All Kids Left Behind!

  • #51
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By saying my prof gives me a giant equation sheet full of all the equations we'll need to either do the problems or derive the equations to do the problems.
Be more clear next time then, this was not what you said!
Read this again:
my physics prof actually gives us the necessary equations before each exam.
To me that sounds like your professor gave you a sheet of formulas you should study for the exam, not like you got a sheet to use on the exam. You don't just say "got before each exam" for things you get to use on the exam. If I for example say "We got a set of problems together with solutions before each exam" you wouldn't read that as if I got to take solved problems with me at each exam.
At this point, you're either purposefully misconstruing my argument simply to continue the argument, or you're rushing through my post without reading it carefully.
Or you are rushing through your posts without writing them carefully, most of your points are really unclear. Like this:
So if I'm the best one in my real calculus-based intro physics class (read: not AP) without having had a shred of algebra physics, does this cancel out your 'proof'?
I never said that I had any 'proof' and neither is this a proof. Also when you say "real calculus-based intro physics class (read: not AP)" for example do you mean that it is easier or harder than AP physics and what would be the difference then? Can you tell more clearly what this course includes, at what level it is instead of what it isn't etc.
One wonders whether you would've just gone equation hunting.
Why would you think that just because I took physics classes much earlier than you I didn't understand the physics but instead just looked up/memorized my equations? I have taught calculus classes at my university and I already got a degree in physics. I think that I know the subjects in question well enough to have an educated opinion and I think that I got a good understanding of the general physical concepts back in that class. At least I understood it to such a degree that when I later studied calculus I quickly realized how it could be applied to the physics I already knew.
 
  • #52
Borek
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I never said they were worse at maths than other subjects. Just that the average person is bad at maths.
You see - you said that again.

But there is a flawed logic here - you can't be on average bad at math, and at the same time be not on average worse at math than at other subjects. That's why comparing results of math exam with results of other exams should show whether math is harder (or - the way you put it - average person is bad at math). If you are right - math exam results should be substantially worse than those for other subjects. And they are not.

Answer this: What 'data' would convince you that most are poor at maths?
The main academic barometer for how good you are at something is an exam result. As you have clearly just dismissed results that show that 70% (which is a majority) don't meet the required standard for futher education in mathematics.
Easiest thing - compare exam result of the same population for math and for other subject. If there is a substantial difference, they are on average bad ad math. But results you have linked to don't show substantial difference.

EDIT: I will say that (I was going to leave this out as it weakens my argument), exam results aren't a perfect way of gauging someones natural ability. The quality of teaching and school makes a huge difference. You can send a good pupil to a bad school they will out perform their peers, but not reach their potential. You can send a 'bad' pupil to a good school and the will maximise thir potential.
As the results listed on BBC site are national averages (or at least that's what I understand) this problem can be safely ignored.
 
  • #53
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All sorts of comparisons of maths with other subjects like that is flawed since you can make any subject harder or easier just by ramping up or slowing down the rate at which new material is presented. I mean, what in social science is at the same level as calculus? Impossible to say since you can't compare subjects like that.

People in general have a hard time learning maths but people in general also have a hard time learning new languages. However just about everyone know at least one language so it can't be that hard, right? So we can roughly conclude that it is hard to learn languages when you are only exposed to it at school but not when it is all around you.

I'd say that this is the major reason people have a hard time with maths, because it is a subject which you almost solely encounter at school. Things like social science and such are encountered all the time in a normal life like when you read the newspaper, literature, watch movies, look at TV shows or listen to debates.

So maths is a new way to think while social science is our natural way to think and people have a hard time adjusting the way they are thinking. Like languages, it is natural to think in your own language so to learn a foreign language is to learn something which isn't natural to you which makes it hard.

I think that what makes a person good at maths is that he either is just good at developing new ways to think for himself or he being nerdy enough to live in a way were maths is most of his life. To get really good you obviously need to surround yourself with the subject but I mean at early levels like high school/college.

Social science on the other hand just builds on a strong foundation everyone already got.

Edit: And of course this post contains mostly my opinions and is not something I claim to be facts.
 
  • #54
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You see - you said that again.

But there is a flawed logic here - you can't be on average bad at math, and at the same time be not on average worse at math than at other subjects. That's why comparing results of math exam with results of other exams should show whether math is harder (or - the way you put it - average person is bad at math). If you are right - math exam results should be substantially worse than those for other subjects. And they are not.


Easiest thing - compare exam result of the same population for math and for other subject. If there is a substantial difference, they are on average bad ad math. But results you have linked to don't show substantial difference.
You can't compare exam grades like that though. Most people are bad at most subjects and may be outstanding at one.

To make the point simpler you have a class of 5, taking 5 subjects.

Maths, English, Art, PE, Music.

Student A gets an A in Maths, but fails everything else.
Student B gets an A in English, but fails everything else.
So on and so forth.

Your results then show an identical trend for each subject, 1 A and 4 fails. Meaning that none is 'harder' than the other. Yet in this case a clear majorty of those taking the subject failed. This is why at GCSE you get fairly identical profiles for all subjects, barring subjects that are deemed 'easy'. It's also why this trend breaks at A level, where people are taking courses that are more suited to them, be it academically or their interests (plus you have got rid of the people who don't want to be at school, so those who take A elvels put the effort in).


You are being skewed by being obsessed with the notion that i'm trying to say that people are particulally bad at maths, and maths alone, becuase 'maths is hard'. I'm not singling maths out, i'm saying people are mostly bad at everything. It's just this thread was about maths.
 
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  • #55
Borek
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You are being skewed by being obsessed with the notion that i'm trying to say that people are particulally bad at maths, and maths alone, becuase 'maths is hard'. I'm not singling maths out, i'm saying people are mostly bad at everything. It's just this thread was about maths.
So you failed to communicate it clearly, you started with:

The basic fact is most people in the world are dreadful at at mathematics.
And later enforced it with

The average person, is just that. Average. They will have telents in some areas, but be bad at others. Most are poor at maths.
I also think your analysis of GCSE result is wrong - we are talking about large, well averaged sample, and results for different subjects are far from being identical. Compare Humanities with Art for example. There are substantial differences and they tell us something - either about abilities, or about subject difficulty, or perhaps about some social processes taking place in school or society. Information we are looking for (relative difficulty of subjects) is in this results. It is not easy to filter it out, but some conclusions are possible.

Edit: Oops, we have hijacked the thread.
 
  • #56
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So you failed to communicate it clearly,
Probably, communication isn't one of my strong points.

I also think your analysis of GCSE result is wrong - we are talking about large, well averaged sample, and results for different subjects are far from being identical. Compare Humanities with Art for example.
Humanites and art are not core subjects. Therefore people who take them, have chosen to. People only take art if they are good at it, which is why results will be slightly weighted towards higher grades. Humanities is generally considered to be a suject taken by weaker students in an attempt to get a 'passing' grade, so much so that many schools don't offer it as an option. As such it also suffers from sample size issues.

Maths, English and Science are the three core subjects that every pupil must take to GCSE level. Compare the trends.

All have the modal grade as a C. Optional subjects are weighted towards better grades. The Core subjects all have roughly the same distribution of grades. Science is a tricky one as there are several different ways of taking GCSE science, I did the double award so I chose that.

If you take this as face value, it shows that out of the core subjects mathematics has the slight edge. Fortunately as I wan't trying to prove that maths was hard, it doesn't affect my conclusion that most people are not good at most subjects. If a B is considered good, and a C ok and anything less is a fail. Most people can't be considered 'good', as most score a C or lower. all subjects, maths included.

#data for the graph was taken from the 2005 GCSE statistics. The A* is the first result a U is the last result.
 

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  • #57
Andy Resnick
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So you failed to communicate it clearly, you started with:
Probably, communication isn't one of my strong points.
If I may jump in- I've been tracking the back-and-forth, and I would hate to see a perfectly good discussion become overrun with emotion:

AFAICT:

Borek's main claim is that people are no worse at math than any other academic subject.

xxChrisxx's claim that a large fraction of the world population is functionally illiterate in mathematics (innumeracy).

Borek's point (if I am correct) is most likely valid- there is no reason to suppose that a disinterested student will be better at world history than math, or that on average, people have better grammar skills than calculation skills.

xxChrisxx's point (if I am correct) is also valid- it is well documented that people can be easily fooled by probability (gambling: a good result must follow, eventually), and I've taught several math classes where the goal is little more than to teach people- adults with jobs and families- how to balance a checkbook.

We can all agree that an educated populace is preferable to an uneducated populace. The fundamental question, as I see it, is "does innumeracy pose greater problems than illiteracy?", and I would have to answer 'no'.

Even so, there is more stigma associated with illiteracy than innumeracy. Furthermore, the definition of illiteracy v. innumeracy is distorted. If we equate an inability to add and subtract with an inability to write a sentence, what are we to make of a calculator (or abacus)? In the US primary schools (ages 5-18), the calculator is being introduced earlier and earlier. Is this bad, or is any distaste simply our inner Luddite? Abacuses (Abaci?) have been around for thousands of years, after all...

Or did I misunderstand your conversation entirely?
 
  • #58
Borek
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Borek's main claim is that people are no worse at math than any other academic subject.
I can speak for myself only - yes, that's what I think. I hesitate to call it "my claim" - it is rather that I have a feeling that common belief (math is hard) is just a... say, unsubstantiated urban legend - hence before accepting it I would like to see data supporting it.
 
  • #59
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Borek's main claim is that people are no worse at math than any other academic subject.
This is something I agree with.

xxChrisxx's claim that a large fraction of the world population is functionally illiterate in mathematics (innumeracy).
I am claiming that, but not just that. People who spend their lives in an academic enviroment become acclimatised to the average level of intelligence around them. They then start to lose touch with how low the average level of intelligence is in this world in comarison to your average or even poor university student.

The only reason why I singled out mathematics, was this was a thread about maths.
When people start saying we should teach calculus younger and younger. They overlook that most people simply don't have the intellectual capacity to learn and understand it.

It's difficult not to sound like a big headed, condecending arse when saying the above. It's kind of a socially awkward thing to comment on peoples intelligence. Most of us could never be an olympic class sprinter no matter how hard we trained due to a limit of natural physical ability, some poeple will never be able to learn advanced mathematics as the lack the natural intellectual ability.

Borek's point (if I am correct) is most likely valid- there is no reason to suppose that a disinterested student will be better at world history than math, or that on average, people have better grammar skills than calculation skills.
I agree with that too. I won't quote the rest of your post as I dont want this to become tl;dr, but yeah I agee with all that too.
 
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  • #60
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To give some sort of valid response to the ops question requires some knowledge of his kid such as the course he is following and his age.The op has volunteered none of that information so what are we to think? Perhaps his kid is a fourty year old consultant surgeon moving into physics or perhaps a four year old who is taking a basic physics course which the op thinks is shamefully lacking a calculus content.
 
  • #61
Andy Resnick
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When people start saying we should teach calculus younger and younger. They overlook that most people simply don't have the intellectual capacity to learn and understand it.
I agree, we should stop pushing calculus earlier and earlier in the curriculum.

There's a vague tension in education, because there's more and more material to master, children are expected to 'grow up' faster and take on more and more responsibilities, yet nobody has figured out how to *learn* faster or more efficiently.
 
  • #62
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I agree, we should stop pushing calculus earlier and earlier in the curriculum.

There's a vague tension in education, because there's more and more material to master, children are expected to 'grow up' faster and take on more and more responsibilities, yet nobody has figured out how to *learn* faster or more efficiently.
I, respectfully, disagree. Having taken calculus in high school, I felt that it was a very valuable set of skills to have.
 
  • #63
Moonbear
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I, respectfully, disagree. Having taken calculus in high school, I felt that it was a very valuable set of skills to have.
Try telling that to my sister. :wink: Seriously.

Calculus in high school was useful for those of us who went on to get further educations in the sciences where we used it extensively. However, we could have also obtained that entirely at the university level. At most, it was a luxury that allowed us to lighten our first year course load by skipping over a few required classes.

On the other hand, neither calculus nor a calculus-based physics course are useful for quite a large part of the population. This is why I mention my sister. She went to college majoring in social work, and currently works as a probation officer. The closest she has ever come to needing physics knowledge might have been when she still worked as a social worker in a shelter for abused women. They had a keen appreciation of the influence of gravity when her former clients did things like jump out of second floor windows to escape their abusive husbands.

Most people can suffice with a conceptual understanding of basic kinematics, such as the need for a longer stopping distance when driving a heavier vehicle at higher speeds, or that if you jump out of the third floor window, it's more likely to hurt you a lot worse than jumping out of a first floor window.

It's been a good 20+ years since I was in high school. From my own experience, I think it would be far better to teach students a conceptual understanding of physics without using calculus rather than the way it was taught when I was in school, which was to use calculus in our physics class the year before we were taught calculus in our math classes. It did make the calculus class easier, but we got very little out of the physics class other than a strong dislike for our teacher.

I think it's great when schools can offer the variety of classes that students who want to go into a variety of majors can get a taste of that coursework before heading off to college, but not all communities have education budgets that make that feasible. In those cases, the priority really shifts to making sure those who are not going to get any further education have the essentials for functioning in society. That starts boiling math lessons down to knowing how to balance a checkbook or stick to a family budget or being smart shoppers able to compare prices on a per unit basis. Science lessons start getting reduced to things like understanding enough biology not to get anyone pregnant until they want to be pregnant and knowing enough about bacteria to avoid contaminating their entire kitchen with E. coli or salmonella, enough chemistry to know not to mix bleach and ammonia when doing that cleaning, or perhaps to keep the more basic things like Draino away from the acidic things when storing them, and not pouring water on a grease fire.

If parents are not satisfied that their kids are learning enough in school, it is up to them to supplement their kids' education as they see fit.
 
  • #64
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Well in New York, we had a mandatory Physics Regents class that was pretty easy, and excluded any calculus. It was pure algebra and trigonometry, and was a joke for most students. The ones who wanted to challenge themselves were then given the opportunity to take AP Physics the next year, which was already a calculus based class. Even there, the teacher avoided using calculus because we were taking it simultaneously with the physics class, and did not know anywhere near enough to think of physics from a purely-mathematical point of view.

This had its pros and cons. The pros were that it was incredibly easy to grasp complicated concepts. For example, we used the right-hand-rules to solve 90% of E&M problems asking about vector fields and whatnot.

The cons, as I found out this year, are that this knowledge is severely limited, and I have very limited knowledge about how to solve these problems mathematically.

There were a lot of examples of such simplifications, and they were all valid when taking the AP test. You could, for example, get 10/15 points on any given question by writing an essay on HOW to solve it. You needed 65% of the points to get a "5" on the test, which is a stellar grade.

I think the way things are taught in New York, or at least in my specialized technical high school, are very adequate and appropriate. We were given the most fundamental knowledge of every subject, just to be well-rounded, and if we were interested in a given subject, we were offered an AP class which took things to the next level.
 

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