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A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underly

by atroyn 11y ago

A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underlying concepts. Teachers who only remember the procedures can of course only teach procedures. Most adults don't even remember any procedures, since they have no need to in daily life. This condemns children to repeat the cycle. They (completely rationally) decide that they're just 'not math people' because they can't follow lists of arbitrary seeming steps to do something that no one they have ever met ever actually does in daily life. And some of them grow up to be teachers themselves.

Thriptic 11y ago
> A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underlying concepts. Teachers who only remember the procedures can of course only teach procedures Sigh, your statement reminds me of one time when I was in 6th grade geometry and was asked to complete this one proof. The problem was intended to get us to apply a concept we had been taught verbatim, but I couldn't remember it well and so I completed the proof a different way by extrapolating other basic concepts we had gone over into a method we had not been taught. I remember feeling very proud of myself when I finished, as I had created something which in my 12 year old eyes was a "novel proof". I ended up being given 0 points on the problem because I did not complete my proof using cookie cutter methods we had been taught (even though my proof was correct and it was not specified that I use a particular concept in the instructions). I remember complaining to my teacher about how this was unfair and she kept saying something akin to "well you didn't do the problem the right way". The incident pretty much killed any interest I had in math, which wasn't rekindled until I stumbled upon machine learning recently in my 20s.
- Xcelerate 11y ago
  That kind of story makes me irrationally upset. That's horrible — killing a child's interest in math because they didn't do the problem the "right way". It's completely antagonistic to the spirit of the field. Teachers shouldn't be teaching subjects if they don't understand them.
  - Kluny 11y ago
    Same - I vow to make sure that never happens to my kids, even if I have to homeschool them.
    - _rpd 11y ago
      We had to homeschool for a year because of this (substitute teacher just going through the motions). My son has been a year ahead in math ever since. We've had to supplement to keep him challenged.
  - zeidrich 11y ago
    Its these kind of experiences that I want to learn to teach my child to make it through. There are a lot of other people out there who will unknowingly be very discouraging, to both children and adults, but their opinions have no bearing on our ability to learn. I remember being in music class in grade 1 and it was my absolute favorite class. Near the end of the year I was told that I wasn't very good at singing by my teacher. I never tried to sing again, but I learned later that I have good pitch and a decent voice. I am not really interested in singing now, but I might have learned a different set of skills if I didn't avoid it. Is there a way that I could have been prepared so that being told by the person I looked up to for validation, that I was no good wouldn't make me stop trying to improve? I don't know about that, but if there's a way to teach that, it would definitely be a good lesson. It would certainly be nice if teachers didn't do things like that, but even if you could guarantee they didn't, you won't stop the bullies or the critics or anyone other hater as you get older.
    - mikeash 11y ago
      As they say, don't let your schooling get in the way of your education. To the grandparent: I don't think getting upset is at all irrational.
- aianus 11y ago
  This still happens to me when getting graded by peers on coursera. Makes me feel good about my job security :)
bitwize 11y ago
This itself explains the worship of the Standard Algorithm, and why people see a New World Order conspiracy behind every attempt to reform math education. Not helping matters is the fact that most of the reformers are themselves ignorant chuckleheads who identify the heuristics that skilled arithmeticians use and codify them as a NEW set of rules to be memorized...
- stdbrouw 11y ago
  FWIW, this is certainly not what people who do research into how to teach math advocate. In fact, one of the recommendations for teachers is that they should try to get students to come up with the algorithms themselves, or to "guide" them to these algorithms, and then let students use whichever they prefer, because that's the only way to get students to really understand and use them. That said, I've definitely seen some of that "let's just replace method X with method Y" – how harmful that is depends on whether it is just presented as a default or as The New Standard Algorithm, I guess.
  - bitwize 11y ago
    > FWIW, this is certainly not what people who do research into how to teach math advocate. Of course it isn't, because such lunacy wouldn't be supported by competent research. But the people who do education research, the administrators making curriculum decisions, and the concerned parents trolling about the dangers of "Common Core" on Facebook are distinct sets with little overlap.
- milspec 11y ago
  Standard algorithms are standard for very good reasons. They are 100% reliable and at least reasonably fast, if not the fastest. Failure to learn the standard algorithms impedes progress. You are unlikely to do well in the next course if you are slow and can't handle numerous cases. Learning alternate algorithms is great... once you have the standard algorithms down solid and are ready to prove equivalence.
  - keithpeter 11y ago

by atroyn 11y ago

Thriptic 11y ago

> A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underlying concepts. Teachers who only remember the procedures can of course only teach procedures Sigh, your statement reminds me of one time when I was in 6th grade geometry and was asked to complete this one proof. The problem was intended to get us to apply a concept we had been taught verbatim, but I couldn't remember it well and so I completed the proof a different way by extrapolating other basic concepts we had gone over into a method we had not been taught. I remember feeling very proud of myself when I finished, as I had created something which in my 12 year old eyes was a "novel proof". I ended up being given 0 points on the problem because I did not complete my proof using cookie cutter methods we had been taught (even though my proof was correct and it was not specified that I use a particular concept in the instructions). I remember complaining to my teacher about how this was unfair and she kept saying something akin to "well you didn't do the problem the right way". The incident pretty much killed any interest I had in math, which wasn't rekindled until I stumbled upon machine learning recently in my 20s.

Xcelerate 11y ago
That kind of story makes me irrationally upset. That's horrible — killing a child's interest in math because they didn't do the problem the "right way". It's completely antagonistic to the spirit of the field. Teachers shouldn't be teaching subjects if they don't understand them.
- Kluny 11y ago
  Same - I vow to make sure that never happens to my kids, even if I have to homeschool them.
  - _rpd 11y ago
    We had to homeschool for a year because of this (substitute teacher just going through the motions). My son has been a year ahead in math ever since. We've had to supplement to keep him challenged.
- zeidrich 11y ago
  Its these kind of experiences that I want to learn to teach my child to make it through. There are a lot of other people out there who will unknowingly be very discouraging, to both children and adults, but their opinions have no bearing on our ability to learn. I remember being in music class in grade 1 and it was my absolute favorite class. Near the end of the year I was told that I wasn't very good at singing by my teacher. I never tried to sing again, but I learned later that I have good pitch and a decent voice. I am not really interested in singing now, but I might have learned a different set of skills if I didn't avoid it. Is there a way that I could have been prepared so that being told by the person I looked up to for validation, that I was no good wouldn't make me stop trying to improve? I don't know about that, but if there's a way to teach that, it would definitely be a good lesson. It would certainly be nice if teachers didn't do things like that, but even if you could guarantee they didn't, you won't stop the bullies or the critics or anyone other hater as you get older.
  - mikeash 11y ago
    As they say, don't let your schooling get in the way of your education. To the grandparent: I don't think getting upset is at all irrational.
aianus 11y ago
This still happens to me when getting graded by peers on coursera. Makes me feel good about my job security :)

bitwize 11y ago

This itself explains the worship of the Standard Algorithm, and why people see a New World Order conspiracy behind every attempt to reform math education. Not helping matters is the fact that most of the reformers are themselves ignorant chuckleheads who identify the heuristics that skilled arithmeticians use and codify them as a NEW set of rules to be memorized...

stdbrouw 11y ago
FWIW, this is certainly not what people who do research into how to teach math advocate. In fact, one of the recommendations for teachers is that they should try to get students to come up with the algorithms themselves, or to "guide" them to these algorithms, and then let students use whichever they prefer, because that's the only way to get students to really understand and use them. That said, I've definitely seen some of that "let's just replace method X with method Y" – how harmful that is depends on whether it is just presented as a default or as The New Standard Algorithm, I guess.
- bitwize 11y ago
  > FWIW, this is certainly not what people who do research into how to teach math advocate. Of course it isn't, because such lunacy wouldn't be supported by competent research. But the people who do education research, the administrators making curriculum decisions, and the concerned parents trolling about the dangers of "Common Core" on Facebook are distinct sets with little overlap.
milspec 11y ago
Standard algorithms are standard for very good reasons. They are 100% reliable and at least reasonably fast, if not the fastest. Failure to learn the standard algorithms impedes progress. You are unlikely to do well in the next course if you are slow and can't handle numerous cases. Learning alternate algorithms is great... once you have the standard algorithms down solid and are ready to prove equivalence.
- keithpeter 11y ago