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I would agree, but qualify by saying that not all the blame lies with the student. Precisely because mathematics is so interconnected, beginning students reall

I would agree, but qualify by saying that not all the blame lies with the student. Precisely because mathematics is so interconnected, beginning students really do require an experienced guide to navigate through the tangled web of concepts. A particularly bad or lazy professor can be worse than no professor at all.

kkylin 6y ago
Not arguing with your point, because it has merit, but do want to add that part of the problem with math education (at least here in the US) is structural: for most students, to start with what they know when they enter and to graduate in 4 years with a engineering / science / math / CS degree that means something, there is just too much to "cover." So we tend to cover "methods and tools," e.g., calculus first, with the motivation (e.g., electrical circuits or statistical regression or what have you) later. This lack of context makes it very hard to see how things fit together. For my own part, I usually learned the material from one course when I needed to use it in a subsequent course -- it's in going back to review the material when I really learn it. Edit: also want to add that providing context in early courses isn't always easy, because students are much more diverse now in their career plans. It used to be (this tells you how old I am) that many of the students taking calculus would also be taking (or have taken) a calculus-based physics course. Those days are long gone.
- johnsonjo 6y ago
  I took Physics as an elective in University, but it really didn’t sharpen my Calculus skills. Which is sad, but probably because I did so bad in Calculus as an undergraduate. But, one thing I absolutely did take away from Physics was the idea of units and their conversions. It has come in handy so often though in and outside my degree of computer science. If I had to simplify it, it really helps you not to compare apples to oranges. At the beginning of Street Fighting Mathematics it brings up that point. For example it isn’t a good comparison to compare the wealth in assets of a given company to a countries GDP. Because, GDP is happening over every year in time whereas the wealth is merely effected by what point in time it’s observed. Units help one see that in order to be truly and more fairly comparable they have to be the same type of units. I used an analogy of units in physics recently to help a teammate with types and generics, sadly I can’t remember exactly what I said haha other than don’t compare apples to oranges, but I think I had further insight than just that.
  - kkylin 6y ago
    Absolutely! internalizing dimensional analysis has been one of the most useful things I learned in grad school -- even though converting units was something many of us learn, in one form or another, before college.
    - lmilcin 6y ago
      It is interesting how some of the things just feel like common knowledge when they are not. I frequently see people comparing things that aren't really comparable and it always seems to me it should be obvious this can't be done. Most common example is mixing watts and watt*hours. Which should be pretty obvious. Nobody mixes by accident the speed at which you travel with the distance you have to travel. Nobody says "My car can pull off 200kms" or "I have 120km/h to cover" yet the same happens for energy vs power on a daily basis, even in publications.
- ghaff 6y ago
  >It used to be (this tells you how old I am) Why do you say that? Maybe it's atypical but MIT seems to have the same calculus and physics sequence, taken in parallel, that they did ages ago.
  - vitus 6y ago
    At Berkeley, for instance, there were multiple Physics sequences: engineering + physics + chem majors took the 7 series ("Physics for Scientists and Engineers"), which used calculus; for most other majors (e.g. premed), the 8 series ("Introductory Physics") sufficed for degree requirements. http://guide.berkeley.edu/courses/physics/ http://guide.berkeley.edu/courses/physics/ (Also, note that this is similar to the split between the AP Physics B and C courses that high school students might take. Physics B has apparently been replaced with Physics 1 / 2, both of which are algebra- rather than calculus-based.) I think ultimately this is a function of where you went to school, more than anything.
  - kkylin 6y ago
    I think tech-oriented schools, e.g., Caltech, MIT, Georgia Tech, etc., are exceptions rather than the rule. Most large state universities in the US are likely to have different physics / chemistry / math courses for students heading in different directons. Not all intro physics courses will be calculus-based, yet some of the students in those courses will still have to take calculus. Many US medical schools, for example, silll require 1 semester calculus and some physics, but I don't think the physics course needs to be calculus-based. Many used to require a second calculus, but I think that has largely shifted to biostatistics instead.
hawkice 6y ago
> students really do require an experienced guide to navigate through the tangled web of concepts. Consider how much people pay for education and don't get this, and how much some people are paid to be teachers who do not provide it.
- benrbray 6y ago
  Oh yeah, I'm with you there. Teaching quality at both my undergrad math program and my graduate compsci program was abysmal, with the exception of a handful of dedicated teachers. Both at well-ranked research institutions, which is the problem. The whole system is crazy. Why on earth do we allow tuition money to be spent on anything else but full-time teaching staff?!
  - wolfram74 6y ago
    I'm now interested in a list of transactions ordered by participant dissatisfaction, like, paying for gym memberships and not getting the outcomes they want, therapy or medical attention to mostly be ignored by the provider, ISPs in the US, online shopping to get something wildly different. Is education especially bad compared to these things? or just that it's such a large expenditure we just-world-fallacy ourselves into thinking it ought to work better?
    - spijdar 6y ago
      Is it really a logical fallacy to assume that we should have better outcomes from spending tens to hundreds of thousands of dollars on academia vs e.g. spending thirty dollars on amazon? At least naively, that money could (should?) be going towards paying for staff and a support system/hierarchy to ensure a higher quality. That's at least nominally why accredited, non-profit education is so expensive, because it's nominally supposed to be capable of paying decent salaries to intelligent people dedicated to teaching, compared to say amazon or the gym where the incentives are to cost cut and maximize profit. In reality, I suspect the same applies to colleges, but I don't think it should, in some ideal world.
  - abdullahkhalids 6y ago

kkylin 6y ago

Not arguing with your point, because it has merit, but do want to add that part of the problem with math education (at least here in the US) is structural: for most students, to start with what they know when they enter and to graduate in 4 years with a engineering / science / math / CS degree that means something, there is just too much to "cover." So we tend to cover "methods and tools," e.g., calculus first, with the motivation (e.g., electrical circuits or statistical regression or what have you) later. This lack of context makes it very hard to see how things fit together. For my own part, I usually learned the material from one course when I needed to use it in a subsequent course -- it's in going back to review the material when I really learn it. Edit: also want to add that providing context in early courses isn't always easy, because students are much more diverse now in their career plans. It used to be (this tells you how old I am) that many of the students taking calculus would also be taking (or have taken) a calculus-based physics course. Those days are long gone.

johnsonjo 6y ago
I took Physics as an elective in University, but it really didn’t sharpen my Calculus skills. Which is sad, but probably because I did so bad in Calculus as an undergraduate. But, one thing I absolutely did take away from Physics was the idea of units and their conversions. It has come in handy so often though in and outside my degree of computer science. If I had to simplify it, it really helps you not to compare apples to oranges. At the beginning of Street Fighting Mathematics it brings up that point. For example it isn’t a good comparison to compare the wealth in assets of a given company to a countries GDP. Because, GDP is happening over every year in time whereas the wealth is merely effected by what point in time it’s observed. Units help one see that in order to be truly and more fairly comparable they have to be the same type of units. I used an analogy of units in physics recently to help a teammate with types and generics, sadly I can’t remember exactly what I said haha other than don’t compare apples to oranges, but I think I had further insight than just that.
- kkylin 6y ago
  Absolutely! internalizing dimensional analysis has been one of the most useful things I learned in grad school -- even though converting units was something many of us learn, in one form or another, before college.
  - lmilcin 6y ago
    It is interesting how some of the things just feel like common knowledge when they are not. I frequently see people comparing things that aren't really comparable and it always seems to me it should be obvious this can't be done. Most common example is mixing watts and watt*hours. Which should be pretty obvious. Nobody mixes by accident the speed at which you travel with the distance you have to travel. Nobody says "My car can pull off 200kms" or "I have 120km/h to cover" yet the same happens for energy vs power on a daily basis, even in publications.
ghaff 6y ago
>It used to be (this tells you how old I am) Why do you say that? Maybe it's atypical but MIT seems to have the same calculus and physics sequence, taken in parallel, that they did ages ago.
- vitus 6y ago
  At Berkeley, for instance, there were multiple Physics sequences: engineering + physics + chem majors took the 7 series ("Physics for Scientists and Engineers"), which used calculus; for most other majors (e.g. premed), the 8 series ("Introductory Physics") sufficed for degree requirements. http://guide.berkeley.edu/courses/physics/ http://guide.berkeley.edu/courses/physics/ (Also, note that this is similar to the split between the AP Physics B and C courses that high school students might take. Physics B has apparently been replaced with Physics 1 / 2, both of which are algebra- rather than calculus-based.) I think ultimately this is a function of where you went to school, more than anything.
- kkylin 6y ago
  I think tech-oriented schools, e.g., Caltech, MIT, Georgia Tech, etc., are exceptions rather than the rule. Most large state universities in the US are likely to have different physics / chemistry / math courses for students heading in different directons. Not all intro physics courses will be calculus-based, yet some of the students in those courses will still have to take calculus. Many US medical schools, for example, silll require 1 semester calculus and some physics, but I don't think the physics course needs to be calculus-based. Many used to require a second calculus, but I think that has largely shifted to biostatistics instead.

hawkice 6y ago

> students really do require an experienced guide to navigate through the tangled web of concepts. Consider how much people pay for education and don't get this, and how much some people are paid to be teachers who do not provide it.

benrbray 6y ago
Oh yeah, I'm with you there. Teaching quality at both my undergrad math program and my graduate compsci program was abysmal, with the exception of a handful of dedicated teachers. Both at well-ranked research institutions, which is the problem. The whole system is crazy. Why on earth do we allow tuition money to be spent on anything else but full-time teaching staff?!
- wolfram74 6y ago
  I'm now interested in a list of transactions ordered by participant dissatisfaction, like, paying for gym memberships and not getting the outcomes they want, therapy or medical attention to mostly be ignored by the provider, ISPs in the US, online shopping to get something wildly different. Is education especially bad compared to these things? or just that it's such a large expenditure we just-world-fallacy ourselves into thinking it ought to work better?
  - spijdar 6y ago
    Is it really a logical fallacy to assume that we should have better outcomes from spending tens to hundreds of thousands of dollars on academia vs e.g. spending thirty dollars on amazon? At least naively, that money could (should?) be going towards paying for staff and a support system/hierarchy to ensure a higher quality. That's at least nominally why accredited, non-profit education is so expensive, because it's nominally supposed to be capable of paying decent salaries to intelligent people dedicated to teaching, compared to say amazon or the gym where the incentives are to cost cut and maximize profit. In reality, I suspect the same applies to colleges, but I don't think it should, in some ideal world.
- abdullahkhalids 6y ago