All Kids Left Behind!

[Mike_In_Plano]

I was pleased the day I found my kid was taking physics - until I found how woefully unprepared ALL the kids were and how the entire course was dummied down to fit a mathematically immature age.

How are they to even begin to understand kinematics, when they have NO modicum of a gleaming upon the concept of calculus. They have these kids memorizing formulas, without a clue as to their meaning, derivation...

Argh.... I'm too upset to continue

[Pythagorean]

what age group we talking?

[Borek]

There are many basic concepts and laws that you can grasp and learn to use without calculus, it doesn't have to be a problem. Problem starts when the course is dumbed down not because kids don't know enough math, but to allow Joe Slow crawl through it, while all other kids wait bored. That's the problem.

[Pengwuino]

Argh.... I'm too upset to continue

The best part is? No one I know even remembers when this wasn't the case. Though as already mentioned, you don't need calculus to learn many basic things about physics. Hell, a university typically has an entire series of physics courses aimed at not-really-engineers-but-not-art-majors type students that does physics without calculus.

[BobG]

If you're talking about high school Physics, then I think that's been the case for at least 40 years and probably forever.

If you're talking about college, well, a lot of students don't take high school Physics and aren't in majors that require more than an awareness of physics.

[Mike_In_Plano]

Okay, well I feel better in that this isn't a unique occurance, but I still need to communicate with my kid, I'm frustrated at the lack of conceptual background. Where do I go and what do I do to find a common grounds?

[xxChrisxx]

You are asking a forum how to communicate with your own offspring? Interesting.

Pythag had the 1st and most vital question. How old is your child?

[Greg Bernhardt]

yeah I took two physics classes in HS without a lesson of calc.

[Angry Citizen]

I fail to understand the relevance of physics without calculus. Speaking as a student going through introductory physics, the link between the equations v=v0+at and x=x0+vt+1/2at^2 would not exist. Now I know it's connected by integration/differentiation, which allows me to go between a, v, and x without even a second thought. Physics is pointless without calculus, even if the equations do not specifically require calculating derivatives or integrals.

[Klockan3]

I fail to understand the relevance of physics without calculus. Speaking as a student going through introductory physics, the link between the equations v=v0+at and x=x0+vt+1/2at^2 would not exist. Now I know it's connected by integration/differentiation, which allows me to go between a, v, and x without even a second thought. Physics is pointless without calculus, even if the equations do not specifically require calculating derivatives or integrals.
Of course those links exists, calculus don't magically create the link. The only math prerequisite for those formulas is the area of a triangle + square and the reasoning behind it is really simple and nothing of this gets any easier just because you have studied calculus. Sure you got more mathematical tools to apply to more variations of functions but the actual physical understanding do not come any easier just because you know calculus.

The way I derived those equations when I took early physics was by first calculating the average speed and then multiplying with the time. Not hard at all and it makes perfect sense... I think it is people like you who don't see these obvious links which should go back and think a while. Remember that most didn't derive the formulas found in calculus, so they are just tricking themselves into thinking that they "derive" physics formulas. So in fact they are still just memorizing, the only difference is that the new set of rules is more powerful.

[Pythagorean]

I fail to understand the relevance of physics without calculus. Speaking as a student going through introductory physics, the link between the equations v=v0+at and x=x0+vt+1/2at^2 would not exist. Now I know it's connected by integration/differentiation, which allows me to go between a, v, and x without even a second thought. Physics is pointless without calculus, even if the equations do not specifically require calculating derivatives or integrals.

It's a lesson in synthesis. We learn a handful of useful things with algebra in fundamental physics courses. Then we put them together with calculus.

If you're just handed calculus, there's no significance filter, and applying calculus to numerous different physical situations is (at first) daunting.

Imagine if we started learning electromagnetism just from Maxwell's equations. No, we share the chronological history with The Giants because the order of discovery has a big influence on the development of theory. Sure, there was a better way....

There's a better way to run government too. But if we just told everybody to start acting that way, all the infrastructure built on the old ways would become unstable, and that is (by manner of a series of events) the foundation on which "the new way" stands.

In fact, I still make more algebra mistakes than calculus mistakes in page of long derivations. Algebra is not trivial when you go beyond add/subtract/divide/multiply.

[Borek]

Stating physics is pointless without calculus is an arrogance. Browse "Introductory physics" forum - it could be named "Precalculus physics". A lot of good, interesting questions that can be solved using just a basic algebra and good understanding of basic concepts.

[xxChrisxx]

I think the following is rather fitting.

You've got to learn to walk before you can run.


It's like trying teaching an engineering student fracture mechanics before teaching them stress and strain.

[Angry Citizen]

Of course those links exists, calculus don't magically create the link. The only math prerequisite for those formulas is the area of a triangle + square and the reasoning behind it is really simple and nothing of this gets any easier just because you have studied calculus.

Like I said, I'm studying intro physics right now, and no, I'm hardly bad at math. The connections are far more lucid when one understands calculus. They may exist without calculus, but if you're telling me the average modern student will understand the relationship you described, you're deluding yourself.

Stating physics is pointless without calculus is an arrogance. Browse "Introductory physics" forum - it could be named "Precalculus physics". A lot of good, interesting questions that can be solved using just a basic algebra and good understanding of basic concepts.

I haven't done a physics problem yet in my class that required calculus. I didn't say it did. I did, however, say that calculus makes introductory physics concepts much easier to digest. You have the intuitive sense that is required of physics. Like the OP said, without calculus, you're just memorizing formulas. I derive them simply by understanding what an indefinite integral is.

I think the following is rather fitting.
You've to to walk before you can run.


It's like trying teaching an engineering student fracture mechanics before teaching them stress and strain.

Well, as an engineering major who never took algebra-based physics, we'll see if you're right. My calculus-based physics course, however, is probably easier to digest than any algebra-based physics course would've been prior to calculus. In fact, I can assert this positively, as I tried my hand at physics without the proper calculus background, and failed miserably (of course, it's very possible this has something to do with the fact that I crave structure in my learning, and I tried to self-teach myself out of an algebra physics book).

[xxChrisxx]

Well, as an engineering major who never took algebra-based physics, we'll see if you're right. My calculus-based physics course, however, is probably easier to digest than any algebra-based physics course would've been prior to calculus. In fact, I can assert this positively, as I tried my hand at physics without the proper calculus background, and failed miserably (of course, it's very possible this has something to do with the fact that I crave structure in my learning, and I tried to self-teach myself out of an algebra physics book).

Well done for totally missing the point. This is not about the end game, it's about how people learn to get there.

The learning process requires:
foundation -> basics -> advanced tools.

You can't solve an advanced problem with basic tools. But you need to master the basic tools before you can progress to more advanced concepts.

[Angry Citizen]

Your point was that one must learn the basic, algebra-based tools before one learns the calculus-based tools, yes? Well, my point addressed this. It's unnecessary in my eyes. One can teach them both simultaneously. The calculus and algebra are not disconnected from another. In fact, they compliment one another. Knowing calculus before tackling the algebra-based physics makes the physics more intuitive and understandable. Just my observation of course. I would certainly be the first to admit I am the epitome of 'outlier' when it comes to learning.

[xxChrisxx]

Well it was a more general point about learning, it applies to everything. I'm finding it hard to pick out an example, as when you can do calculus it makes it difficult to think of a time before you could do it.

The only example I can think of is silly, it's how you get the area under a curve.

In primary school, you drew it on a peice of square paper and counted the squares. (arithmatic and basic counting)
In secondary school pre calculus, you learn the trapezium rule, and the error associated with using different sized trapeziums.
In secondary shool when you learn calculus you simply integrate the curve.

EDIT: I'm getting nostalgic flashbacks of my maths classes. I remember being set simulaneous equations homework, and just using matrices to solve them (AS further maths for the win). I let someone copy without thinking and us both getting bollocked because they hadn't done matrices. good times.

[Klockan3]

Your point was that one must learn the basic, algebra-based tools before one learns the calculus-based tools, yes? Well, my point addressed this. It's unnecessary in my eyes. One can teach them both simultaneously. The calculus and algebra are not disconnected from another. In fact, they compliment one another. Knowing calculus before tackling the algebra-based physics makes the physics more intuitive and understandable. Just my observation of course. I would certainly be the first to admit I am the epitome of 'outlier' when it comes to learning.
The problem with this view is that physics gets even more logical and all that once you start doing it with functional analysis, differential geometry etc, rather than calculus. I'd say that it is good to build your physical intuition up from the basics rather than waiting with it till you know basic maths.

Personally I did roughly all non calculus based physics you can do before I started high school. We did basic kinematics, electrical circuits, basic em theory such as how two charged particles effects each other, how magnetic fields effects charged particles which leads to how to make an ac engine and how coils transforms voltages, we did the atom model together with the quantization of light and light spectrum's from different gases, we did the interference experiments of waves, explained why that happens and then explained that the same thing happens with particles such as electrons, we went through special relativity by first explaining that the speed of light is constant and then derived the other relations from that, we did a very basic treatment of some thermodynamic systems and explained the general idea even though we didn't calculate anything on it except for just calculating how much energy it is required to melt/heat things up just had some heuristic description of entropy and such.

None of that required any calculus at all and I'd argue that I had a better understanding of physics when I started high school than you do currently. By the way, can you explain in what way you are an 'outlier', because just saying 'outlier' doesn't really say anything at all except that you aren't in the mainstream. I'd argue that most who posts outside the help forums here are 'outliers'.

[Andy Resnick]

Personally I did roughly all non calculus based physics you can do before I started high school.

I really appreciated your post- especially the middle paragraph. The sentence above is the critical point, and I'll note the OP never said *how old* his child is. Clearly, material presented at elementary school (ages 5-11 in the US) will be conceptually simpler than the material represented at middle school, high school, undergraduate, graduate, postdoc.... and there's no reason to demand that calculus-based physics should be taught in elementary school.

[Angry Citizen]

By the way, can you explain in what way you are an 'outlier', because just saying 'outlier' doesn't really say anything at all except that you aren't in the mainstream.

Well, for one, I didn't go to high school. For two, I had about a 4th grade math level before entering college last fall. For three, I keep a keen eye on pedagogical techniques. I discuss it with both the educators and those being educated. But mostly, my point was simply that I am relatively unique in my learning style. I do not learn from books very well. I'm not a very visual learner either. Now, either you must accept that I have a very keen intuitive grasp on physics, or that it is entirely unnecessary to know how to do all that gobbeldygook during middle school, because I'm doing quite well in my intro physics class without it.

Believe me, I understand your mentality. It's typical of the modern take on education. Drill it into them young, drill it into them again, drill it into them when they go to college, and maybe, just maybe, once they get a job they remember some part of chapter 2. I just think there are better ways of going about it.

[Angry Citizen]

there's no reason to demand that calculus-based physics should be taught in elementary school.

I'm actually of the opinion that calculus should be taught far earlier than it is now. Not as a separate subject, but linked with the algebra techniques. For instance, once slope, function manipulation, and rational expressions are taught, there is absolutely no reason in the world not to teach derivatives.

But forgive me my tangent (pun intended).

[xxChrisxx]

I'm actually of the opinion that calculus should be taught far earlier than it is now.

Well you could cartainly try. This kind of thing was tried back in the 60s, it didn't get very far. There is no point in designing a curriculum that only targets a small minority of people.

The basic fact is most people in the world are dreadful at at mathematics. This is something this forums seems to overlook, people who acutally enjoy physics and mathematics are very much in the minority in this world. It's largely pointless in teaching children something that will serve them no purpose in later life. Statistics would serve the general denizens of this world far better than calculus ever could.

[Borek]

The basic fact is most people in the world are dreadful at at mathematics.

Do you have something to support this statement? From what I remember (and no, I don't have any research to quote) this is kind of a self-fulfilling prophecy, everyone one knows Math Is Hard, so math is hard - those that were not told MIH don't have so much troubles.

[Angry Citizen]

Well you could cartainly try. This kind of thing was tried back in the 60s, it didn't get very far. There is no point in designing a curriculum that only targets a small minority of people.

The basic fact is most people in the world are dreadful at at mathematics. This is something this forums seems to overlook, people who acutally enjoy physics and mathematics are very much in the minority in this world. It's largely pointless in teaching children something that will serve them no purpose in later life. Statistics would serve the general denizens of this world far better than calculus ever could.

I think people tend to be dreadful at mathematics because it is not taught properly. Calculus isn't just useful for analyzing physics and chemistry and assorted other topics, it has explanatory value in and of itself. Again speaking from personal experience, algebra became so much clearer once I knew why those techniques were taught. For instance, I couldn't give a darn less about multiplying by conjugates until I started studying limits. I didn't appreciate the beauty of e until I heard the definition of the natural logarithm. I certainly didn't much understand the purpose of being able to discern the equation of a line from a point and a slope. To me, learning calculus is like a myopic person putting on glasses. Sure, you can vaguely understand some concepts, but it's so much clearer in light of calculus.

[xxChrisxx]

Do you have something to support this statement?

What? Like a survey that asks 'do you like maths'? Or some in depth 10 years study into school leavers lives asking the amount of times they've used pythagoras's theroum or algebra in their stock repleshiment duties at the local Tesco?

Experience is what supports this statement. It may be self fulfilling, but it's bloody true. Even I dislike maths and i'm an engineer, of one of the necessary evils of my job.

I've also known people that adore maths, and it came completely naturally to them. The people who hate it most certainly outweigh them.

[Borek]

I see frustration, but no facts.

I vaguely recall thare was some kind of research done on the subject. Something like two groups, one being constantly told that math is hard and they are being taught difficult math subject, the other one being told they are just playing logical game or something like that. The group that was not aware of learning math did much better. (I partially made it up, but I remember reading about something like that).

[Klockan3]

I see frustration, but no facts.

I vaguely recall thare was some kind of research done on the subject. Something like two groups, one being constantly told that math is hard and they are being taught difficult math subject, the other one being told they are just playing logical game or something like that. The group that was not aware of learning math did much better. (I partially made it up, but I remember reading about something like that).
There are no facts, but the chances that it isn't a fact is too small. No matter where you go in the world or at which time in history you look you will always find that most had issues with maths.

You are right in that telling kids or people in general that maths is hard makes them perform worse but that doesn't mean that it isn't true. The reason people say that maths is hard is due to their own experience, it wouldn't have gotten so well accepted all over the world if it didn't have some truth to it. Maths is hard, but not for everyone. For teaching purposes it is advantageous to come with cliché statements like "Maths is all about hard work", even though it isn't true it helps the students perform better on average.

[lisab]

There are no facts, but the chances that it isn't a fact is too small. No matter where you go in the world or at which time in history you look you will always find that most had issues with maths.

You are right in that telling kids or people in general that maths is hard makes them perform worse but that doesn't mean that it isn't true. The reason people say that maths is hard is due to their own experience, it wouldn't have gotten so well accepted all over the world if it didn't have some truth to it. Maths is hard, but not for everyone. For teaching purposes it is advantageous to come with cliché statements like "Maths is all about hard work", even though it isn't true it helps the students perform better on average.

It's also culturally acceptable to say you're terrible at math (in the US at least). It's even considered funny, in some circles, to 'brag' about how you can't do algebra. I don't understand it at all. Would anyone 'brag' about being functionally illiterate?

[Borek]

It's also culturally acceptable to say you're terrible at math (in the US at least). It's even considered funny, in some circles, to 'brag' about how you can't do algebra. I don't understand it at all. Would anyone 'brag' about being functionally illiterate?

Same in Poland. This is stupid.

[Borek]

No matter where you go in the world or at which time in history you look you will always find that most had issues with maths.

Will I?

I am not saying you are wrong, but my experience is limited to western culture at best, so I have no idea how it looks in - say - Korea. Or Vietnam. Heck, I have no idea how it looks in Russia.

[Klockan3]

Believe me, I understand your mentality. It's typical of the modern take on education. Drill it into them young, drill it into them again, drill it into them when they go to college, and maybe, just maybe, once they get a job they remember some part of chapter 2. I just think there are better ways of going about it.
Believe me, you don't understand my mentality. I don't say that things should be drilled in at all or that it is the only way to do things, I just note that there is no need to know calculus before you start to learn physics. In the same way calculus helps you learn physics if you were taught well physics will also help you when learning calculus so stating that you need one to know the other is ridiculous. I'd say for example that studying calculus without first having a proper notion of things like velocity and acceleration is really strange, but it works since you can develop intuition for the same thing from a large variety of sources.

By the way, I wouldn't call a course where you drill formulas a physics course. Just because your precalculus physics course was taught badly don't necessarily mean that everyones precalculus physics was bad. And I can assure you that there is mostly formula drills in calculus based physics as well, understanding is not prioritized in general in academia.
Will I?

I am not saying you are wrong, but my experience is limited to western culture at best, so I have no idea how it looks in - say - Korea. Or Vietnam. Heck, I have no idea how it looks in Russia.
Yup, media might try to make you believe differently but there is no magical country where children learn maths with joy.

[Angry Citizen]

I'd say for example that studying calculus without first having a proper notion of things like velocity and acceleration is really strange.


*shrug* I managed.

By the way, I wouldn't call a course where you drill formulas a physics course. Just because your precalculus physics course was taught badly don't necessarily mean that everyones precalculus physics was bad.

I didn't have precalculus physics. I'm glad I didn't.

And I can assure you that there is mostly formula drills in calculus based physics as well, understanding is not prioritized in general in academia.

Well then, perhaps my calculus-based physics course is an outlier, because my physics prof actually gives us the necessary equations before each exam. The point is to reduce the necessity for memorizing equations, and learning the intuitive process behind introductory physics.

But maybe I just have a super-awesome physics prof who knows how to teach, and I'm just an absolutely brilliant engineering student who can get on just fine without precalculus physics. I wouldn't count on it though.

[Borek]

Yup, media might try to make you believe differently but there is no magical country where children learn maths with joy.

I am not talking about media. I hear the same "Math is Hard" statement from everyone every time. Now and then I am tutoring students and I have heard it even from those that were catching math ideas without problems - so I tend to doubt universality of the statement, I am rather inclined to see it as fashionable.

[xxChrisxx]

I see frustration, but no facts.

I vaguely recall thare was some kind of research done on the subject. Something like two groups, one being constantly told that math is hard and they are being taught difficult math subject, the other one being told they are just playing logical game or something like that. The group that was not aware of learning math did much better. (I partially made it up, but I remember reading about something like that).

Ok fine.

UK GCSE (A*-C is generally considered a pass) and lets face it, GCSE maths is by no means taxing.

From 2005 statistics for average:
http://news.bbc.co.uk/1/shared/bsp/hi/education/05/exam_results/gcse_fc/html/mathematics.stm

I can't find how to get the newer ones, as im just doing this quickly.

46.6% got a grade that was considered a fail. The average grade of C isn't particulally fantastic, as to do A level maths generally requires a B at GCSE (depending on 6th form acceptance criteria).

So to be considered 'good' at the are 16 range you've got to get a B.

This means that in 2005 nearly 70% of all people did not meet the required standard for A level maths at the 6th form college I went to.

It really isn't difficult to get a C at GCSE, some just don't have the required intelligence, most just plain dont give a crap.

This is a typical pass rate year on year for maths in the UK. However, of those 30ish% many go on to do maths A level where the trend flips, the majority get an A or a B (which is pretty good).

Add those who really love maths at A level (the optional further maths) 80% get an A or B.

[Klockan3]

*shrug* I managed.
Yeah, and I managed to learn a lot of useful things from precalculus physics which weren't instantly made obsolete by calculus based physics.
I didn't have precalculus physics. I'm glad I didn't.
How can you have an opinion about it when you haven't taken any of it?

Well then, perhaps my calculus-based physics course is an outlier, because my physics prof actually gives us the necessary equations before each exam.
Um, what? How is this relevant at all in terms of understanding? Do you realize that just knowing equations doesn't really mean anything at all? It seems to me that you don't know at what physical intuition is and just learns a lot of equations. Physics is not about learning equations or learning how to solve problem X, it is about giving you a better understanding of how the world works.

I can understand that you would think that learning physics before calculus is a waste if you just look at it as memorizing X equations which would mean that you don't need as many once you know calculus...

I am not talking about media. I hear the same "Math is Hard" statement from everyone every time. Now and then I am tutoring students and I have heard it even from those that were catching math ideas without problems - so I tend to doubt universality of the statement, I am rather inclined to see it as fashionable.
But as I said people have that oppinion all over the world...
The international test results from 2003 and related surveys from 46 countries show that the world's most confident eighth-grade math students are found in the Middle East, Africa and the United States. Of the 10 countries with the highest levels of student confidence, only Israel and the United States scored higher than average on the international test, and their scores were far below those of the much less confident students in Japan, Korea, Hong Kong and Taiwan.
http://nomorequo.blogspot.com/2007/04/why-asians-are-better-at-math.html

[Borek]

This means that in 2005 nearly 70% of all people did not meet the required standard for A level maths at the 6th form college I went to.

But it is not proof that math is hard. As Lisa already pointed out being weak at math is something that people are not afraid of, many are even proud of it. Combine this with the self-fulfilling prophecy mechanism and you may have results that you see.

Besides - social sciences were failed by 51.2%, so math is not the worst case. Surprisingly, statistics - which is nothing else but application of math - was failed by just 29.7%.

[xxChrisxx]

But it is not proof that math is hard. As Lisa already pointed out being weak at math is something that people are not afraid of, many are even proud of it. Combine this with the self-fulfilling prophecy mechanism and you may have results that you se/

I never set out to prove that maths is hard, because I don't think it is. I just wanted to confirm that:


The basic fact is most people in the world are dreadful at at mathematics.
Do you have something to support this statement?

The data applies specifically to the UK, but the general idea stands. Most people are poor at maths.

Besides - social sciences were failed by 51.2%, so math is not the worst case. Surprisingly, statistics - which is nothing else but application of math - was failed by just 29.7%.

Thats because there are many people who aren't too bright. Which is something that is forgotten on boards like this.

I subscribe to the concept that peoples brains are 'wired up' differently. I find maths easy, but boring. My brain just isn't wired up to appreciate literature or art, I found English lit a real struggle, i'm a numbers person.

[Borek]

Besides - social sciences were failed by 51.2%, so math is not the worst case. Surprisingly, statistics - which is nothing else but application of math - was failed by just 29.7%.

Thats because there are many people who aren't too bright. Which is something that is forgotten on boards like this.

Ah, so if you fail at social sciences, that's because you are not too bright, but when you fail at math, that's because math is hard? Sorry, it doesn't make sense. Especially when you are trying to prove quite the opposite - that people are not mathematically bright, but they are reasonably good at other things.

[xxChrisxx]

Ah, so if you fail at social sciences, that's because you are not too bright, but when you fail at math, that's because math is hard? Sorry, it doesn't make sense. Especially when you are trying to prove quite the opposite - that people are not mathematically bright, but they are reasonably good at other things.

What? No.

You fail at any GCSE then it's either you aren't bright enough, or total apathy or a mix. I never said maths is hard, or social sciences is hard. Compare this so a less mentally taxing subject, Physical education. 30% fail, 70% pass.

The average person, is just that. Average. They will have telents in some areas, but be bad at others. Most are poor at maths.

If you work hard for the GCSEs you can make up for a lack of raw intelligence. Most with strict discipline can achieve a C. The national average for 5 grade A*-C is about 45%. The school I went to was not selective, but it was an old all boys grammar school with very strict discipline. As such it took people who, were thick as two short planks and forced them to work hard. As such the pass rate of 5 A*-C was significantly above the national average. You are never going to get a D student to get a B or an A, but you can get them to a C.

[Borek]

Most are poor at maths.

You are repeating it all the time, but you are still failing to support it with data. As far as I can tell results of the GCSE doesn't show that people are substantially worse at math than at other subjects. At least - these results are not worse enough to show math is substantially harder, as the difference can be attributed to things I have mentioned earlier. Plus results of stats exam can be supporting the idea that people have no problems dealing with math when they are not aware they are dealing with it.

[xxChrisxx]

You are repeating it all the time, but you are still failing to support it with data. As far as I can tell results of the GCSE doesn't show that people are substantially worse at math than at other subjects.

I never said they were worse at maths than other subjects. Just that the average person is bad at maths. A 50% failure rate at something easy, is poor no matter what the subject. 70% not being considered good enough to continue to more taxing education in the subect shows that that the majority aren't good enough.

It's perfectly possible to be rubbish at everything.

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.

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.

[thehacker3]

So how old is the OPs son?

I think a short story of my physics background should demonstrate how calculus isn't necessary at all when learning physics.

In my high school, physics is taught on two levels - the first one being in our junior year. We go into physics knowing algebra and most of us are taking pre-calculus simultaneously. In my junior level class, I was very good and understood pretty much every concept thrown at me - THIS is the key in a good physics education. Concepts are what made me so good at physics. When the teacher said that the ball fell to the ground because of gravity and gravity was influenced by mass and distance, it made sense. I didn't need a single calculus lesson to understand why things fell down.

Furthermore, in my senior year, I took AP Physics C - arguably the hardest physics class any high school student ever experiences. The class was not calculus based in the beginning because we were taking calculus simultaneously with it. After a few weeks, the teacher started integrating calculus techniques in his examples to help those who were challenged by concepts.

I was top of the class.

I refused to use calculus until it was absolutely necessary because I felt it was unnecessary and too complicated. Being, literally, the best one in my AP Physics C class without utilizing a single concept of calculus for half a year should prove to anyone that you don't need calculus to be good at physics or understand it.


I should also mention that one of my best friends took the class with me and he taught himself calculus in his freshman year. Naturally, being a math lover, he tried to apply calculus to every physics problem and was still doing worse than I.

[Ryker]

In my high school, physics is taught on two levels - the first one being in our junior year. ...

Furthermore, in my senior year, I took AP Physics C - arguably the hardest physics class any high school student ever experiences.I digress, but from what I understand you only had two years of Physics in high school, but still believe your second year you took the hardest physics class any high school student ever experiences? I know you put "arguably" there, but nevertheless ...

[thehacker3]

Well AP classes are the hardest classes in high school and...

http://talk.collegeconfidential.com/high-school-life/203729-hardest-ap-course.html


and I didn't find it difficult but then again, the teacher said he's never seen anyone who has picked it up so easily and quickly

[Ryker]

Oh OK, you probably meant hardest in the US then, right?

[thehacker3]

That is what I meant, correct. Sorry if I implied other countries as I didn't mean it. I'm currently having an argument in another thread about how education in other countries seems superior to ours.

[Ryker]

I think there's different systems and it's hard to say whether other countries are superior in that regard, but I know we've covered more Maths than the Canadians have, and from what I hear, Canadian high school cover the same or more than pupils in the US. I don't really know about Physics, to be honest, but I can hardly believe US high school education would be superior to, say, the one in European countries. I think there's just as many bright students in the US than there are across the world, but I think this is more due to their own engagement, whereas if you compared averages I'm pretty sure it would be lower in the US. This is just a general impression I have, so of course I may be wrong.

[Angry Citizen]

How can you have an opinion about it when you haven't taken any of it?

Like I said, I tried on my own.

Um, what? How is this relevant at all in terms of understanding? Do you realize that just knowing equations doesn't really mean anything at all? It seems to me that you don't know at what physical intuition is and just learns a lot of equations. Physics is not about learning equations or learning how to solve problem X, it is about giving you a better understanding of how the world works.

If you'll reread my statement, this is actually my point. I know what physical intuition is, or at least the physical intuition employed by intro physics students. 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, I am saying that he focused on the intuition and essentially ignores the dreaded equation memorization. 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. What happens if you do that in physics? A large red x. Please read people's posts thoroughly before responding to them. Thank you.

[Angry Citizen]

Being, literally, the best one in my AP Physics C class without utilizing a single concept of calculus for half a year should prove to anyone that you don't need calculus to be good at physics or understand it.

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'? It's week four. This morning while doing problems I encountered one that was so much simpler if one took two indefinite integrals of the information at hand in order to calculate the time at which an object's position was x meters. Instead of going equation hunting, I knew how to derive that equation with calculus, and knew what that derivation meant, and how to apply it. One wonders whether you would've just gone equation hunting.

[thehacker3]

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'? It's week four. This morning while doing problems I encountered one that was so much simpler if one took two indefinite integrals of the information at hand in order to calculate the time at which an object's position was x meters. Instead of going equation hunting, I knew how to derive that equation with calculus, and knew what that derivation meant, and how to apply it. One wonders whether you would've just gone equation hunting.

Notice how you said it was a calculus-based class... AP Physics C was the type of class that could be tackled without knowing much calculus at all. You didn't give nearly enough information about the problem to allow me to comment on how I would have went about solving it so leave the wondering aside please.

[Klockan3]

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.

[Borek]

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.

[Klockan3]

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.

[xxChrisxx]

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.

[Borek]

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.

[xxChrisxx]

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.

[Andy Resnick]

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?

[Borek]

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.

[xxChrisxx]

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.

[Dadface]

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.

[Andy Resnick]

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.

[thehacker3]

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.

[Moonbear]

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.

[thehacker3]

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.