5 ms·

Stop trying to make maths "fun" - lessons also for coding?

hasenj 16y ago
If I was taught programming in high school the same way I was taught math, I would've hated it, deeply. Most of math was about number crunching and the application of arbitrary formulas to arbitrary equations. I can imagine, 20 years from now, a high school student will have to solve the following question: "Write a recursive function in C that finds the minimum number in an array of integers". Then imagine the teacher himself/herself has absolutely no interest in programming what so ever, and is only teaching it because the board of education decided that children must learn it.
- randrews 16y ago
  That's actually a reasonable question. What's a lot more likely: "Here are fifteen for loop headers. For each one, write how many times the loop body will execute."
  - xyzzyz 16y ago
    This is undecidable.
    - amalcon 16y ago
      Only in general.
      - xyzzyz 16y ago
        The problem of distinguishing when it is decidable and when it is not, is undecidable itself (Rice theorem).
        amalcon 16y ago
        Well yes, but the questions could be trivially decidable. Not that this would make them good questions.
        randrews 16y ago
        it's kind of my point that it would make them bad questions. :) I think expecting a public school textbook to ask questions that require thought is really optimistic.
  - hasenj 16y ago
    It's reasonable for us. Most people (who are not into programming) would find it ridiculous and pointless.
    - dkarl 16y ago
      It's a reasonable way (the only way) to develop a skill -- even after you have a conceptual understanding of how to do something, you still have to practice a little bit at it. Practice is required first of all to clarify your understanding, but even then practice is necessary to polish your skill enough that you can use it to accomplish something. (I.e., you have to be able to execute the skill and have enough attention left over to understand something else.) So many problems in education come from the stigmatization of anything resembling practice as "rote" and "unstimulating." When you stigmatize repetition, you make it very hard to develop skills. In effect, students are expected to develop "understanding" (the fun, easy part) without developing any skills (the boring, repetitive part.) Unfortunately, working without any polished, dependable skills is awful. It's anxiety-inducing. You have a little bit of doubt about every single step, and as you complete step after step, your confidence in getting the right answer goes down and down. Having a set of solid skills gives you base of confidence, a security blanket that reassures you while you tackle new ideas.
      - hasenj 16y ago
        I think you missed the point. Most people find first year of computer science very hard. For me it was easy, but plenty of people found it hard, and I think many people changed majors because of that. Now imagine if it was mandatory in high school. Teachers probably won't understand it much. The curriculum will probably focus on "formula"-like things (perhaps, patterns?), syntax maybe, and a whole bunch of boring details, and ignore the most important part: problem solving. Students might study (read: memorize) all kinds of functions for doing things. Grade 8: loops for sorting numbers, loops for finding min and max numbers, loops for calculating factorials. for-loop synatx in C. for-loop syntax in python. Grade 9: recursive functions for sorting (e.g. merge sort), recursive functions for calculating factorials, recursive functions for finding min/max numbers in a list. I only realized this very recently, but math has a lot in common with computer science. Its core is about problem solving. Unfortunately, that's not how it gets taught in high school. In high school, math is a set of arbitrary formulas you have to memorize and use to "solve" arbitrary equations. We were given a lot of "practice problems"; they were the most boring thing in the world. They didn't teach you anything; their only purpose is brush up your muscle memory so that when you see a problem of the form "A B C" you know which formula to use and how to use it.
  - daxelrod 16y ago
    The above exactly the kind of exercise we were assigned in my high school's intro CS course. The course was taught by a math teacher. BUT: The school waited until a month before the semester started to tell the math teacher that she'd be teaching the course. Worse, they had already picked out a textbook that was filled with exercises like this. Worst of all, she had basically never done any programming before. As time went on, and she actually had a chance to learn the material, this kind of coursework was replaced with more interesting and useful programming assignments. I later took a calculus course from this teacher, and in that course, she actually took great pains to avoid repetitive problem sets; almost every problem she assigned was designed to teach us something different. Repetitve exercises are likely easiest to assign and grade.
RiderOfGiraffes 16y ago
If you like this, you might be interested in these: http://news.ycombinator.com/item?id=2209991 http://news.ycombinator.com/item?id=2209991 http://news.ycombinator.com/item?id=2209970 http://news.ycombinator.com/item?id=2209970
- deleted 16y ago
  [deleted]
- hasenj 16y ago
  spam?
wgrover 16y ago
I feel like math teachers have a fundamentally different task than coding teachers. Everyone needs at least a low level of proficiency in math - being able to make change correctly and balance your checkbook. Not everyone needs a low level of coding proficiency. If you've reached the level in your education where you need to learn to code, then you've probably already advanced past the point where everything has to be presented as "fun" before you'll learn it.
- hasenj 16y ago
  Hey, there was a time when most people could get by just fine without even knowing how to read and write. With the proliferation of computers into every aspect of life, it's not unimaginable for programming to be considered essential knowledge that should be taught in schools.
  - wgrover 16y ago
    I'd agree with you if it weren't for the iPad. Computers have proliferated, but they're also evolving in a way that makes programming knowledge less important (at least for the majority of people).
    - hasenj 16y ago
      Math knowledge beyond 5th grade is not important for the majority of people, but it still gets taught in schools.
- dwc 16y ago
  I'm sure that's how basic math proficiency was viewed in the past. These days almost everyone would benefit from some rudimentary knowledge of programming, but it's not yet viewed as essential. Every day I see people doing repetitive manual tasks on the computer that could be automated with just a tiny amount of basic shell scripting. How long before this is taught to all kids in primary school, and facing many of the same problems as math today?
  - 16y ago
bluekeybox 16y ago
> if you have to tell somebody that something is fun, it means that you have lost the argument. Couldn't agree more.
mnutt 16y ago
I have very fond memories from when I was 9 or 10 about a book called I Hate Mathematics: http://www.amazon.com/Brown-Paper-School-book-Mathematics/dp/0316117412 http://www.amazon.com/Brown-Paper-School-book-Mathematics/dp... It was the thing that really made math fun for me. So sure, stop telling kids that "math is fun", but don't stop trying to make it interesting; it's definitely possible.
Mahh 16y ago
>But I’m convinced that almost anyone can be drawn into maths if they are presented with something intriguing or surprising which prompts them to want to investigate That's what I used to think when trying to get other students into programming -- like getting a kid do say 'Holy crap, I just created multiplication'. But it doesn't seem to work that way. I've come to be used to the concept that other people think on a completely different plane than me, so it's pretty hard or often just doesn't work at all to try to find this 'intriguing or surprising' thing that can get them others to be interested.
- dwc 16y ago
  I agree with you. But I have to add that there's a big difference between math anxiety and disinterest in pursuing a graduate degree. There's nothing wrong with someone choosing to pursue something else even when shown the intrigue and beauty of math (or programming). But there's everything wrong with the mind-numbing approach to math taken now.
dkarl 16y ago
"Making math fun" is fine, but most teachers interpret it as "mixing fun stuff into math, which is inherently painful and boring," because they're focused on the kids who aren't doing well. To them, making math fun is the same idea as bringing a clown into the pediatric burn ward: "Let's make this suck a little less." That attitude rubs off on the kids. What those teachers don't get is that math is most fun when you are using solid, polished skills to explore an area where you're still learning. The teachers are stuck in the standard educational mindset, which is that getting enough practice at anything to develop polished skills is "rote" and horrible. Plus it slows down their curriculum. So they move on and just do some review now and then, and the mediocre students end up with no solid skills they can rely on. All their skills are a little iffy, so they can't do anything with confidence, and everything is stressful.
chanux 16y ago
Agree with the argument but the title (on HN) doesn't sound right. I suggest, Stop trying to make maths look "fun"
adnam 16y ago
Eeee, when I were a lad, maths weren't fun! You did 14 hours down't mine and only then were you allowed to try yer 'and at partial differential equations. And if yer got one wrong'un, teacher'd beat you with a wooden pole (etc etc) (yorkshire post, scnr)
Tycho 16y ago
Hmm. Finding maths so dull was probably one of the main reasons that I didn't peruse a degree and CS or physics. Which was a disastrous decision for me personally. Not that I just couldn't face studying anything unexciting per se, but that I (wrongly) assumed that if I didn't find something interesting then i could never be sufficiently good at it. At high school I was 'streamed' into one of the lower tier math classes, which I resented - result was getting a higher mark in the end than most of the top-tier students. But perhaps I would have been better off in a more advanced class where I'd struggle more but at least find the stuff interesting. Anyway my point is it's a shame to turn people away from maths by offering such stale curriculum.
Mz 16y ago
My oldest son has dyscalculia and just sucks at crunching numbers. He had a terrible, terrible time with math in public school and really hated and dreaded the subject by the time we pulled the kids out to homeschool. It was clear to me he would not be able to memorize his way through math like his mom had. (I was in my thirties when I discovered some of this stuff had actual uses. sigh) My top priority for math with this child was to teach him "math is your friend". He's a science geek (which is tough when math is not something you are good at) and loves physics. He taught me most of the physics I know (speaking in little words and repeating himself a lot) when he was 14, which stood me in very good stead when taking certain college classes later on. A few things we did: Chapter books, full of discussion about math and light on formulas. Let him choose a statistics track over an algebra/geometry/trig track. (We did some algebra and geometry but not too much.) Read about halfway through "A tour of the calculus". I dropped out of calculus my first quarter in college and never wanted to see the subject again, after having been inducted into Mu Alpha Theta in 11th grade. He would spend an hour on this with me because it was the only math that made more sense to him than to me and he was happy to watch me get a headache (which I played for all it was worth). This book was chosen because he loves physics and calculus is the math of physics and because calculus really requires you to learn all that algebra/geometry/trig stuff he wanted nothing to do with. I knew I had won the battle when he was whining and complaining one day about not wanting to do math and then got all perked up at the idea of working on reading a couple more pages of this book with me. We also did "fun" stuff, like card games and such in place of workbooks and that did have some value. But reading part of "A tour of the calculus" was the single biggest thing I did to get him past this mental and emotional block. Which I guess largely agrees with this article, though perhaps framed a little differently.
gaurav_v 16y ago
This "Mathematician's Lament" is (by far) the best critique of the modern mathematics education that I've seen to date: http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf

If I was taught programming in high school the same way I was taught math, I would've hated it, deeply. Most of math was about number crunching and the application of arbitrary formulas to arbitrary equations. I can imagine, 20 years from now, a high school student will have to solve the following question: "Write a recursive function in C that finds the minimum number in an array of integers". Then imagine the teacher himself/herself has absolutely no interest in programming what so ever, and is only teaching it because the board of education decided that children must learn it.

randrews 16y ago
That's actually a reasonable question. What's a lot more likely: "Here are fifteen for loop headers. For each one, write how many times the loop body will execute."
- xyzzyz 16y ago
  This is undecidable.
  - amalcon 16y ago
    Only in general.
    - xyzzyz 16y ago
      The problem of distinguishing when it is decidable and when it is not, is undecidable itself (Rice theorem).
      - amalcon 16y ago
        Well yes, but the questions could be trivially decidable. Not that this would make them good questions.
        randrews 16y ago
        it's kind of my point that it would make them bad questions. :) I think expecting a public school textbook to ask questions that require thought is really optimistic.
- hasenj 16y ago
  It's reasonable for us. Most people (who are not into programming) would find it ridiculous and pointless.
  - dkarl 16y ago
    It's a reasonable way (the only way) to develop a skill -- even after you have a conceptual understanding of how to do something, you still have to practice a little bit at it. Practice is required first of all to clarify your understanding, but even then practice is necessary to polish your skill enough that you can use it to accomplish something. (I.e., you have to be able to execute the skill and have enough attention left over to understand something else.) So many problems in education come from the stigmatization of anything resembling practice as "rote" and "unstimulating." When you stigmatize repetition, you make it very hard to develop skills. In effect, students are expected to develop "understanding" (the fun, easy part) without developing any skills (the boring, repetitive part.) Unfortunately, working without any polished, dependable skills is awful. It's anxiety-inducing. You have a little bit of doubt about every single step, and as you complete step after step, your confidence in getting the right answer goes down and down. Having a set of solid skills gives you base of confidence, a security blanket that reassures you while you tackle new ideas.
    - hasenj 16y ago
      I think you missed the point. Most people find first year of computer science very hard. For me it was easy, but plenty of people found it hard, and I think many people changed majors because of that. Now imagine if it was mandatory in high school. Teachers probably won't understand it much. The curriculum will probably focus on "formula"-like things (perhaps, patterns?), syntax maybe, and a whole bunch of boring details, and ignore the most important part: problem solving. Students might study (read: memorize) all kinds of functions for doing things. Grade 8: loops for sorting numbers, loops for finding min and max numbers, loops for calculating factorials. for-loop synatx in C. for-loop syntax in python. Grade 9: recursive functions for sorting (e.g. merge sort), recursive functions for calculating factorials, recursive functions for finding min/max numbers in a list. I only realized this very recently, but math has a lot in common with computer science. Its core is about problem solving. Unfortunately, that's not how it gets taught in high school. In high school, math is a set of arbitrary formulas you have to memorize and use to "solve" arbitrary equations. We were given a lot of "practice problems"; they were the most boring thing in the world. They didn't teach you anything; their only purpose is brush up your muscle memory so that when you see a problem of the form "A B C" you know which formula to use and how to use it.
- daxelrod 16y ago
  The above exactly the kind of exercise we were assigned in my high school's intro CS course. The course was taught by a math teacher. BUT: The school waited until a month before the semester started to tell the math teacher that she'd be teaching the course. Worse, they had already picked out a textbook that was filled with exercises like this. Worst of all, she had basically never done any programming before. As time went on, and she actually had a chance to learn the material, this kind of coursework was replaced with more interesting and useful programming assignments. I later took a calculus course from this teacher, and in that course, she actually took great pains to avoid repetitive problem sets; almost every problem she assigned was designed to teach us something different. Repetitve exercises are likely easiest to assign and grade.

RiderOfGiraffes 16y ago

If you like this, you might be interested in these: http://news.ycombinator.com/item?id=2209991 http://news.ycombinator.com/item?id=2209991 http://news.ycombinator.com/item?id=2209970 http://news.ycombinator.com/item?id=2209970

deleted 16y ago
[deleted]
hasenj 16y ago
spam?

wgrover 16y ago

I feel like math teachers have a fundamentally different task than coding teachers. Everyone needs at least a low level of proficiency in math - being able to make change correctly and balance your checkbook. Not everyone needs a low level of coding proficiency. If you've reached the level in your education where you need to learn to code, then you've probably already advanced past the point where everything has to be presented as "fun" before you'll learn it.

hasenj 16y ago
Hey, there was a time when most people could get by just fine without even knowing how to read and write. With the proliferation of computers into every aspect of life, it's not unimaginable for programming to be considered essential knowledge that should be taught in schools.
- wgrover 16y ago
  I'd agree with you if it weren't for the iPad. Computers have proliferated, but they're also evolving in a way that makes programming knowledge less important (at least for the majority of people).
  - hasenj 16y ago
    Math knowledge beyond 5th grade is not important for the majority of people, but it still gets taught in schools.
dwc 16y ago
I'm sure that's how basic math proficiency was viewed in the past. These days almost everyone would benefit from some rudimentary knowledge of programming, but it's not yet viewed as essential. Every day I see people doing repetitive manual tasks on the computer that could be automated with just a tiny amount of basic shell scripting. How long before this is taught to all kids in primary school, and facing many of the same problems as math today?
- 16y ago

bluekeybox 16y ago

> if you have to tell somebody that something is fun, it means that you have lost the argument. Couldn't agree more.

mnutt 16y ago

I have very fond memories from when I was 9 or 10 about a book called I Hate Mathematics: http://www.amazon.com/Brown-Paper-School-book-Mathematics/dp/0316117412 http://www.amazon.com/Brown-Paper-School-book-Mathematics/dp... It was the thing that really made math fun for me. So sure, stop telling kids that "math is fun", but don't stop trying to make it interesting; it's definitely possible.

Mahh 16y ago

>But I’m convinced that almost anyone can be drawn into maths if they are presented with something intriguing or surprising which prompts them to want to investigate That's what I used to think when trying to get other students into programming -- like getting a kid do say 'Holy crap, I just created multiplication'. But it doesn't seem to work that way. I've come to be used to the concept that other people think on a completely different plane than me, so it's pretty hard or often just doesn't work at all to try to find this 'intriguing or surprising' thing that can get them others to be interested.

dwc 16y ago
I agree with you. But I have to add that there's a big difference between math anxiety and disinterest in pursuing a graduate degree. There's nothing wrong with someone choosing to pursue something else even when shown the intrigue and beauty of math (or programming). But there's everything wrong with the mind-numbing approach to math taken now.

dkarl 16y ago

"Making math fun" is fine, but most teachers interpret it as "mixing fun stuff into math, which is inherently painful and boring," because they're focused on the kids who aren't doing well. To them, making math fun is the same idea as bringing a clown into the pediatric burn ward: "Let's make this suck a little less." That attitude rubs off on the kids. What those teachers don't get is that math is most fun when you are using solid, polished skills to explore an area where you're still learning. The teachers are stuck in the standard educational mindset, which is that getting enough practice at anything to develop polished skills is "rote" and horrible. Plus it slows down their curriculum. So they move on and just do some review now and then, and the mediocre students end up with no solid skills they can rely on. All their skills are a little iffy, so they can't do anything with confidence, and everything is stressful.

chanux 16y ago

Agree with the argument but the title (on HN) doesn't sound right. I suggest, Stop trying to make maths look "fun"

adnam 16y ago

Eeee, when I were a lad, maths weren't fun! You did 14 hours down't mine and only then were you allowed to try yer 'and at partial differential equations. And if yer got one wrong'un, teacher'd beat you with a wooden pole (etc etc) (yorkshire post, scnr)

Tycho 16y ago

Hmm. Finding maths so dull was probably one of the main reasons that I didn't peruse a degree and CS or physics. Which was a disastrous decision for me personally. Not that I just couldn't face studying anything unexciting per se, but that I (wrongly) assumed that if I didn't find something interesting then i could never be sufficiently good at it. At high school I was 'streamed' into one of the lower tier math classes, which I resented - result was getting a higher mark in the end than most of the top-tier students. But perhaps I would have been better off in a more advanced class where I'd struggle more but at least find the stuff interesting. Anyway my point is it's a shame to turn people away from maths by offering such stale curriculum.

Mz 16y ago

My oldest son has dyscalculia and just sucks at crunching numbers. He had a terrible, terrible time with math in public school and really hated and dreaded the subject by the time we pulled the kids out to homeschool. It was clear to me he would not be able to memorize his way through math like his mom had. (I was in my thirties when I discovered some of this stuff had actual uses. sigh) My top priority for math with this child was to teach him "math is your friend". He's a science geek (which is tough when math is not something you are good at) and loves physics. He taught me most of the physics I know (speaking in little words and repeating himself a lot) when he was 14, which stood me in very good stead when taking certain college classes later on. A few things we did: Chapter books, full of discussion about math and light on formulas. Let him choose a statistics track over an algebra/geometry/trig track. (We did some algebra and geometry but not too much.) Read about halfway through "A tour of the calculus". I dropped out of calculus my first quarter in college and never wanted to see the subject again, after having been inducted into Mu Alpha Theta in 11th grade. He would spend an hour on this with me because it was the only math that made more sense to him than to me and he was happy to watch me get a headache (which I played for all it was worth). This book was chosen because he loves physics and calculus is the math of physics and because calculus really requires you to learn all that algebra/geometry/trig stuff he wanted nothing to do with. I knew I had won the battle when he was whining and complaining one day about not wanting to do math and then got all perked up at the idea of working on reading a couple more pages of this book with me. We also did "fun" stuff, like card games and such in place of workbooks and that did have some value. But reading part of "A tour of the calculus" was the single biggest thing I did to get him past this mental and emotional block. Which I guess largely agrees with this article, though perhaps framed a little differently.

gaurav_v 16y ago

This "Mathematician's Lament" is (by far) the best critique of the modern mathematics education that I've seen to date: http://www.maa.org/devlin/LockhartsLament.pdf http://www.maa.org/devlin/LockhartsLament.pdf