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Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last on

Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I never had any problems with math until I went to university, so I was merely a passive observer of everyday struggle for some people. I honestly believe that foundations are the key. Either you're taught to think critically, see patterns and focus on the train of thought, or you focus on numbers and memorization. The latter obviously fails at some point, in many cases sufficiently late to make it really hard to go back and relearn everything. Math is extremely hierarchical and I believe schools do not do enough to make sure students are on the same page. If we want to fix teaching math, I would start there, instead of working on motivation and general attitude. Those are consequences, not the reasons.

sixo 9y ago
Not sure it's exactly the early years. But I think there's zero point to moving past a topic until you have mastery & can think WITH it (not just, about it, or hack through it on paper). And since the early years are often where that fails, they need to be rethought.
- jamesrcole 9y ago
  I remember listening to an episode of The Science Show podcast where the guest was arguing (based on their experience) that chemistry and physics concepts should be taught to young children as it's actually easier to teach it to them. With the stated reason being that if they're taught it at a later age, as they are now, they've already built a view of the world where those concepts are somewhat unintuitive. If they learn the concepts earlier they are more easily absorbed. I found their point fairly compelling, and I wonder if it applies to mathematics as well. The episode was http://www.abc.net.au/radionational/programs/scienceshow/young-kids-lap-up-molecular-structure-and-the-periodic-table/8405686 http://www.abc.net.au/radionational/programs/scienceshow/you...
  - alasdair_ 9y ago
    One of the most fun things I ever did with my five year old son (now six) is build a cloud chamber with dry ice and a fish tank and talk about it. Strongly recommend.
devmunchies 9y ago
school teachers, administrators, and legislators most likely did not do STEM, so that pattern will most likely continue.
kungito 9y ago
To this point, I have been doing a plenty of 1on1 lessons with kids trying to catch up with Math in high school/college/matura exams and one this I have noticed is that things which are problematic to these people are things which were covered quite well already in elementary school. Later the curriculum only expands on these problems so it's even harder and harder to catch up. I have been working with college freshmen struggling with basic linear equations and such. While the profession is marginally unrelated to Math (e.g. Graphical Designer), I still wonder to this day how people can have 20-30-40 years and not know how they could (with a calculator in their hand!!) calculate the price after the discount. How can someone feel ok with this?
- ashark 9y ago
  Schools (at least around here) do not hold kids back anymore. No matter what. Some of them get behind in one or more subjects (math, say) as early as 1st or 2nd grade and all their later teachers are stuck trying to give them the remedial math help the desperately need, while teaching their other students on-grade-level material, and also trying to teach the remedial kids enough of the new stuff that their scores on that year's standardized test don't land the teacher in hot water (though the kids won't get it at all). The result is that the kids fall farther behind every year but keep failing up to the next grade. They'll enter e.g. 6th grade with ~Dec. of 3rd grade math skills (more often than not their other subjects aren't much farther along, though not always). If they get an LD diagnosis they'll get some extra help but by then it's too late. It sucks for all concerned.
  - throwawayjava 9y ago
    Tying students' progress through the curriculum to their age is silly. If you think about it for a single second, the whole thing is totally absurd. Vague pre-puberty/tween/teenager distinctions make sense, but within each grouping/building? totally unmotivated. Yearly age-to-competency distinctions continue by sheer force of tradition, and are harmful to all but the totally mythological "average" student.
    - 9y ago
Ntrails 9y ago
> I never had any problems with math until I went to university So, here's the thing. Did I have no problems with math until uni because I'm smart? Because I have a specific type of brain? Because of my upbringing? Because I had very good education in my early years? Some combination of the above? I struggle to believe that people can't do algebra. I am convinced that with some thought and help they'd find it trivial. However, is that my own experience overriding my ability to take their perspective as true? I dismiss "I can't" as "I don't think I can", but who am I to judge that better than them?
- jharger 9y ago
  I saw what looked like this sort of thing with my daughter. She struggled in her high-school algebra 1 class, but whenever I would sit down with her and she would work out problems, she had no trouble (but she also had no confidence that she could do it).. She ended up having to repeat the class, which ruined her confidence even more, and she hated it even more the second time through. At the start of middle school, her teachers were recommending accelerated math classes, but she never ended up doing that, because she stopped liking math and stopped trying. Why? Maybe because it was unpopular or she didn't like her teacher... I don't know. In any case, she went from kinda-liking math to completely hating it over the couple of years, even though when I was there, she seemed to understand it just fine.
  - throwawayjava 9y ago
    Encourage her to give it another try when she gets to late high school or college. I know a lot of math phds who fell out of love with math around middle school and then fell back in love during their first proof-based course in college.
    - BeenThere888 9y ago
      Yeah, this. I hated math in middle-school and early high-school. It was boring and rote. But proofs based math, and learning how to think of math as a language, instead of a collection of overly specific "solutions" crammed into my head by teachers, was the key.
jacobolus 9y ago
Absolutely. See Toom (2010) Word Problems in Russia and America, http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pdf http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pd...
taco_emoji 9y ago
I think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables. Think of stuff like the quadratic equation, or formula for the surface area of a cone. How many of us were just taught these magic formulae without first deriving them? Why do we start talking about pi without first explaining how it's calculated? Where does the "four-thirds" part come from in calculating the volume of a sphere? Not to mention that there's never enough history to go along with the mechanics - who discovered the quadratic formula? What was their life like? Why were they playing with quadratic equations in the first place? This make math seem less like magic incantations and more like something that was sort of cobbled together by flawed weirdos in order to solve real-life problems, and evolved over time.
- bitwize 9y ago
  > I think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables. This was tried. It was called "New Math". Spectacular failure. Do you want to know what worked? Memorizing times tables. There's just no way around the fact that drilling is key to early mathematical learning.
  - acjohnson55 9y ago
    It's way too early to judge "New Math" to be a failure. I think the idea of focusing on concepts over computation 100% in the right spot. The biggest problem to its acceptance is cultural. Parents don't feel comfortable with math concepts, and in my opinion, most of the negativity is coming from that insecurity. So they demand for things to be taught the "old way", even though that's produced a generation or two of mathphobic Americans. EDIT: As pointed out, I mistook OPs invocation of New Math to be talking about the much maligned Common Core rethinking of math education. I was briefly a high school math teacher, but before the roll out of these changes, so I can't comment first-hand on what the new curriculum looks like in the actual teaching. But I do know how poorly prepared my students were for math beyond arithmetic. They were trained with similar curriculum that I had experienced growing up in the 90s, which I think is poorly thought out. Apologies for the confusion caused by me not recognizing the term New Math.
joe_the_user 9y ago
I don't really think the situation in the article is directly about people not being skilled in math. It's about math-phobia with it's after-affect of people not having skills in math. It seems like an especially American thing - being good at math makes someone a freak and so it's something kids actively avoid at the ages in which being a freak is not tolerable. That kind of attitude would need to be actively confronted because what happens is that kids who previously were developing skills tend to drop out given the peer-pressure. Edit: best documenting link I could find but Google book won't let me copy a quote: https://books.google.com/books?id=CzmpDAAAQBAJ&lpg=PA74&ots=CI694iHhym&dq=math%20achievement%20for%20american%20european%20women&pg=PA74#v=onepage&q=math%20achievement%20for%20american%20european%20women&f=false https://books.google.com/books?id=CzmpDAAAQBAJ&lpg=PA74&ots=...
- SubiculumCode 9y ago
  I blame TV in the 80's and 90's..and to today. The smart kid is the dorky, beat up kid. The dad is usually a guy who thinks he can figure stuff out and repair stuff, but hes wrong and just breaks everything.. better just buy it at the depot. Our media praises stupidity
swiley 9y ago
>I never had any problems with math until I went to university, so I was merely a passive observer of everyday struggle for some people. This is the opposite of my experience, I did horribly in math and hated it until I took calculus (which, I guess I should have taken in highschool but I tried to avoid it since the rest of math sucked.) EDIT: just want to clarify: I did have a reasonably intuitive understanding the whole time, the earlier stuff just felt like busy work.
- d3ckard 9y ago
  I couldn't develop internal understanding of calculus, so while solving the equations wasn't that hard, I never felt really comfortable with it. Discrete mathematics - total opposite. Proofs were very intuitive to me.
Merovius 9y ago
> Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I indeed believe you are wrong. I started getting interested in STEM when I was 16 and now have a masters in math on the one hand and work for one of the most prestigious Tech firms in existence on the other. Meanwhile, when I was young, I was encouraged to enter creative fields (mostly writing in my case) which I did have enthusiasm for but then dropped as a teenager. So I switched at least twice, what I wanted to do with my life and still turned out fine. 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. I rather find the idea pretty harming; I've met a lot of people who did not pursue the career they wanted, because they bought into the myth, that you need to start programming at 6 to get a job at a company like Google or Facebook. Let kids be kids for a while. Don't worry, they can always figure out what they love later and it's never too late to reconsider.
- shas3 9y ago
  > 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.
  - Merovius 9y ago
    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.
greenmana 9y ago
If I was to review (CS-related) math after a break of many years, what would be a good starting point? High school math? Discrete math? What are the foundations and the path like for the stuff more closely related to algorithms and core CS stuff?
- aphextron 9y ago
  https://en.m.wikipedia.org/wiki/Concrete_Mathematics https://en.m.wikipedia.org/wiki/Concrete_Mathematics
  - iclouddrive 9y ago
    https://www.csie.ntu.edu.tw/~r97002/temp/Concrete%20Mathematics%202e.pdf https://www.csie.ntu.edu.tw/~r97002/temp/Concrete%20Mathemat...
gdfer 9y ago
I wouldn't make math/STEM a special emphasis when they're young. It's more important to foster an positive learning environment and encourage/draw out curiosity and creativity at this age. Help them become curious about the world, fascinated with what they're learning and find enjoyment in learning. In terms of subjects, aim for a strong reading focus at an early age as it will pay dividends in all other subjects (even math) if they can read/comprehend well.
- sekou 9y ago
  Salman Khan's One World Schoolhouse does a good job exploring this topic I think. On the one hand many students struggle with what he calls a "swiss cheese" understanding of math: lacking mastery of fundamental concepts that leads them to struggle as they grow older. On the other hand he advocates for a more holistic approach to learning overall from the beginning, exposing children to various subjects and exploring how everything is connected.
WalterBright 9y ago
> memorization I clearly recall memorizing the times tables when I was young. It suddenly dawned on me that "times" wasn't just a word, it meant adding the number so many times. I no longer needed to memorize the table, I just applied the rule. Some university engineering classes present formulae and tell the students to just apply them. This is disastrous in my not-so-humble opinion. Where the formula comes from should always be taught, so students understand the formula and the assumptions it was derived from.
paganel 9y ago
> By the time people go to high school it is to late Just anecdotal evidence, I know, but for me it was the exact contrary that happened. As a 5-year old kid I had learn to read all by myself (my dad had taught me to recognize the letters and how to pronounce them), but I had huge conceptual difficulties in teaching myself things like subtraction (what do you mean you can take/subtract a thing from another thing? what happens when the thing which you're taking/subtracting is bigger than the thing from which you're subtracting? you cannot do that, it would result in a non-thing, a thing that is below 0, and all things below 0 technically do not exist). In elementary and middle-school I was passable in maths, while very good in humanities, but all this changed in high-school, mostly because of my teacher, who taught me (and my colleagues) how to think about math. He's one of the reasons why I decided to pursue a STEM education and why I'm currently a programmer.
munchbunny 9y ago
I disagree that you have to get them young... but I do think that math classes need to start involving proof-based work rather than calculation-based work by the time students hit middle school because it's such an explicit exercise of critical thinking muscles. Recalling my own experiences with middle school and high school, I saw my peers frequently fall into the trap of trying to memorize pipelines of steps while we were learning algebra, geometry, trig, pre-calc, and then calculus. The ones who "didn't get it" would fall apart to varying degrees when confronted with problems where you had to think in terms of combining toolboxes of strategies to unfamiliar but analogous patterns, but I don't necessarily think it was their fault, because they didn't know better and rote memorization had worked consistently until this point. I often feel a bit sad about it because I did a ton of proof based stuff outside of class (as a mathlete), and that was a HUGE part of my development in logical reasoning, intellectual rigor, and critical thinking.
agumonkey 9y ago
My experience differs. My brain was intuitively ok until high school. The abstraction shift around cross references between log / exp / S 1/x went right above my head; same for discrete math basis such as prime relationships. My conclusion is that every one will have strong and weak spots, and it's very important to stay alert to this and not beat around the bush thinking it's not important. Took me more than a decade to get back into intuitive thinking, where you can play mentally with symbols and ideas just like LEGOs (as I was around high school).
wisty 9y ago
"School is about the advanced stuff, not the basics" is the call of good students, often ones who learnt the basics from their parents. It's also kind of popular with bad students, who think that they might suck at the basics but have untapped powers if they were doing something else. It's nice, vague, and populist. Everything thinks they know how to do critical thinking. Everyone thinks they know how it could be taught. I suspect most people think that they have above average critical thinking skills. As long as they don't have to agree on how or what critical thinking is, everyone can agree it's a good thing. The other one that's dumb is "you learn best when you teach yourself". Sure, if you are really super-interested in something then you learn better, and tend to teach yourself a bit, but correlation is not causation.
findoer 9y ago
Anecdotally, I am also not in agreement with you on this. Another poster mentioned not 'getting' algebra until 10th grade--this didn't happen to me until roughly my second year of college. Anyway, I eventually became very motivated to excel at math. I ended up changing majors, transferring to a school with a more serious math program, and doing so well under a very heavy courseload that I won some department honors and scholarships. I basically went from not knowing high school (middle school?) algebra to demolishing my Rudin course in about 3 years. Honestly I think most people could do this and probably a lot more if they had the desire and access to a university/books
deleted 9y ago
[deleted]
bagacrap 9y ago
I was always relatively at ease with math even though throughout lower education it was mainly about memorizing rules or formulas. In college it became about proofs, which was a completely different ball game and not something I'd been prepared for from preschool. To me the real important thing is the attitudes imparted by your parents and peers. As noted in the article, it's acceptable to fail at math. Parents who have their own history of math anxiety probably don't really push their kids to excel in that field. Just the notion that I was expected to "get it" and keep trying until I did (perhaps helped along by some natural stubbornness) may have made the difference in my case.

sixo 9y ago

Not sure it's exactly the early years. But I think there's zero point to moving past a topic until you have mastery & can think WITH it (not just, about it, or hack through it on paper). And since the early years are often where that fails, they need to be rethought.

jamesrcole 9y ago
I remember listening to an episode of The Science Show podcast where the guest was arguing (based on their experience) that chemistry and physics concepts should be taught to young children as it's actually easier to teach it to them. With the stated reason being that if they're taught it at a later age, as they are now, they've already built a view of the world where those concepts are somewhat unintuitive. If they learn the concepts earlier they are more easily absorbed. I found their point fairly compelling, and I wonder if it applies to mathematics as well. The episode was http://www.abc.net.au/radionational/programs/scienceshow/young-kids-lap-up-molecular-structure-and-the-periodic-table/8405686 http://www.abc.net.au/radionational/programs/scienceshow/you...
- alasdair_ 9y ago
  One of the most fun things I ever did with my five year old son (now six) is build a cloud chamber with dry ice and a fish tank and talk about it. Strongly recommend.

devmunchies 9y ago

school teachers, administrators, and legislators most likely did not do STEM, so that pattern will most likely continue.

kungito 9y ago

To this point, I have been doing a plenty of 1on1 lessons with kids trying to catch up with Math in high school/college/matura exams and one this I have noticed is that things which are problematic to these people are things which were covered quite well already in elementary school. Later the curriculum only expands on these problems so it's even harder and harder to catch up. I have been working with college freshmen struggling with basic linear equations and such. While the profession is marginally unrelated to Math (e.g. Graphical Designer), I still wonder to this day how people can have 20-30-40 years and not know how they could (with a calculator in their hand!!) calculate the price after the discount. How can someone feel ok with this?

ashark 9y ago
Schools (at least around here) do not hold kids back anymore. No matter what. Some of them get behind in one or more subjects (math, say) as early as 1st or 2nd grade and all their later teachers are stuck trying to give them the remedial math help the desperately need, while teaching their other students on-grade-level material, and also trying to teach the remedial kids enough of the new stuff that their scores on that year's standardized test don't land the teacher in hot water (though the kids won't get it at all). The result is that the kids fall farther behind every year but keep failing up to the next grade. They'll enter e.g. 6th grade with ~Dec. of 3rd grade math skills (more often than not their other subjects aren't much farther along, though not always). If they get an LD diagnosis they'll get some extra help but by then it's too late. It sucks for all concerned.
- throwawayjava 9y ago
  Tying students' progress through the curriculum to their age is silly. If you think about it for a single second, the whole thing is totally absurd. Vague pre-puberty/tween/teenager distinctions make sense, but within each grouping/building? totally unmotivated. Yearly age-to-competency distinctions continue by sheer force of tradition, and are harmful to all but the totally mythological "average" student.
  - 9y ago

Ntrails 9y ago

> I never had any problems with math until I went to university So, here's the thing. Did I have no problems with math until uni because I'm smart? Because I have a specific type of brain? Because of my upbringing? Because I had very good education in my early years? Some combination of the above? I struggle to believe that people can't do algebra. I am convinced that with some thought and help they'd find it trivial. However, is that my own experience overriding my ability to take their perspective as true? I dismiss "I can't" as "I don't think I can", but who am I to judge that better than them?

jharger 9y ago
I saw what looked like this sort of thing with my daughter. She struggled in her high-school algebra 1 class, but whenever I would sit down with her and she would work out problems, she had no trouble (but she also had no confidence that she could do it).. She ended up having to repeat the class, which ruined her confidence even more, and she hated it even more the second time through. At the start of middle school, her teachers were recommending accelerated math classes, but she never ended up doing that, because she stopped liking math and stopped trying. Why? Maybe because it was unpopular or she didn't like her teacher... I don't know. In any case, she went from kinda-liking math to completely hating it over the couple of years, even though when I was there, she seemed to understand it just fine.
- throwawayjava 9y ago
  Encourage her to give it another try when she gets to late high school or college. I know a lot of math phds who fell out of love with math around middle school and then fell back in love during their first proof-based course in college.
  - BeenThere888 9y ago
    Yeah, this. I hated math in middle-school and early high-school. It was boring and rote. But proofs based math, and learning how to think of math as a language, instead of a collection of overly specific "solutions" crammed into my head by teachers, was the key.

jacobolus 9y ago

Absolutely. See Toom (2010) Word Problems in Russia and America, http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pdf http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pd...

taco_emoji 9y ago

I think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables. Think of stuff like the quadratic equation, or formula for the surface area of a cone. How many of us were just taught these magic formulae without first deriving them? Why do we start talking about pi without first explaining how it's calculated? Where does the "four-thirds" part come from in calculating the volume of a sphere? Not to mention that there's never enough history to go along with the mechanics - who discovered the quadratic formula? What was their life like? Why were they playing with quadratic equations in the first place? This make math seem less like magic incantations and more like something that was sort of cobbled together by flawed weirdos in order to solve real-life problems, and evolved over time.

bitwize 9y ago
> I think math education needs to be reworked from top to bottom to focus more on building blocks. E.g. I'm not sure there's enough focus on what multiplication is before you're expected to memorize the times tables. This was tried. It was called "New Math". Spectacular failure. Do you want to know what worked? Memorizing times tables. There's just no way around the fact that drilling is key to early mathematical learning.
- acjohnson55 9y ago
  It's way too early to judge "New Math" to be a failure. I think the idea of focusing on concepts over computation 100% in the right spot. The biggest problem to its acceptance is cultural. Parents don't feel comfortable with math concepts, and in my opinion, most of the negativity is coming from that insecurity. So they demand for things to be taught the "old way", even though that's produced a generation or two of mathphobic Americans. EDIT: As pointed out, I mistook OPs invocation of New Math to be talking about the much maligned Common Core rethinking of math education. I was briefly a high school math teacher, but before the roll out of these changes, so I can't comment first-hand on what the new curriculum looks like in the actual teaching. But I do know how poorly prepared my students were for math beyond arithmetic. They were trained with similar curriculum that I had experienced growing up in the 90s, which I think is poorly thought out. Apologies for the confusion caused by me not recognizing the term New Math.

joe_the_user 9y ago

I don't really think the situation in the article is directly about people not being skilled in math. It's about math-phobia with it's after-affect of people not having skills in math. It seems like an especially American thing - being good at math makes someone a freak and so it's something kids actively avoid at the ages in which being a freak is not tolerable. That kind of attitude would need to be actively confronted because what happens is that kids who previously were developing skills tend to drop out given the peer-pressure. Edit: best documenting link I could find but Google book won't let me copy a quote: https://books.google.com/books?id=CzmpDAAAQBAJ&lpg=PA74&ots=CI694iHhym&dq=math%20achievement%20for%20american%20european%20women&pg=PA74#v=onepage&q=math%20achievement%20for%20american%20european%20women&f=false https://books.google.com/books?id=CzmpDAAAQBAJ&lpg=PA74&ots=...

SubiculumCode 9y ago
I blame TV in the 80's and 90's..and to today. The smart kid is the dorky, beat up kid. The dad is usually a guy who thinks he can figure stuff out and repair stuff, but hes wrong and just breaks everything.. better just buy it at the depot. Our media praises stupidity

swiley 9y ago

>I never had any problems with math until I went to university, so I was merely a passive observer of everyday struggle for some people. This is the opposite of my experience, I did horribly in math and hated it until I took calculus (which, I guess I should have taken in highschool but I tried to avoid it since the rest of math sucked.) EDIT: just want to clarify: I did have a reasonably intuitive understanding the whole time, the earlier stuff just felt like busy work.

d3ckard 9y ago
I couldn't develop internal understanding of calculus, so while solving the equations wasn't that hard, I never felt really comfortable with it. Discrete mathematics - total opposite. Proofs were very intuitive to me.

Merovius 9y ago

> Maybe I'm wrong, but I have always believed that if you want people to be good at math, it's their first years of education which are important, not the last ones. In other worlds, push for STEM should be present in kindergartens and elementary schools. By the time people go to high school it is to late. I indeed believe you are wrong. I started getting interested in STEM when I was 16 and now have a masters in math on the one hand and work for one of the most prestigious Tech firms in existence on the other. Meanwhile, when I was young, I was encouraged to enter creative fields (mostly writing in my case) which I did have enthusiasm for but then dropped as a teenager. So I switched at least twice, what I wanted to do with my life and still turned out fine. 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. I rather find the idea pretty harming; I've met a lot of people who did not pursue the career they wanted, because they bought into the myth, that you need to start programming at 6 to get a job at a company like Google or Facebook. Let kids be kids for a while. Don't worry, they can always figure out what they love later and it's never too late to reconsider.

shas3 9y ago
> 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.
- Merovius 9y ago
  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.

greenmana 9y ago

If I was to review (CS-related) math after a break of many years, what would be a good starting point? High school math? Discrete math? What are the foundations and the path like for the stuff more closely related to algorithms and core CS stuff?

aphextron 9y ago
https://en.m.wikipedia.org/wiki/Concrete_Mathematics https://en.m.wikipedia.org/wiki/Concrete_Mathematics
- iclouddrive 9y ago
  https://www.csie.ntu.edu.tw/~r97002/temp/Concrete%20Mathematics%202e.pdf https://www.csie.ntu.edu.tw/~r97002/temp/Concrete%20Mathemat...

gdfer 9y ago

I wouldn't make math/STEM a special emphasis when they're young. It's more important to foster an positive learning environment and encourage/draw out curiosity and creativity at this age. Help them become curious about the world, fascinated with what they're learning and find enjoyment in learning. In terms of subjects, aim for a strong reading focus at an early age as it will pay dividends in all other subjects (even math) if they can read/comprehend well.

sekou 9y ago
Salman Khan's One World Schoolhouse does a good job exploring this topic I think. On the one hand many students struggle with what he calls a "swiss cheese" understanding of math: lacking mastery of fundamental concepts that leads them to struggle as they grow older. On the other hand he advocates for a more holistic approach to learning overall from the beginning, exposing children to various subjects and exploring how everything is connected.

WalterBright 9y ago

> memorization I clearly recall memorizing the times tables when I was young. It suddenly dawned on me that "times" wasn't just a word, it meant adding the number so many times. I no longer needed to memorize the table, I just applied the rule. Some university engineering classes present formulae and tell the students to just apply them. This is disastrous in my not-so-humble opinion. Where the formula comes from should always be taught, so students understand the formula and the assumptions it was derived from.

paganel 9y ago

> By the time people go to high school it is to late Just anecdotal evidence, I know, but for me it was the exact contrary that happened. As a 5-year old kid I had learn to read all by myself (my dad had taught me to recognize the letters and how to pronounce them), but I had huge conceptual difficulties in teaching myself things like subtraction (what do you mean you can take/subtract a thing from another thing? what happens when the thing which you're taking/subtracting is bigger than the thing from which you're subtracting? you cannot do that, it would result in a non-thing, a thing that is below 0, and all things below 0 technically do not exist). In elementary and middle-school I was passable in maths, while very good in humanities, but all this changed in high-school, mostly because of my teacher, who taught me (and my colleagues) how to think about math. He's one of the reasons why I decided to pursue a STEM education and why I'm currently a programmer.

munchbunny 9y ago

I disagree that you have to get them young... but I do think that math classes need to start involving proof-based work rather than calculation-based work by the time students hit middle school because it's such an explicit exercise of critical thinking muscles. Recalling my own experiences with middle school and high school, I saw my peers frequently fall into the trap of trying to memorize pipelines of steps while we were learning algebra, geometry, trig, pre-calc, and then calculus. The ones who "didn't get it" would fall apart to varying degrees when confronted with problems where you had to think in terms of combining toolboxes of strategies to unfamiliar but analogous patterns, but I don't necessarily think it was their fault, because they didn't know better and rote memorization had worked consistently until this point. I often feel a bit sad about it because I did a ton of proof based stuff outside of class (as a mathlete), and that was a HUGE part of my development in logical reasoning, intellectual rigor, and critical thinking.

agumonkey 9y ago

My experience differs. My brain was intuitively ok until high school. The abstraction shift around cross references between log / exp / S 1/x went right above my head; same for discrete math basis such as prime relationships. My conclusion is that every one will have strong and weak spots, and it's very important to stay alert to this and not beat around the bush thinking it's not important. Took me more than a decade to get back into intuitive thinking, where you can play mentally with symbols and ideas just like LEGOs (as I was around high school).

wisty 9y ago

"School is about the advanced stuff, not the basics" is the call of good students, often ones who learnt the basics from their parents. It's also kind of popular with bad students, who think that they might suck at the basics but have untapped powers if they were doing something else. It's nice, vague, and populist. Everything thinks they know how to do critical thinking. Everyone thinks they know how it could be taught. I suspect most people think that they have above average critical thinking skills. As long as they don't have to agree on how or what critical thinking is, everyone can agree it's a good thing. The other one that's dumb is "you learn best when you teach yourself". Sure, if you are really super-interested in something then you learn better, and tend to teach yourself a bit, but correlation is not causation.

findoer 9y ago

Anecdotally, I am also not in agreement with you on this. Another poster mentioned not 'getting' algebra until 10th grade--this didn't happen to me until roughly my second year of college. Anyway, I eventually became very motivated to excel at math. I ended up changing majors, transferring to a school with a more serious math program, and doing so well under a very heavy courseload that I won some department honors and scholarships. I basically went from not knowing high school (middle school?) algebra to demolishing my Rudin course in about 3 years. Honestly I think most people could do this and probably a lot more if they had the desire and access to a university/books

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bagacrap 9y ago

I was always relatively at ease with math even though throughout lower education it was mainly about memorizing rules or formulas. In college it became about proofs, which was a completely different ball game and not something I'd been prepared for from preschool. To me the real important thing is the attitudes imparted by your parents and peers. As noted in the article, it's acceptable to fail at math. Parents who have their own history of math anxiety probably don't really push their kids to excel in that field. Just the notion that I was expected to "get it" and keep trying until I did (perhaps helped along by some natural stubbornness) may have made the difference in my case.