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One other suggestion: read some research on mathematics education. Look through some of the proceedings of some of the recent RUME (research on undergraduate m

One other suggestion: read some research on mathematics education. Look through some of the proceedings of some of the recent RUME (research on undergraduate math education) conferences, for example: http://sigmaa.maa.org/rume/Site/Proceedings.html http://sigmaa.maa.org/rume/Site/Proceedings.html This book How Students Learn (PDF can be downloaded for free) covers math education (as well as history and science) http://www.nap.edu/catalog.php?record_id=10126 http://www.nap.edu/catalog.php?record_id=10126 it is a sequel to the excellent (and free) book How People Learn: http://www.nap.edu/catalog.php?record_id=9853 http://www.nap.edu/catalog.php?record_id=9853 Students need a motivating context, a reason to learn mathematics (or any topic). It's called situated learning (also situated cognition, situated action) - with techniques like problem-based learning, challenge-based learning, service learning, project-based learning, learning by design, learning through games, simulations, modeling, programming, etc. That's one side of it. Another is embodied learning. That's how we understand math (and other) concepts. See for example work by Rafael Nunez http://vislab.cs.vt.edu/~quek/classes/aware+embodiedinteraction/papers/nunem99.pdf http://vislab.cs.vt.edu/~quek/classes/aware+embodiedinteract... http://www.cogsci.ucsd.edu/~nunez/web/FM.PDF http://www.cogsci.ucsd.edu/~nunez/web/FM.PDF

wisty 14y ago
OK, I know a bit about pedagogy, and a lot of it is crap. There's an awful lot of relativism in most of it. Many of the people who teach teachers simply don't care about what works in classrooms, because empiricism is an evil capitalist plot (or something like that). When the Wikipedia page for Education has gems like "Based on the works of Jung", you know you're not in a field which cares about hard facts. Not that it's a real problem - the statistics show that first year teachers are pretty poor (regardless of the amount of pedagogy training they have), but they learn on the job and are pretty good after about 2 years (unless they are just doing a year of teaching to pad their resume, but that's another debate). I've got a lot of respect for cognitive science though, and that seems to be what you are recommending.
- disgruntledphd2 14y ago
  Note that Jung was one of the first people to invetigate the use of words in schizophrenia (in his thesis, as a matter of fact). Secondly, he created the conception of extroverts and introverts that we typically use to describe people today. Seriously, go read some of the works of Jung before you sound off on his issues. I did, and I was pleasantly surprised at just how sensible he was. I completely agree that much of modern educational training is quite poor, but take aim at (for example, the Myers Briggs or visual, auditory, kinesthetic learning) rather than poor old Jung.
  - marshallp 14y ago
    Except the examples you've given like extroverts vs introverts are not scientifically rigorous and the terms already existed well before him all around the world in different cultures (outgoing vs shy/retiring etc).
    - disgruntledphd2 14y ago
      Statistics was pretty much in its infancy back then, how would you have proposed he be scientifically rigorous? Actually, if you could give me your definition of scientific rigour that would probably help.
      - marshallp 14y ago
        Statistics was around then. I consider science to be the art of making correct predictions. So you need a hypothesis (in the form of equations or computer programs) that can be tested on observations leading to correct predictions. Extroversion/introversion might be scientifically rigorours by that definition (they might have done quantitative studies) but I'm not sure Jung did those, and even that it makes sense to create such a classificaton - people are a lot more complex and I don't really see the need for use of such classifications. That's a problem I see with psychology, sociology, economics, and other "soft" fields. The quantification of things which are far more complex than the simplistic models created to the point that they are essentially meaningless. It's meaningless to quantify people into races or skin colors and that's about the level that those sciences are at.
- keithpeter 14y ago
  "OK, I know a bit about pedagogy, and a lot of it is crap." Any hard empirical evidence for this assertion? "There's an awful lot of relativism in most of it." Well, yes, people are not Turing machines or well defined physical systems. As Peter Medawar reminded us, science is the 'art of the solvable'. We need an 'art' for the things that are not solvable in the way he meant. "...you know you're not in a field which cares about hard facts..." Yes, teaching and learning is not a field that depends on hard facts alone. The 'soft' factors are important as well. Student teachers need some pointers, models, methods, examples of how to deal with the soft factors. Situated learning big time. "...but they learn on the job and are pretty good after about 2 years..." In the UK, most teacher training is based around a supervised teaching practice already, and our government is planning to make it more so. You do not become qualified until after your probationary year is complete (that is on top of the minimum one year training). Another strand is reflective practice, actually looking at your own teaching, its impact (or lack of impact) on students and how to change things. That means a student teacher can 'learn on the job' more effectively.
  - wisty 14y ago
    > Any hard empirical evidence for this assertion? There's no hard empirical evidence that Scientology is crap, but I'm comfortable making that statement too. Statistical studies showing little to no positive correlation between level of training (not including practicums - which the UK is obviously using extensively, good on them) and student outcomes is pretty damning though. There's some correlation between doing a masters level education course, and English teaching ability, but OLS shows this is just because students with good English ability (high writing scores in high school) are more likely to do a masters level teaching course. > Yes, teaching and learning is not a field that depends on hard facts alone. The 'soft' factors are important as well. Student teachers need some pointers, models, methods, examples of how to deal with the soft factors. For example, they should be learning psychology that's not so outdated that the Cosmopolitan magazine should be embarrassed to write articles on it (Myers-Briggs is totally discredited). I'm not saying I'm a hard reductionist. Education should be based on fundamental psychological foundations if possible, and while that's not always possible they should at least try to either teach stuff which is fundamentally sound, or actually works in the classroom.
capnrefsmmat 14y ago
(author here) Thanks. I'm a physics major, and I've done quite a lot of research into physics education, but I haven't looked into math education. I'll have to take a look into your references. I wrote this article a few months back when there was a flood of "why do we need math?!" articles after some editorial said it's worthless; I only got around to putting it up Friday. So it's aimed more to why we need math, rather than how we should teach it. I've got a whole separate article on physics education which I'll have to put up soon.
hdivider 14y ago
Useful resources - thank you for that. "with techniques like problem-based learning, challenge-based learning, service learning, project-based learning, learning by design, learning through games, simulations, modeling, programming, etc." I'm glad you mention games, because currently this field is mostly all about teaching arithmetic and other elementary subjects. Notable innovative exceptions are DragonBox and a few others in development. It's probably a clichè to say that mathematics education is archaic, but it's true in a lot of cases. I've been to lectures where a simple 3-D program like Blender a few minutes of simple 3D work would have significantly helped countless students to imagine the mathematical entities being discussed. But alas, such things seem to be too advanced for much of academia - instead they build plastic models that only 1 person can use at a time.

wisty 14y ago

OK, I know a bit about pedagogy, and a lot of it is crap. There's an awful lot of relativism in most of it. Many of the people who teach teachers simply don't care about what works in classrooms, because empiricism is an evil capitalist plot (or something like that). When the Wikipedia page for Education has gems like "Based on the works of Jung", you know you're not in a field which cares about hard facts. Not that it's a real problem - the statistics show that first year teachers are pretty poor (regardless of the amount of pedagogy training they have), but they learn on the job and are pretty good after about 2 years (unless they are just doing a year of teaching to pad their resume, but that's another debate). I've got a lot of respect for cognitive science though, and that seems to be what you are recommending.

disgruntledphd2 14y ago
Note that Jung was one of the first people to invetigate the use of words in schizophrenia (in his thesis, as a matter of fact). Secondly, he created the conception of extroverts and introverts that we typically use to describe people today. Seriously, go read some of the works of Jung before you sound off on his issues. I did, and I was pleasantly surprised at just how sensible he was. I completely agree that much of modern educational training is quite poor, but take aim at (for example, the Myers Briggs or visual, auditory, kinesthetic learning) rather than poor old Jung.
- marshallp 14y ago
  Except the examples you've given like extroverts vs introverts are not scientifically rigorous and the terms already existed well before him all around the world in different cultures (outgoing vs shy/retiring etc).
  - disgruntledphd2 14y ago
    Statistics was pretty much in its infancy back then, how would you have proposed he be scientifically rigorous? Actually, if you could give me your definition of scientific rigour that would probably help.
    - marshallp 14y ago
      Statistics was around then. I consider science to be the art of making correct predictions. So you need a hypothesis (in the form of equations or computer programs) that can be tested on observations leading to correct predictions. Extroversion/introversion might be scientifically rigorours by that definition (they might have done quantitative studies) but I'm not sure Jung did those, and even that it makes sense to create such a classificaton - people are a lot more complex and I don't really see the need for use of such classifications. That's a problem I see with psychology, sociology, economics, and other "soft" fields. The quantification of things which are far more complex than the simplistic models created to the point that they are essentially meaningless. It's meaningless to quantify people into races or skin colors and that's about the level that those sciences are at.
keithpeter 14y ago
"OK, I know a bit about pedagogy, and a lot of it is crap." Any hard empirical evidence for this assertion? "There's an awful lot of relativism in most of it." Well, yes, people are not Turing machines or well defined physical systems. As Peter Medawar reminded us, science is the 'art of the solvable'. We need an 'art' for the things that are not solvable in the way he meant. "...you know you're not in a field which cares about hard facts..." Yes, teaching and learning is not a field that depends on hard facts alone. The 'soft' factors are important as well. Student teachers need some pointers, models, methods, examples of how to deal with the soft factors. Situated learning big time. "...but they learn on the job and are pretty good after about 2 years..." In the UK, most teacher training is based around a supervised teaching practice already, and our government is planning to make it more so. You do not become qualified until after your probationary year is complete (that is on top of the minimum one year training). Another strand is reflective practice, actually looking at your own teaching, its impact (or lack of impact) on students and how to change things. That means a student teacher can 'learn on the job' more effectively.
- wisty 14y ago
  > Any hard empirical evidence for this assertion? There's no hard empirical evidence that Scientology is crap, but I'm comfortable making that statement too. Statistical studies showing little to no positive correlation between level of training (not including practicums - which the UK is obviously using extensively, good on them) and student outcomes is pretty damning though. There's some correlation between doing a masters level education course, and English teaching ability, but OLS shows this is just because students with good English ability (high writing scores in high school) are more likely to do a masters level teaching course. > Yes, teaching and learning is not a field that depends on hard facts alone. The 'soft' factors are important as well. Student teachers need some pointers, models, methods, examples of how to deal with the soft factors. For example, they should be learning psychology that's not so outdated that the Cosmopolitan magazine should be embarrassed to write articles on it (Myers-Briggs is totally discredited). I'm not saying I'm a hard reductionist. Education should be based on fundamental psychological foundations if possible, and while that's not always possible they should at least try to either teach stuff which is fundamentally sound, or actually works in the classroom.

capnrefsmmat 14y ago

(author here) Thanks. I'm a physics major, and I've done quite a lot of research into physics education, but I haven't looked into math education. I'll have to take a look into your references. I wrote this article a few months back when there was a flood of "why do we need math?!" articles after some editorial said it's worthless; I only got around to putting it up Friday. So it's aimed more to why we need math, rather than how we should teach it. I've got a whole separate article on physics education which I'll have to put up soon.

hdivider 14y ago

Useful resources - thank you for that. "with techniques like problem-based learning, challenge-based learning, service learning, project-based learning, learning by design, learning through games, simulations, modeling, programming, etc." I'm glad you mention games, because currently this field is mostly all about teaching arithmetic and other elementary subjects. Notable innovative exceptions are DragonBox and a few others in development. It's probably a clichè to say that mathematics education is archaic, but it's true in a lot of cases. I've been to lectures where a simple 3-D program like Blender a few minutes of simple 3D work would have significantly helped countless students to imagine the mathematical entities being discussed. But alas, such things seem to be too advanced for much of academia - instead they build plastic models that only 1 person can use at a time.