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IMHO, the tl;dr here is "math is hard." I do feel like math is the sticking point. At my school, it wasn't intro programming courses that weeded out so many CS

IMHO, the tl;dr here is "math is hard." I do feel like math is the sticking point. At my school, it wasn't intro programming courses that weeded out so many CS students, it was sophomore level discrete math. That class had a 50+% failure rate. Edited to add: I'd like to pose a question. I've always felt that math divided people into two classes -- those for whom it was mostly easy (or at least approachable) and fun and those for whom it was inherently unpleasant. As someone from the first group, it's hard for me to relate to some of the ideas in the article, such as making classes feel more socially relevant. To me, that seems superfluous. My question is, has anyone experienced these sorts of approaches directly, and how did they work for you?

brador 15y ago
Math isn't hard. It's just difficult to teach well.
- jerf 15y ago
  #include <LockhartsLament.pdf> In the end, I don't think absolutely everybody will be able to do the heavy math degrees, but the horrifying state of math education does bear a significant share of the responsibility as well. We have sucked all the life out of mathematics in the name of pedagogy and it's a bit much to expect that to pass by without effect. We can't accommodate all the student's desires for easier degrees, but the students complaining about looking at years of abstract theory without grounding are fundamentally correct, too. http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf
  - flatline 15y ago
    I would argue the opposite problem: those who are interested in math at the college level are forced to sit through two years of applications-based mathematics before ever touching the theory behind it. Nearly all of higher-level undergrad mathematics is hidden behind courses designed to teach engineers problem solving techniques using calculus. As a result, the intro calc courses don't do a particularly good job of imparting either theory or applications, unless you have an unusually talented professor. I came out of Calc II being able to solve some nasty integrals only to realize that you really only need a couple simple techniques, and with no idea how to set up problems until I went through a few physics courses. What was the point of all that - we could have learned integration by parts and u-substitution in a two week session and moved on, or actually spent a semester of analytical work preparing for higher level math. (edit: differentiation -> integration)
    - March_Hare 15y ago
      As a senior in CS and math, I completely agree. Calc II, III, elementary differential equations, and matrix theory classes are about 85% engineers at my university. As such, theory was not the focus. All I had to do to get an A was learn an algorithm and apply it. Most of my friends in CS seem to think that higher level math courses are the same and if that is the general assumption I don't blame people for not pursuing math degrees.
      - jerf 15y ago
        I wasn't sure about flatline's post, but I'm sure about yours: You should read the PDF I posted. You certainly aren't disagreeing with me (or Lockheart).
  - brohee 15y ago
    My pet theory is that math is not taught well because teachers for the 6-12 group just aren't good at math. They may be good at pedagogy but may lack the deep understanding that may be needed to teach more effectively. Now can society can divert a bigger proportion of the few people that somehow got it to teach kids?
    - Fliko 15y ago
      Some teachers don't even try, my Grade 11 Principles of Math teacher just took us on field trips to the park every day instead of teaching because she didn't have enough balls to say no to the kids who asked if we could go to the park. It made my Grade 12 year and first college math class a bit difficult at some points.
- TDL 15y ago
  I completely agree with this. I went to one of the top 10 private high schools in Illinois and I was stuck with a math teacher, for two years, who's job it was to make sure no one got less than a C average. Understanding the material was not a primary concern, making sure no one had an abysmal average was. We had a 99% college matriculation rate to preserve after all. If this is the attitude in an elite school, I can only imagine what it is like in the public school system.
romanows 15y ago
It sounds a bit like it's also the shock of encountering such hard math. I'm jealous of other countries that work their high school students hard. I remember meeting international students that had learned all of my engineering college math in high school. Back then, neither me nor my parents knew that I could and that I _should_ absorb that kind of math, let alone how to go about doing it. It would be nice if that notion was more institutionalized in the USA.
gammarator 15y ago
I don't think it's simply that math is hard. Many of these courses are taught in ways that make it hard for students to see how the tools they're using are going to be useful. Students would be better-motivated to take the challenge if they were applying it to problems that seem relevant to them. In CS, for instance, which is more fun: slogging through an algorithms book front to back, or researching the best way to solve a problem you face in one of your own code projects? To answer your question about relevance: I made it through my undergraduate physics major not because lectures and homeworks were fun, but because I got involved in research early on. I found it much more fun to learn in the context of a project I felt a sense of ownership of.
tsmith 15y ago
"At my school, it wasn't intro programming courses that weeded out so many CS students, it was sophomore level discrete math. That class had a 50+% failure rate." At my school, the CS program was designed so that the Intro to Programming class and the Calc I class were filter functions: students had to get at least XX% in one and YY% in the other in order to be admitted to the CS program (and thus be permitted to enroll in the upper level courses required for the degree). As at your school, more students bombed the Calc class than the CS class. There was no effort made at disguising the filtering function of these courses - in fact, when program enrollment was high, XX and YY increased, and when program enrollment fell around 2004-2005 they decreased (at one point YY was 50%, effectively meaning you simply had to pass the class).
Dn_Ab 15y ago
The tl;dr I got was different. What I got was a.) that our society has focused too much on the stimulation of our dopamine pathways. b.) Many professors forget that the enthusiasm they posess for a subject is not self evident. The hardness of STEM was orthogonal to this piece; the focus was on how pointless the seemingly unapplicable dry list of equations and facts were to many students. This made it hard to continue the perceived self flagellation to little gain. They gave an example of a smart kid with an 800 SAT score in math who quit to psychology because his mechanics class was dull in comparison to the more active psych class. They also mention that classes like english give better grades than chemistry and math so people switch cause they feel they are doing better. Their prescription is more interesting and interactive classes. That is a good idea as long as the essence is not lost to fluff and education does not degenerate to an exercise in marketing I guess.
- chernevik 15y ago
  But if the more important problem is diminution of student capacity / capability for the work, better teaching helps only so much. Anecdata like "helicopter parenting" suggest more kids lack emotional preparation hard work and differentiating curricula. I certainly don't see any sign that K-12 has gotten _better_ at math preparation. Then there is the premium attached to integration into social networks. Wall Street bankers are scarfing down large chunks of the national income, more from government guarantee of leverage than productivity. Prices are signalling to focus on placement in the social network, rather than on productive work; and once there, to get good at predicting / managing regulatory intervention. The interest in studies orienting people to the political and social milieu shouldn't be surprising. Especially when these offer less risk of marked out as a loser by poor grades. There is a premium for government work, too. It's less remunerative, but more secure, and has very high status, in many circles. The effect carries over to nearby careers like law, and journalism. Median income, housing prices, and unemployment rates in greater Washington D.C. all suggest that the worldly payoff for public service isn't bad. So I worry that we're training less capable people, and encouraging them to think more about where they work than how they work. It can't go on forever, but a lot of folks will get hurt as it ends.
- Apocryphon 15y ago
jisaacstone 15y ago
I hated hated hated math through to high school Pre-calculus. Algebra was a terror. I could get the concepts easily enough but I'd always make some mistake in the calculation. Calc I and II in university were difficult but fun. There was a lot of problem solving and very little tedious calculation. I switched from a chemistry major not because it was difficult but because it was tedious and uninteresting. Not the classes. The lab. And as an 18-year-old I thought the lab was simulating what my future career in chemistry would be like. And so I switched to a liberal arts major.
mjw 15y ago
As someone doing a second master's degree in a mathematical field, I can't say I've found it 'mostly easy', or even mostly approachable. It can be fun once you've developed strong intuitions for the material, but often a hard slog to get there. Those who give the impression of finding it easy, I reckon tend to be either: (a) freakish geniuses of the rare-even-in-academia variety (b) modestly hiding the fact they've actually spent hours and hours of hard study to push past a series of brick walls in order to get here (c) both the above (d) overconfident and heading for a slip-up (e) not challenging themselves enough.
- msluyter 15y ago
  "Mostly easy" was probably a bad way of putting it. Perhaps a better way would be that, at the outset, some students can handle mathematical challenges, even when they require hard work and perseverance; after a while, a positive feedback loop ensues, where being good at math makes it more enjoyable and finding it enjoyable makes you better at it. (That doesn't imply you'll never hit roadblocks.) If, early on, math is painful and frustrating (perhaps through no fault of your own), then that cycle never develops and you form an aversion to the subject.
matwood 15y ago
At my school, it wasn't intro programming courses that weeded out so many CS students, it was sophomore level discrete math. That class had a 50+% failure rate. In classes that have brand new or complex topics the teacher matters a lot. Intro programming and discrete math 1 were the weed out classes at my school. Many people failed both. I managed to get an A in the intro programming only because it was all old material to me. The now retired teacher was horrible. I go an F in the discrete math course. On the last day of class the teacher admitted to being horrible and then failed everyone. The weirdest thing was I actually felt like I understood the material, but was lost on every test. I had alway done well in math until that class with that teacher. When I retook the class with a different teacher I got an A. The same goes for discrete 2 and every other math course I took in college. Now, to your question. I don't think the classes need to be more socially relevant, but teachers need to figure out ways to connect the material with students. The problem is you need a teacher who deeply understands the material and cares enough to figure out various ways of teaching it. A good teacher is akin to a good artist. They can take the same base concepts and materials that every other teacher receives, but can weave them into a coherent lesson.
dj_axl 15y ago
The tl;dr I got was that high school didn't adequately prepare students for college. Just to have h.s. kids enthusiastic (as someone else mentions in the comments here, high on dopamine) they make things entertaining/easy. While some may argue that college level should have more real world applications, I would argue that high school level should have more hard challenges that fail half the class. Maybe have a class that doesn't count towards your GPA that is super-challenging.

brador 15y ago

Math isn't hard. It's just difficult to teach well.

jerf 15y ago
#include <LockhartsLament.pdf> In the end, I don't think absolutely everybody will be able to do the heavy math degrees, but the horrifying state of math education does bear a significant share of the responsibility as well. We have sucked all the life out of mathematics in the name of pedagogy and it's a bit much to expect that to pass by without effect. We can't accommodate all the student's desires for easier degrees, but the students complaining about looking at years of abstract theory without grounding are fundamentally correct, too. http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf
- flatline 15y ago
  I would argue the opposite problem: those who are interested in math at the college level are forced to sit through two years of applications-based mathematics before ever touching the theory behind it. Nearly all of higher-level undergrad mathematics is hidden behind courses designed to teach engineers problem solving techniques using calculus. As a result, the intro calc courses don't do a particularly good job of imparting either theory or applications, unless you have an unusually talented professor. I came out of Calc II being able to solve some nasty integrals only to realize that you really only need a couple simple techniques, and with no idea how to set up problems until I went through a few physics courses. What was the point of all that - we could have learned integration by parts and u-substitution in a two week session and moved on, or actually spent a semester of analytical work preparing for higher level math. (edit: differentiation -> integration)
  - March_Hare 15y ago
    As a senior in CS and math, I completely agree. Calc II, III, elementary differential equations, and matrix theory classes are about 85% engineers at my university. As such, theory was not the focus. All I had to do to get an A was learn an algorithm and apply it. Most of my friends in CS seem to think that higher level math courses are the same and if that is the general assumption I don't blame people for not pursuing math degrees.
    - jerf 15y ago
      I wasn't sure about flatline's post, but I'm sure about yours: You should read the PDF I posted. You certainly aren't disagreeing with me (or Lockheart).
- brohee 15y ago
  My pet theory is that math is not taught well because teachers for the 6-12 group just aren't good at math. They may be good at pedagogy but may lack the deep understanding that may be needed to teach more effectively. Now can society can divert a bigger proportion of the few people that somehow got it to teach kids?
  - Fliko 15y ago
    Some teachers don't even try, my Grade 11 Principles of Math teacher just took us on field trips to the park every day instead of teaching because she didn't have enough balls to say no to the kids who asked if we could go to the park. It made my Grade 12 year and first college math class a bit difficult at some points.
TDL 15y ago
I completely agree with this. I went to one of the top 10 private high schools in Illinois and I was stuck with a math teacher, for two years, who's job it was to make sure no one got less than a C average. Understanding the material was not a primary concern, making sure no one had an abysmal average was. We had a 99% college matriculation rate to preserve after all. If this is the attitude in an elite school, I can only imagine what it is like in the public school system.

romanows 15y ago

It sounds a bit like it's also the shock of encountering such hard math. I'm jealous of other countries that work their high school students hard. I remember meeting international students that had learned all of my engineering college math in high school. Back then, neither me nor my parents knew that I could and that I _should_ absorb that kind of math, let alone how to go about doing it. It would be nice if that notion was more institutionalized in the USA.

gammarator 15y ago

I don't think it's simply that math is hard. Many of these courses are taught in ways that make it hard for students to see how the tools they're using are going to be useful. Students would be better-motivated to take the challenge if they were applying it to problems that seem relevant to them. In CS, for instance, which is more fun: slogging through an algorithms book front to back, or researching the best way to solve a problem you face in one of your own code projects? To answer your question about relevance: I made it through my undergraduate physics major not because lectures and homeworks were fun, but because I got involved in research early on. I found it much more fun to learn in the context of a project I felt a sense of ownership of.

tsmith 15y ago

"At my school, it wasn't intro programming courses that weeded out so many CS students, it was sophomore level discrete math. That class had a 50+% failure rate." At my school, the CS program was designed so that the Intro to Programming class and the Calc I class were filter functions: students had to get at least XX% in one and YY% in the other in order to be admitted to the CS program (and thus be permitted to enroll in the upper level courses required for the degree). As at your school, more students bombed the Calc class than the CS class. There was no effort made at disguising the filtering function of these courses - in fact, when program enrollment was high, XX and YY increased, and when program enrollment fell around 2004-2005 they decreased (at one point YY was 50%, effectively meaning you simply had to pass the class).

Dn_Ab 15y ago

The tl;dr I got was different. What I got was a.) that our society has focused too much on the stimulation of our dopamine pathways. b.) Many professors forget that the enthusiasm they posess for a subject is not self evident. The hardness of STEM was orthogonal to this piece; the focus was on how pointless the seemingly unapplicable dry list of equations and facts were to many students. This made it hard to continue the perceived self flagellation to little gain. They gave an example of a smart kid with an 800 SAT score in math who quit to psychology because his mechanics class was dull in comparison to the more active psych class. They also mention that classes like english give better grades than chemistry and math so people switch cause they feel they are doing better. Their prescription is more interesting and interactive classes. That is a good idea as long as the essence is not lost to fluff and education does not degenerate to an exercise in marketing I guess.

chernevik 15y ago
But if the more important problem is diminution of student capacity / capability for the work, better teaching helps only so much. Anecdata like "helicopter parenting" suggest more kids lack emotional preparation hard work and differentiating curricula. I certainly don't see any sign that K-12 has gotten _better_ at math preparation. Then there is the premium attached to integration into social networks. Wall Street bankers are scarfing down large chunks of the national income, more from government guarantee of leverage than productivity. Prices are signalling to focus on placement in the social network, rather than on productive work; and once there, to get good at predicting / managing regulatory intervention. The interest in studies orienting people to the political and social milieu shouldn't be surprising. Especially when these offer less risk of marked out as a loser by poor grades. There is a premium for government work, too. It's less remunerative, but more secure, and has very high status, in many circles. The effect carries over to nearby careers like law, and journalism. Median income, housing prices, and unemployment rates in greater Washington D.C. all suggest that the worldly payoff for public service isn't bad. So I worry that we're training less capable people, and encouraging them to think more about where they work than how they work. It can't go on forever, but a lot of folks will get hurt as it ends.
Apocryphon 15y ago

jisaacstone 15y ago

I hated hated hated math through to high school Pre-calculus. Algebra was a terror. I could get the concepts easily enough but I'd always make some mistake in the calculation. Calc I and II in university were difficult but fun. There was a lot of problem solving and very little tedious calculation. I switched from a chemistry major not because it was difficult but because it was tedious and uninteresting. Not the classes. The lab. And as an 18-year-old I thought the lab was simulating what my future career in chemistry would be like. And so I switched to a liberal arts major.

mjw 15y ago

As someone doing a second master's degree in a mathematical field, I can't say I've found it 'mostly easy', or even mostly approachable. It can be fun once you've developed strong intuitions for the material, but often a hard slog to get there. Those who give the impression of finding it easy, I reckon tend to be either: (a) freakish geniuses of the rare-even-in-academia variety (b) modestly hiding the fact they've actually spent hours and hours of hard study to push past a series of brick walls in order to get here (c) both the above (d) overconfident and heading for a slip-up (e) not challenging themselves enough.

msluyter 15y ago
"Mostly easy" was probably a bad way of putting it. Perhaps a better way would be that, at the outset, some students can handle mathematical challenges, even when they require hard work and perseverance; after a while, a positive feedback loop ensues, where being good at math makes it more enjoyable and finding it enjoyable makes you better at it. (That doesn't imply you'll never hit roadblocks.) If, early on, math is painful and frustrating (perhaps through no fault of your own), then that cycle never develops and you form an aversion to the subject.

matwood 15y ago

At my school, it wasn't intro programming courses that weeded out so many CS students, it was sophomore level discrete math. That class had a 50+% failure rate. In classes that have brand new or complex topics the teacher matters a lot. Intro programming and discrete math 1 were the weed out classes at my school. Many people failed both. I managed to get an A in the intro programming only because it was all old material to me. The now retired teacher was horrible. I go an F in the discrete math course. On the last day of class the teacher admitted to being horrible and then failed everyone. The weirdest thing was I actually felt like I understood the material, but was lost on every test. I had alway done well in math until that class with that teacher. When I retook the class with a different teacher I got an A. The same goes for discrete 2 and every other math course I took in college. Now, to your question. I don't think the classes need to be more socially relevant, but teachers need to figure out ways to connect the material with students. The problem is you need a teacher who deeply understands the material and cares enough to figure out various ways of teaching it. A good teacher is akin to a good artist. They can take the same base concepts and materials that every other teacher receives, but can weave them into a coherent lesson.

dj_axl 15y ago

The tl;dr I got was that high school didn't adequately prepare students for college. Just to have h.s. kids enthusiastic (as someone else mentions in the comments here, high on dopamine) they make things entertaining/easy. While some may argue that college level should have more real world applications, I would argue that high school level should have more hard challenges that fail half the class. Maybe have a class that doesn't count towards your GPA that is super-challenging.