7 ms·

I did A-level maths, I've programmed computers for 30 years since I was a kid. Ive implanted algorithms to calculate solar irradiance varying by orientation, i

I did A-level maths, I've programmed computers for 30 years since I was a kid. Ive implanted algorithms to calculate solar irradiance varying by orientation, inclination and latitude. I don't understand what my 7yo stepsons maths homework is asking him to do/learn. It's just weird and I'm not sure he always does either, it teaches the how (weirdly) but never the why, I've started teaching him how to understand the practical uses for maths. We play games now like "how many bricks in the wall" when we are out and about. I struggled with maths as a child because I never saw what it was for, once you realise that it's the language of the universe things click why it is important, I'm not a mathematician nor do I need to be but I still appreciate those who are.

ColinWright 9y ago
My (very limited) experience of more recent homework is that it makes perfect sense in the context of what the teachers are trying to teach, but no sense out of context to people who learned their maths decades ago. If you'd care to send me a photo of an example of the homework then I can try to give you some context and understanding. My contact details can be derived from my HN profile. I might be a little slow to reply at the moment as I'm in the middle of other things and only surfacing occasionally.
- jonsen 9y ago
  ... makes perfect sense in the context of what the teachers are trying to teach ... What's the point with homework then? School takes the best part of a childs day, and when they don't make it through, the parents can finish with a tired child.
  - ColinWright 9y ago
    "Homework" is supposed to be practising skills they have already learned so they can make it more fluent, and have to concentrate on it less when they come to the next thing to learn. Learning things is done with the teacher there to help anticipate, identify, and correct misconceptions. If you want the parent to help with the homework, the parent will have to know the material they want to help with. In maths, that's rarely the case unless it's the same thing they learned. And that's now out-of-date. Parents say they want their students to learn new, modern maths, and then insist that they are taught exactly what they were taught. And hated. Having said that, I'm really not going to defend anything about the existing setup and system. This is a huge mess, and while I have my own ideas, there's no way a discussion here will change anything, and it's likely that things I do say will be taken out of context, twisted, and mis-understood.
    - boblivion 9y ago
      As someone not from the U.S. I wonder, what does "outdated" mean? Can you give a simple example - e.g. comparison - what would be "math back then" and "math nowadays". Because to me math was always just math especially if it comes to numbers.
      - throwawaybbqed 9y ago
        I wanted to echo the parent poster. I'm in my 30s and math made no sense as a kid - precisely because the problems were all artificial and uninteresting. I had to fight major math phobia in undergrad. For me personally, the most interesting application of math was figuring out orbits/positions of stars, etc. I have a 2 year old so if you have another favorite example like this, I'd love to hear about it.
        noir_lord 9y ago
        > the most interesting application of math was figuring out orbits/positions of stars. For me math started to click when I started writing simple games for the spectrum, I realized quite quickly that what I needed was trigonometry and once I knew the name I could go to the library and get out books. I was implementing a text based destroyer game (similar to mtrek/jtre though I didn't know those existed) and I had to implement handling bearings from the ship to the enemy ships, handle firing guns and missiles all that stuff, I made lots of horrible simplifications (shells experienced no air resistance so flew in perfect parabola's, the surface of the sea was a perfectly flat plane, no curvature (non-euclidean geometry would have been a step too far at 10-11) etc) but fundamentally it worked and was playable as a game, you could issue orders, fire shells (and later missiles though that made the game a lot more brutal and short) with bracketing and taking into time of flight - I was a strange child. I got the original idea from a ZX81 kids book on game programming that implemented a simple side projection game where you set the elevation and velocity of your shot and aimed for the opponents ship, it was simple (couple of pages of code) and I wanted to do something a bit more realistic - as a side benefit I ended up reading up on naval warfare in quite a lot of depth, again a strange child.
      - 9y ago
  - michaelchisari 9y ago
    I don't mind this new way of teaching math, but on this note, I liked what Sal Khan had to say about flipping the process for school and homework. He proposed that students should watch lectures at home with a few problems for familiarity, and that classroom time should be spent working through problems in a guided environment. This allows students to pause, rewind, rewatch, etc. the lectures and move at their own pace, while getting expert guidance on the problems in person (and not relying on parents who may not have even looked at the source material in decades).
    - dorchadas 9y ago
      As a math teacher (Algebra II), I think this would be great. The problem is that most of my students won't go home and watch the videos. Either because they can't (lack of internet access, have to work to help support family, etc.) or are just lazy and won't. I've had to quit giving homework, even to the upper level classes, because nobody would do it. They'd just come in the next day and make excuses and have nothing done. This includes when they're homework was just to watch videos explaining problems they missed on a standardized test they took. Most just refused to watch the videos at home. It'd be great if they would watch the lectures and then be able to practice in the hour I see them daily, asking questions to clarify and such. But I can guarantee you it won't happen without a huge shift in the culture of education.
      - sethammons 9y ago
        As a former inner city math teacher, I feel you. Getting students to do _anything_ outside the classroom was practically impossible. What worked for me for homework for a little while was having the students do 5 push ups for each day they missed homework in a row. I suddenly was getting 90%+ participation on students completing their homework! It was fantastic until someone told the VP, and the VP asked me if I was actually doing that, whereby they informed me that it was corporal punishment and absolutely against the rules. I could rant about that for a bit, but I'm sure you can guess what happened after the pushups stopped: homework stopped. As for the shift needed in the culture of education, I totally agree. There needs to be a shift in accountability for the students, their families, and for schools. While there were parents who hoped their kids would do well at the school where I taught, there was a pervasive home attitude of school will get you nowhere. Many of the kids had no role models in their life where they could see any value to education. One VP I knew, in a neighboring district, married into a poorer latino family. They valued hard work, but only really understood hard manual labor type efforts. He was constantly hounded as he was going through schooling by them. "Why are you wasting this time at school? Why are you not doing more to provide for my daughter? Go get a real job." After finally becoming a teacher and then a VP and making more money than any other member of the family he married into, they started to see how education could be an investment. I don't know how you do that on a scale where the majority of socio-economically depressed families and communities can be exposed to the value of education.
- TheOtherHobbes 9y ago
  And techers are trying to teach how to make change? I understand “anchoring to fives and tens” but I don’t understand why anyone thinks it’s a good way to do anything except confuse kids. Does independent research prove these approaches increase numeracy?
  - ColinWright 9y ago
    > And teachers are trying to teach how to make change? No, the "making change" comment is an example of how these techniques of thinking about numbers do turn up in real life. > I understand “anchoring to fives and tens” but I don’t understand why anyone thinks it’s a good way to do anything except confuse kids. It's a part of a broader strategy to talk about the structure of numbers and the operations on them. > Does independent research prove these approaches increase numeracy? Yes. I don't have access to it and can't give you any links, but there has been a lot of research about how to move away from the rote learning of algorithms and move towards understanding what numbers are and how they work. I've seen some of the research as a peripheral part of some of the projects I've been involved with, and it seems that these sorts of exercises really do serve to help students see more about what's really going on. The problem is the parents pushing back because they don't understand it, and don't believe it can be useful or helpful. For me, it seems obvious that this is a better way to think about things.
    - garmaine 9y ago
      I’m a parent and I object not because I don’t understand it — it’s not too difficult to pick up — but because it completely misses the why of math. Being able to mentally estimate numbers or do simple arithmetic is a good skill, but having universal algorithms for solving problems and describing the universe is really what math is more about. I can trace my trajectory into computer science all the way back to practicing multiplication tables and discovering that I could multiply numbers in long form too large to fit in my head and yet get the exact result. It is the power of the algorithm. My kids are entirely missing that in their common core education...
      - 9y ago
- contravariant 9y ago
  It's a bit weird when your mathematics education enables you to understand a book written several millennia ago, but not homework written several decades later.
ThomPete 9y ago
Understanding why has always been my primary way to learn things. Do you have any suggestions for books or courses I could dig into to better understand this approach. My oldest who is 8 is quite good at math and on the math team and his school does do a lot to teach them but I want to help him how to think. In almost every other field I can but I am not good enough at math to understand which "games" to play.
- ColinWright 9y ago
  Everyone has a balance of these things, but in my experience there are two extrema to approaching maths. Some people are happy to be solving the puzzles, and simply enjoy the thrill of the chase. Others insist on knowing why they should be learning this, and what it's good for. Both are valid, but if there is A and B and you're naturally good at A, the natural tendency is to ignore or avoid B. But that then limits your box of tricks, and makes you one-dimensional. By all means take advantage of what you're good at, but work hard on the other aspects to enrich your abilities. Also, they cross-fertilise, so you get more than you might expect. With regards your oldest, it's worth trying a bunch of stuff to see if you can work out what they prefer. Then do both, but be prepared for having to work harder on one aspect than the other. Your oldest might like puzzles for their own sake, or might insist on knowing what it's for. Explore both. Find maths in strange places, work through puzzles just for their own sake. The critical key is to be doing stuff all the time. Caveat: I don't have children, I have no formal training, but I do a lot of outreach, enrichment, and enhancement.
- lsc 9y ago
  I personally find Serge Lang's "Basic Mathematics" to be super useful in explaining the "why" of a particular formula in pre-college level math, as most books at my current level just seem to say "memorize this" He has an explanation of why x^0 is 1 and not 0 that doesn't involve calculus, for instance.
  - yorwba 9y ago
    What would be an explanation that involves calculus? The only one I know is that x^(a+b) = x^a * x^b holds for positive a and b, and to uphold that pattern, it's necessary that x^0 = 1, x^-1 = 1/x and so on. For me, all of that was covered long before calculus.
scotty79 9y ago
I think the key thing for making math worth knowing for a kid is making him realize that world is full of numbers. One way I intend to do that is providing kids with a lot of measuring devices as toys. Rulers, calipers, pirometers, timers, you name it. If it can give you number for something real then it's a good toy.
lsc 9y ago
So, I know a lot less about math than you do. However, I have been studying lately myself, and reading a lot of Martin Gardner and Serge Lang; Both of those (and many of the other math types I read) seem to hold that making math practical can be useful... but it's not the point of learning math any more than learning how to spell correctly is the point of studying literature.
DanBC 9y ago
Most teachers are happy if you want to make an appointment to talk to them. Or the book "Maths for mums and dads" is useful. https://www.amazon.co.uk/Maths-Mums-Dads-Mike-Askew/dp/0224086359/ https://www.amazon.co.uk/Maths-Mums-Dads-Mike-Askew/dp/02240... https://www.amazon.co.uk/More-Maths-Mums-Dads-Askew/dp/0224095315/ https://www.amazon.co.uk/More-Maths-Mums-Dads-Askew/dp/02240...
verylittlemeat 9y ago
I don't know if this is useful but Richard Feynman used to play a game with his son where they would try to guess and compare the size differences between things as a way of learning units.

ColinWright 9y ago

My (very limited) experience of more recent homework is that it makes perfect sense in the context of what the teachers are trying to teach, but no sense out of context to people who learned their maths decades ago. If you'd care to send me a photo of an example of the homework then I can try to give you some context and understanding. My contact details can be derived from my HN profile. I might be a little slow to reply at the moment as I'm in the middle of other things and only surfacing occasionally.

jonsen 9y ago
... makes perfect sense in the context of what the teachers are trying to teach ... What's the point with homework then? School takes the best part of a childs day, and when they don't make it through, the parents can finish with a tired child.
- ColinWright 9y ago
  "Homework" is supposed to be practising skills they have already learned so they can make it more fluent, and have to concentrate on it less when they come to the next thing to learn. Learning things is done with the teacher there to help anticipate, identify, and correct misconceptions. If you want the parent to help with the homework, the parent will have to know the material they want to help with. In maths, that's rarely the case unless it's the same thing they learned. And that's now out-of-date. Parents say they want their students to learn new, modern maths, and then insist that they are taught exactly what they were taught. And hated. Having said that, I'm really not going to defend anything about the existing setup and system. This is a huge mess, and while I have my own ideas, there's no way a discussion here will change anything, and it's likely that things I do say will be taken out of context, twisted, and mis-understood.
  - boblivion 9y ago
    As someone not from the U.S. I wonder, what does "outdated" mean? Can you give a simple example - e.g. comparison - what would be "math back then" and "math nowadays". Because to me math was always just math especially if it comes to numbers.
    - throwawaybbqed 9y ago
      I wanted to echo the parent poster. I'm in my 30s and math made no sense as a kid - precisely because the problems were all artificial and uninteresting. I had to fight major math phobia in undergrad. For me personally, the most interesting application of math was figuring out orbits/positions of stars, etc. I have a 2 year old so if you have another favorite example like this, I'd love to hear about it.
      - noir_lord 9y ago
        > the most interesting application of math was figuring out orbits/positions of stars. For me math started to click when I started writing simple games for the spectrum, I realized quite quickly that what I needed was trigonometry and once I knew the name I could go to the library and get out books. I was implementing a text based destroyer game (similar to mtrek/jtre though I didn't know those existed) and I had to implement handling bearings from the ship to the enemy ships, handle firing guns and missiles all that stuff, I made lots of horrible simplifications (shells experienced no air resistance so flew in perfect parabola's, the surface of the sea was a perfectly flat plane, no curvature (non-euclidean geometry would have been a step too far at 10-11) etc) but fundamentally it worked and was playable as a game, you could issue orders, fire shells (and later missiles though that made the game a lot more brutal and short) with bracketing and taking into time of flight - I was a strange child. I got the original idea from a ZX81 kids book on game programming that implemented a simple side projection game where you set the elevation and velocity of your shot and aimed for the opponents ship, it was simple (couple of pages of code) and I wanted to do something a bit more realistic - as a side benefit I ended up reading up on naval warfare in quite a lot of depth, again a strange child.
    - 9y ago
- michaelchisari 9y ago
  I don't mind this new way of teaching math, but on this note, I liked what Sal Khan had to say about flipping the process for school and homework. He proposed that students should watch lectures at home with a few problems for familiarity, and that classroom time should be spent working through problems in a guided environment. This allows students to pause, rewind, rewatch, etc. the lectures and move at their own pace, while getting expert guidance on the problems in person (and not relying on parents who may not have even looked at the source material in decades).
  - dorchadas 9y ago
    As a math teacher (Algebra II), I think this would be great. The problem is that most of my students won't go home and watch the videos. Either because they can't (lack of internet access, have to work to help support family, etc.) or are just lazy and won't. I've had to quit giving homework, even to the upper level classes, because nobody would do it. They'd just come in the next day and make excuses and have nothing done. This includes when they're homework was just to watch videos explaining problems they missed on a standardized test they took. Most just refused to watch the videos at home. It'd be great if they would watch the lectures and then be able to practice in the hour I see them daily, asking questions to clarify and such. But I can guarantee you it won't happen without a huge shift in the culture of education.
    - sethammons 9y ago
      As a former inner city math teacher, I feel you. Getting students to do _anything_ outside the classroom was practically impossible. What worked for me for homework for a little while was having the students do 5 push ups for each day they missed homework in a row. I suddenly was getting 90%+ participation on students completing their homework! It was fantastic until someone told the VP, and the VP asked me if I was actually doing that, whereby they informed me that it was corporal punishment and absolutely against the rules. I could rant about that for a bit, but I'm sure you can guess what happened after the pushups stopped: homework stopped. As for the shift needed in the culture of education, I totally agree. There needs to be a shift in accountability for the students, their families, and for schools. While there were parents who hoped their kids would do well at the school where I taught, there was a pervasive home attitude of school will get you nowhere. Many of the kids had no role models in their life where they could see any value to education. One VP I knew, in a neighboring district, married into a poorer latino family. They valued hard work, but only really understood hard manual labor type efforts. He was constantly hounded as he was going through schooling by them. "Why are you wasting this time at school? Why are you not doing more to provide for my daughter? Go get a real job." After finally becoming a teacher and then a VP and making more money than any other member of the family he married into, they started to see how education could be an investment. I don't know how you do that on a scale where the majority of socio-economically depressed families and communities can be exposed to the value of education.
TheOtherHobbes 9y ago
And techers are trying to teach how to make change? I understand “anchoring to fives and tens” but I don’t understand why anyone thinks it’s a good way to do anything except confuse kids. Does independent research prove these approaches increase numeracy?
- ColinWright 9y ago
  > And teachers are trying to teach how to make change? No, the "making change" comment is an example of how these techniques of thinking about numbers do turn up in real life. > I understand “anchoring to fives and tens” but I don’t understand why anyone thinks it’s a good way to do anything except confuse kids. It's a part of a broader strategy to talk about the structure of numbers and the operations on them. > Does independent research prove these approaches increase numeracy? Yes. I don't have access to it and can't give you any links, but there has been a lot of research about how to move away from the rote learning of algorithms and move towards understanding what numbers are and how they work. I've seen some of the research as a peripheral part of some of the projects I've been involved with, and it seems that these sorts of exercises really do serve to help students see more about what's really going on. The problem is the parents pushing back because they don't understand it, and don't believe it can be useful or helpful. For me, it seems obvious that this is a better way to think about things.
  - garmaine 9y ago
    I’m a parent and I object not because I don’t understand it — it’s not too difficult to pick up — but because it completely misses the why of math. Being able to mentally estimate numbers or do simple arithmetic is a good skill, but having universal algorithms for solving problems and describing the universe is really what math is more about. I can trace my trajectory into computer science all the way back to practicing multiplication tables and discovering that I could multiply numbers in long form too large to fit in my head and yet get the exact result. It is the power of the algorithm. My kids are entirely missing that in their common core education...
    - 9y ago
contravariant 9y ago
It's a bit weird when your mathematics education enables you to understand a book written several millennia ago, but not homework written several decades later.

ThomPete 9y ago

Understanding why has always been my primary way to learn things. Do you have any suggestions for books or courses I could dig into to better understand this approach. My oldest who is 8 is quite good at math and on the math team and his school does do a lot to teach them but I want to help him how to think. In almost every other field I can but I am not good enough at math to understand which "games" to play.

ColinWright 9y ago
Everyone has a balance of these things, but in my experience there are two extrema to approaching maths. Some people are happy to be solving the puzzles, and simply enjoy the thrill of the chase. Others insist on knowing why they should be learning this, and what it's good for. Both are valid, but if there is A and B and you're naturally good at A, the natural tendency is to ignore or avoid B. But that then limits your box of tricks, and makes you one-dimensional. By all means take advantage of what you're good at, but work hard on the other aspects to enrich your abilities. Also, they cross-fertilise, so you get more than you might expect. With regards your oldest, it's worth trying a bunch of stuff to see if you can work out what they prefer. Then do both, but be prepared for having to work harder on one aspect than the other. Your oldest might like puzzles for their own sake, or might insist on knowing what it's for. Explore both. Find maths in strange places, work through puzzles just for their own sake. The critical key is to be doing stuff all the time. Caveat: I don't have children, I have no formal training, but I do a lot of outreach, enrichment, and enhancement.
lsc 9y ago
I personally find Serge Lang's "Basic Mathematics" to be super useful in explaining the "why" of a particular formula in pre-college level math, as most books at my current level just seem to say "memorize this" He has an explanation of why x^0 is 1 and not 0 that doesn't involve calculus, for instance.
- yorwba 9y ago
  What would be an explanation that involves calculus? The only one I know is that x^(a+b) = x^a * x^b holds for positive a and b, and to uphold that pattern, it's necessary that x^0 = 1, x^-1 = 1/x and so on. For me, all of that was covered long before calculus.

scotty79 9y ago

I think the key thing for making math worth knowing for a kid is making him realize that world is full of numbers. One way I intend to do that is providing kids with a lot of measuring devices as toys. Rulers, calipers, pirometers, timers, you name it. If it can give you number for something real then it's a good toy.

lsc 9y ago

So, I know a lot less about math than you do. However, I have been studying lately myself, and reading a lot of Martin Gardner and Serge Lang; Both of those (and many of the other math types I read) seem to hold that making math practical can be useful... but it's not the point of learning math any more than learning how to spell correctly is the point of studying literature.

DanBC 9y ago

Most teachers are happy if you want to make an appointment to talk to them. Or the book "Maths for mums and dads" is useful. https://www.amazon.co.uk/Maths-Mums-Dads-Mike-Askew/dp/0224086359/ https://www.amazon.co.uk/Maths-Mums-Dads-Mike-Askew/dp/02240... https://www.amazon.co.uk/More-Maths-Mums-Dads-Askew/dp/0224095315/ https://www.amazon.co.uk/More-Maths-Mums-Dads-Askew/dp/02240...

verylittlemeat 9y ago

I don't know if this is useful but Richard Feynman used to play a game with his son where they would try to guess and compare the size differences between things as a way of learning units.