-C-Jurgensen/dp/039597727...

The Art of Problem Solving: https://www.amazon.com/Art-Problem-Solving-Vol-Basics/dp/097...

AoPS is pretty good but more geared toward math competitions. The reading is ok but the problems take some serious thought and if you can get your kid to do one a day s/he'll probably be better off for it.

https://archive.is/3HgG5

How do you get past the paywall?

Typically, you pay.

I have a 'Via Facebook' bookmarklet. Something like this uri saved as a bookmark:

    javascript:window.location='https://facebook.com/l.php?u='+window.location

Will redirect you to your current page via the Facebook link service (and thus with a FB referrer). Most publishers are too desperate for traffic to block FB.

If you go to my site[0] in Chrome or Firefox, you can easily install such a bookmarklet by dragging the giant 'Via Facebook' button to your bookmarks bar.

[0] https://emidln.com

not only that but the referrer 't.co' (twitter's url masking service) also bypasses the paywall. it also works for any other dow jones site and sometimes FT if you block cookies

Accessing the WSJ article using incognito mode and a referral from Twitter seems to work.

https://t.co/x7QwmhkWO7

Easiest way: post URL to the article in twitter and then click link from that new twitter post.

Help with the paywall?

This article is full of funny things. If you want to teach people Computer Science just teach them Computer Science. Why waste people's time with math they will push out of their minds as soon as they're finished with the class? I wish we had a specialization-based curriculum for high school. I wasted a lot of time there that I could have spent learning more.

Some funny things in the article:

> Discrete mathematics deals with such problems as...

No it describes solutions to those problems. You could also describe those solutions with other types of math. A computer Scientist wouldn't think of this problem in terms of a formula first. They would likely think of this in terms of a Data Structure and thing about the most efficient way their representation's strengths can be leveraged to obtain a solution.

A "calculus-track" Mathematician may think of this as a shape and attempt to frame this problem as an equation that describes the changes occurring in a subset of the problem. Luckily 3B1B just posted a video demonstrating this: https://www.youtube.com/watch?v=VvCytJvd4H0

> Students need classical math more than ever.

I'd say this is debatable. What's the work/value trade off for teaching someone calculus? I just aced my college's calc program and I've already pushed that crap out of my mind.

I'd say it's much more important to be able to learn how to do these things as needed. Learn how to pick up a book, find the chapters you need to read, read the material, apply it, and test your output.

> But discrete math is fundamental to computing and ubiquitous in the real world

I'd say it's not the only way to express those ideas.

> To understand software, you need a basic understanding of computers; for that you need some basic electronics education. [...] There are many ways to build a von Neumann machine—the world’s standard digital computer since World War II...

Lol. Who wrote that in the press release? I'd consider many micros with in-chip roms as Harvard architecture.

I'm getting ready to laugh at the development and implementation of Common Core 2.

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