How can physics and calculus be effectively taught together?

[terminator88]

I go to a very very messed up school.Its tough and demanding but I feel like I don't learn much there(I cud write a whole essay on this).
Anyways I want knw how shud physics be taught in high school just out of curiousity?
Because in grade 12 I absolutely hated the our core physics course...all we did was memorise formulas and apply them on specific situations(similar to the AP physics B course..I think).In grade 11 I liked a little bit of the theory but then again there was soo much memorising specific things(E.g:Whether a Virtual or real image is formed by a camera?)which just bored me to death.

But then I took the AP C:E&M course (which was mostly self-study as my teacher sux) and it was very interesting and satisfying to learn on my own.So is physics really taught like the way in my school or is it different for u people out there and kept interesting at the same time?

 

[mathwonk]

physics shud not be speld fizix.

to me this does not provoke a desire to respond.

appropriate language is a good beginning for all scientific discussion.

 

[terminator88]

huh?I din do do tht

 

[Shackleford]

Maybe English is not his native language?

 

[DaveC426913]

huh?I din do do tht

You might as well have. You may find that people may only put as much effort into writing an answer as you put into writing the question.

 

[Math Is Hard]

Maybe English is not his native language?

I'm not so sure about that. The grammar is reasonable, but many of the words show pure sloppiness in spelling and a fondness for text-speak abbreviation. The author knows the language well enough to use an appropriate hyperbole ("bored me to death"), suggesting a good conversational familiarity with the language. It's very telling that a more complex word like "absolutely" is spelled correctly, while the words "could" and "you" get mangled in a text-speak abbreviated style.

I don't mean any nastiness to the O.P., but I think others have made it clear that if a post appears to have been made without care and thought, then maybe they shouldn't bother with a thoughtful response.

 

[Ouabache]

Don't worry, the responses you've seen so far, are not trying and discourage you from posting, just help you build better writing habits. We are still on your side and here to help.

I feel high school physics or any technical discipline at the basic level, should not be taught with an emphasis on memorization. They should teach you fundamental principles and how to apply them. They should help you develop physical intuition and strong problem solving skills. If you're lucky to get a good teacher, who expresses enthusiasm for the material, it will be quite fun.

 

[Vanadium 50]

I don't mean any nastiness to the O.P., but I think others have made it clear that if a post appears to have been made without care and thought, then maybe they shouldn't bother with a thoughtful response.

Excellent point.

Note that the poster is not complaining that the teaching style wasn't effective. He's complaining that it wasn't entertaining. It might well have been ineffective as well, but that's not the complaint. I'm afraid that I personally am not terribly moved by that complaint.

 

[Asphodel]

After reading and writing and 'rithmetic, most likely. There is quite a bit of research put into the topic of physics education, you might be able to rustle up some interesting articles on the topic if you're interested.

Part of being a good teacher tends to entail engaging the imaginations of the students, meaning that ideally a good teacher needs to be at least part showman on top of the more academic elements. Bored students tend not to learn as well, it's just part of the package when you have human beings for students. Particularly young ones.

 

[Feldoh]

I go to a very very messed up school.Its tough and demanding but I feel like I don't learn much there(I cud write a whole essay on this).
Anyways I want knw how shud physics be taught in high school just out of curiousity?
Because in grade 12 I absolutely hated the our core physics course...all we did was memorise formulas and apply them on specific situations(similar to the AP physics B course..I think).In grade 11 I liked a little bit of the theory but then again there was soo much memorising specific things(E.g:Whether a Virtual or real image is formed by a camera?)which just bored me to death.

But then I took the AP C:E&M course (which was mostly self-study as my teacher sux) and it was very interesting and satisfying to learn on my own.So is physics really taught like the way in my school or is it different for u people out there and kept interesting at the same time?

I think it varies from school-to-school and at the discretion of the teacher who is in charge of the class.

I believe AP Physics B is more theory and a broader range of topics, while Physics C is a bit more narrow, with more of an emphasis on learning and interpreting the math behind the physics.

 

[ks_physicist]

There are a lot of "specific thing" that you must memorize or become very familiar with in the study of basic physics. If you do not, you are not prepared to study the more complex topics.

 

[Asphodel]

There are a lot of "specific thing" that you must memorize or become very familiar with in the study of basic physics.

Not *nearly* as much as in some other scientific disciplines or engineering fields. Most of the focus (in my experience) is on gaining an understanding of the physical processes involved, on how to use that and a relatively small set of descriptive formulas to analyze a given problem, and on developing a sense of whether the answer you arrive at is reasonable or estimating roughly what the expected result would be. So more on the familiarity, less on the memorizing.

 

[terminator88]

Not *nearly* as much as in some other scientific disciplines or engineering fields. Most of the focus (in my experience) is on gaining an understanding of the physical processes involved, on how to use that and a relatively small set of descriptive formulas to analyze a given problem, and on developing a sense of whether the answer you arrive at is reasonable or estimating roughly what the expected result would be. So more on the familiarity, less on the memorizing.

I agree with Asphodel...especially the part "small set of descriptive formulas to analyze a given problem, and on developing a sense of whether the answer you arrive at is reasonable or estimating roughly what the expected result would be".
Sadly,in my school just getting the right answer and gettting the marks is of utmost importance.

 

[terminator88]

I'm not so sure about that. The grammar is reasonable, but many of the words show pure sloppiness in spelling and a fondness for text-speak abbreviation. The author knows the language well enough to use an appropriate hyperbole ("bored me to death"), suggesting a good conversational familiarity with the language. It's very telling that a more complex word like "absolutely" is spelled correctly, while the words "could" and "you" get mangled in a text-speak abbreviated style.

I don't mean any nastiness to the O.P., but I think others have made it clear that if a post appears to have been made without care and thought, then maybe they shouldn't bother with a thoughtful response.

First of all I am a teenager and this is how we usually talk.But anyways I do not see it as poor english...it was just organised haphazardly.I did not plan it very porperly and I rambled on a bit.I don't understand where you people are coming from...it was not that bad!

 

[uman]

I'm a teenager too but I know how to write. High school is when you should begin to take yourself seriously as an adult and as a scholar, which means following the conventions of your native language when writing.

 

[Moonbear]

First of all I am a teenager and this is how we usually talk.But anyways I do not see it as poor english...it was just organised haphazardly.I did not plan it very porperly and I rambled on a bit.I don't understand where you people are coming from...it was not that bad!

If you wish to attend and do well in college, you need to learn to use language appropriately. It was "that bad." Just because it is common among teens does not make it appropriate, correct, or acceptable. If you're asking a group of professionals or advanced students about their courses and teaching techniques, and wish to receive a thoughtful response, you need to be thoughtful in your language use. If you want to chit chat with a bunch of other teens who are your friends to whine about your class, use whatever language you want, but that's not what we're about here. Besides, bad habits are really hard to break. It's much better to practice using correct English now so you don't have to spend hours you don't have to waste on proofreading and correcting your writing when in college or the working world.

As for your original question, the difference between a real and virtual image is a concept to learn, not a memorized detail. That's about the only example you gave to evaluate your perception of what was taught vs what actually was taught. Too often, students who do not adequately understand the concepts resort to attempting to memorize vast amounts of material when their learning would be far more simplified if they learned the few basic concepts taught. Based on your example, you very well may have been taught the concepts and simply did not grasp them adequately. I have no way to tell beyond that. Physics, like any other subject, is about learning the basic concepts and applying them. Of course, also as in any other subject, you need to memorize some basics in order to understand the concepts to apply them. For example, you need to memorize what the variable V₀ is/means when you see it in an equation, but then you need to understand the concepts to apply using the equations involving it correctly. As you learn more and more of the fundamentals, the emphasis shifts more from memorizing basics to understanding theories and concepts and applying them to more and more challenging problems. But, it shouldn't be dependent on your teacher to do a song and dance routine for you to learn a subject.

 

[Laura1013]

I'm a teenager too but I know how to write. High school is when you should begin to take yourself seriously as an adult and as a scholar, which means following the conventions of your native language when writing.

Well said!

 

[terminator88]

Okay okay I will stop this SMS english.Now can we go back to the actual point of the thread.I just wanted to know about your experiences with physics-the good and the bad.

Moonbear...tell me how would you try to study the chapter about mechanical waves.It is all about memorising the equations and then applying them to different sorts of problems which are all very similar.I cannot possibly motivate myself to study a chapter like that.

 

[lisab]

Okay okay I will stop this SMS english.Now can we go back to the actual point of the thread.I just wanted to know about your experiences with physics-the good and the bad.

Moonbear...tell me how would you try to study the chapter about mechanical waves.It is all about memorising the equations and then applying them to different sorts of problems which are all very similar.I cannot possibly motivate myself to study a chapter like that.

I recognize how hard it is to teach physics "properly" without calculus. Once you know calculus, you can learn where the formulas come from, and derive them yourself from scratch. In addition to being immensely satisfying, you REALLY learn the material that way.

Without calc, you will neccessarily have to memorize more because you don't have the tools yet to derive. In other words, you don't have your deriver's license yet (sorry, I simply cannot resist puns!).

 

[Count Iblis]

I was fortunate enough to have studied math and physics from university books when I was in high school, while skipping the high school curriculum. Physics and math education is just abominable in primary and high school. You are probably better off not learning that crap at all.

In the US this problem even persists at university as http://insti.physics.sunysb.edu/~siegel/plan.html"

 

[Asphodel]

Okay okay I will stop this SMS english.

Good idea; it's a horrible habit.

It is all about memorising the equations and then applying them to different sorts of problems which are all very similar.I cannot possibly motivate myself to study a chapter like that.

Sounds like a crappy text then, if your description is accurate. Also, many cases in introductory physics are made unnecessarily complicated as lisab described...

I recognize how hard it is to teach physics "properly" without calculus.

...here. When I took it, fortunately I already knew most of the material for introductory calculus. So all those extra equations they give you to memorize that are basically pre-integrated or differentiated forms of the fundamental ones? Never bothered with it. Even learning only the very rudiments of calculus and a few key tools (power law) will allow a great deal of insight into what's going on in your introductory texts.

In many cases, freshman physics and freshman calculus are expected to be taken in parallel. Freshman physics is also necessarily accessible to people outside the physics department as many programs will require taking at least part of that sequence; this aside from students who are taking it to fulfill general education requirements. Thus you get this result. On top of this, most physics departments seem to already be stuck footing two instances of this series - the "for scientists / majors" instance is already calculus based to a degree. What this really means is that it uses a very small amount very late in, while relying largely on trigonometry and algebra. The other version is ostentatiously algebra-based, but in turn doesn't use that nearly as much as it could be.

If time and money weren't such an issue, we would probably like to get students already having a firm grasp of things like calculus, circular and hyperbolic trigonometry, vectors, differential equations, linear algebra...well, that's most of it that I've seen used at the undergraduate level. If you're taking physics - or any STEM major - get your math in early and do everything you can to master the material. Passing and forgetting isn't the idea here.

In the US this problem even persists at university as http://insti.physics.sunysb.edu/~siegel/plan.html"

I agree with a number of the points here, but find others completely contrary to my experiences. Of course, he's speaking of books in general. Other matters like the ordering of topics and to some extent questions that doesn't address can really be handled by having a competent instructor, but the points are nonetheless valid. But other people would have a differing set of complaints, as is implicitly shown by him having these complaints at all.

 

[terminator88]

So I guess I will just memorise for now until I get my driving license necessary to derive the equations.
Oh and the book I was talking about was University Physics.

 

[Asphodel]

You should still only have a very small set of equations. Unless they completely disallow notes, you really just need a well-written equation sheet to get rid of that particular problem.

Also - ha ha you got stuck with online homework.

 

[uman]

I don't understand the "driving license" comment, at all.

 

[Barfolumu]

I don't understand the "driving license" comment, at all.

Getting your drivers license is, in a sense, a step towards adulthood.

So, getting your derivers license would be, in a sense, a step towards being a physicist.

They sound similar, so... yeah. That's the pun.

I thought it was funny :D.

 

[Count Iblis]

So I guess I will just memorise for now until I get my driving license necessary to derive the equations.
Oh and the book I was talking about was University Physics.

If you have an exam within the next month or so you have no choice but to follow the course. For the longer term I would suggest to learn everything from first principles. So, study all the core subjects like calculus, linear algebra, complex analysis, classical mechanics, special relativity, electrodynamics, statistical physics, quantum mechanics etc., on your own if necessary.

The idea that you can't do it on your own and that you need to follow a course in class is nonsense. All that happens in class is that the instructor breaks down what is in the book into small chunks that look more manageable. You really master the topic when you are solving problems at home or at a problems session in class anyway.

So, you can just get a book on quantum mechanics from the library and master quantum mechanics on your own by working your way through the book. If you do that that and find that you must master linear algebra a bit better to understand quantum mechanics, then you just go to the library, find a suitable book on that topic, study it and then continue with quantum mechanics. No problem!

 

[Count Iblis]

To answer the question:

How should physics be taught?

more generally, I would say that we should start in primary school with 6 year olds. Teach them some real math and science. Ten year old children play very complicated computer games that require a lot of logical reasoning. But when it comes to math teaching we treat them as if they are babies who can only do very simple logical deductions.

Perhaps we need to make math more fun by designing special computer games so that when you play it you automatically learn math...

 

[DavidWhitbeck]

Moonbear...tell me how would you try to study the chapter about mechanical waves.It is all about memorising the equations and then applying them to different sorts of problems which are all very similar.I cannot possibly motivate myself to study a chapter like that.

It's well known that oscillations and mechanical waves carry with it a large number of terms and formulas that you should memorize just so you understand the language. Your textbook is not really at fault here, there is no real getting around it.

University Physics by Young and Freedman is a decent textbook. I value a few more than it, but it's not terrible.

 

[ks_physicist]

To answer the question:



more generally, I would say that we should start in primary school with 6 year olds. Teach them some real math and science. Ten year old children play very complicated computer games that require a lot of logical reasoning. But when it comes to math teaching we treat them as if they are babies who can only do very simple logical deductions.

Perhaps we need to make math more fun by designing special computer games so that when you play it you automatically learn math...

We can certainly push some math instruction into lower grade levels than it is currently taught in the US system--the main obstacle at the moment is inadequate mathematical preparation for elementary school teachers. If they never had anything beyond college algebra, they probably don't remember enough algebra to properly teach the pre-algebra topics.

However, there are developmental stages that students must pass in order to adequately understand and process increasing levels of mathematical complexity. You simply can't teach algebra (for example) to arbitrarily younger kids, because eventually you hit the point where their brains simply aren't developed enough to handle that level of logic and analysis.

Obviously, mathematical developmental staging will show a bell curve for any cohort of students, but if the majority of the students' can't yet comprehend let alone master a topic then it is unproductive (in fact, negatively productive) to try to push them through it.

Disclaimer: I am not a math education specialist, but I have been consulting several of them regarding the troubles our freshman physics students are having with basic algebra.

 

[Mathemaniac]

I would think that algebra could be taught at a younger age than it usually is. It would be absurd, however, to suggest that they would have the same aptitude for mathematics as high schoolers would.

I'd love to see some research done on this topic, nonetheless, to see just how capable youngsters are of learning higher level math.

Anyway, learning physics isn't about memorizing equations. You need to understand the equations--where they come from and what their implications are--to be able to effectively use them.

 

[terminator88]

Getting your drivers license is, in a sense, a step towards adulthood.

So, getting your derivers license would be, in a sense, a step towards being a physicist.

They sound similar, so... yeah. That's the pun.

I thought it was funny :D.

When I said "driving licence"...I was referring to what lisab said.I still don't know calculus good enough or any other math tools to be able to understand and derive the equations.So I guess I will memorise the equations without really understanding where it comes from.

 

[terminator88]

You should still only have a very small set of equations. Unless they completely disallow notes, you really just need a well-written equation sheet to get rid of that particular problem.

Also - ha ha you got stuck with online homework.

Nope no equations AT ALL allowed in my school exams.So many people cheat in my class and especially in physics because of the insane number of formulas.We even had to memorise relalativity formulas and lorentz equations!

 

[terminator88]

To answer the question:



more generally, I would say that we should start in primary school with 6 year olds. Teach them some real math and science. Ten year old children play very complicated computer games that require a lot of logical reasoning. But when it comes to math teaching we treat them as if they are babies who can only do very simple logical deductions.

Perhaps we need to make math more fun by designing special computer games so that when you play it you automatically learn math...

AN excellent ideas!I will be the first one to buy such a game.I think it is much better if computer games are made to teach physics because in the computer game you can show why it is ncessary to learn something by creating an alternate,interactive world.

 

[Asphodel]

We even had to memorise relalativity formulas and lorentz equations!

Oh no, don't make me memorize that m^2 = E^2 - p^2! Not that!

Special relativity is really, really easy computationally once you get the hang of the concepts. Especially on the level you're likely to encounter in a general physics course. Many of the formulas here are "cases" that make sense and are much easier to understand once you get a feeling for what it's saying.

Same thing works for many equations. Get a feel for what they're "saying" and it becomes fairly easy to recall.

 

[Vanadium 50]

Oh and the book I was talking about was University Physics.

You should learn the authors of your textbooks. As you might imagine, most textbooks on a topic have similar titles. People will ask you what textbook you used, and "Smith, Jones and Johnson" is more descriptive and more professional than "Um...Pink! The cover was pink".

By the way, if it's Young and Freedman, it's not a bad book.

 

[Ouabache]

I also used "University Physics" in my introductory physics course. Seems to me mine was written by Sears and Zemansky. This first course did not use any calculus. There were many fascinating concepts I learned in that class. I didn't formally memorize any formulae, just recalled them after practice using them in problems.

 

[DavidWhitbeck]

I also used "University Physics" in my introductory physics course. Seems to me mine was written by Sears and Zemansky.

Over several editions the authors changed and I guess finally enough of the text had been changed that they just ditched the names of the original authors and went with the new ones. But if you look the older editions are written by Sears and Zemansky and the new ones are written by Young and Freedman.

 

[BioCore]

I have a question about the amount of text that is actually used in courses at university. I usually see Professors skip a few sections from chapters, or almost the whole chapter (this was from my first year university experience)- although it was great not having to read the whole book sometimes. Now I always wondered if this would affect students performance in future subjects related to the same course; such as advanced physics courses?

Or do these advanced courses still manage to review some of the basics before moving on? What would some of you recommend? Would it be best to go through the whole textbook if I have the time, or is it better to just follow up with my Professors recommended readings?

 

[Vanadium 50]

I also used "University Physics" in my introductory physics course. Seems to me mine was written by Sears and Zemansky.

Sears and Zemansky (which might have started as just plain Sears) became Sears, Zemansky and Young and later Young and Freedman.

 

[DavidWhitbeck]

Biocore, that's typical in every class. They don't skip sections to short change students. Every textbook is written for instructors to pick and choose what topics they want to cover. What you don't see is that the instructor editions typically lay out in the preface what the core sections are that should be covered and typical plans for choosing out of the remaining elective sections for what you want to cover in what time frame. Usually it would be impossible to exhaustively cover a textbook in a class.

 

[BioCore]

I see, but if I wanted to teach myself some more advanced physics topics outside of class later on would it be wise to go over the whole book myself or is this unnecessary?

I was also wondering what the ideal study method is for Physics. Should a person read for example one section of a chapter and then answer the questions pertaining to that section or would reading the whole chapter and then answering all questions after be better form of testing your knowledge?

 

[DavidWhitbeck]

That's why many books have section and chapter problems. So that you can immediately do exercises at the end of a section, but also have the change to synthesize the entire chapter with more overarching problem sets. So my answer is yes! Do exercises at the end of sections and at the end of chapters.

 

[terminator88]

How many days should one usually spend reading a chapter?
There are many times I get lost from reading a chapter in a day.

 

[omz222]

A few. You have to let the material sink in, and you exerting some effort by giving thought to it.

 

[kenewbie]

Philosophy and Physics should be thought from the first grade. Start with the easily accessible parts.

Instead of reading to them about Moses or whatnot, how about Socrates? The stories are just as enthralling and a hundred times more relevant.

The same goes for physics. Experiment and play with basic concepts, forget the math for now. Compare the falling-speed of a ball dropped right down with the speed of a ball rolled off a table. Fill a ball with helium and tie balls with air to it, figure out the relative weight. Show what effect the weight of an item has on the time it takes to fall to the ground. Use a scale to weigh different liquids, then see what happens when you mix them together. And so on.

This can all be easily understood and explained, and the earlier you get to take part in these things, the better. This has been a pet peeve of mine for a long time.

k

 

[Count Iblis]

How many days should one usually spend reading a chapter?
There are many times I get lost from reading a chapter in a day.

You should try to get a feel for what the key problems are that prevent you from understanding it. You must take as much time and effort as is necessary to understand it. If you set yourself some artificial time limit of, say, two days, then you are blocking potential ways to resolve the problems.

E.g. it may be the case that you don't understand some other theory well enough and that it would be a good idea to study that but that would take a month. If that's the case you should do that.

When I was studying physics, I decided at some point that I wanted to follow certain math courses intended for math students for about a year. At my university (at the time I was studying at least) there were no obstacles for me to do that.


I think the real problem students face today is that they are not given enough freedom to determine for themselves what they need to study. As a result they then lack the necessary insight that they would need to study on their own. This is a problem if they don't understand the standard curriculum.

Ultimately, you really need to develop the skills to master any subject that you initially know nothing about without any help from others. So, you have to go to the library to find the suitable books or find suitable sources online. Then you have to make decisions on what else you should learn in order to understand the sources you have found etc. etc.

 

[vanesch]

I used to have strong opinions on how physics and math be taught: for me (and as I see, for several other posters here), the earlier, the more, the most abstract was the best. And then - for totally different reasons - I read up on didactics, and teaching and all that, and I learned that there exists psychological research which indicates that there are several clearly distinct "learning profiles" and distinct "learning motivations". Different people have different combinations of these "base profiles". It is part of their personality.
The "most, as abstract, and as early as possible" is exactly one of those profiles - but it is not the most common one. There are the "learning by practical example", or "learning by doing", or "learning by social interaction" etc... profiles.
The motivation "I want to understand how it works" is also one of the different motivation profiles, but it is not the only one. Some are "I want to please", or "I want to use the stuff", or "Can it help me to be successful" or ...

Obviously, for each combination of profiles, there is an "ideal" way of teaching, and a "worse" way of teaching. Unfortunately, what is "ideal" for one profile is often "worse case" for a different profile. Very often, unknowingly, the teacher tries to approach the ideal teaching method for his own profile.

A regular class usually consists of people with totally different profiles. They are usually different from the teacher's profile - except of course in graduate classes, where selection has provided for a more uniform set of profiles, which are moreover closer to the profile of the teacher (who emerged from exactly that kind of classes with high success). Usually they are the profiles of "the most and the most abstract", and "I want to know how it works" type. When these people go and teach a regular class, they will suddenly find out that their method of teaching doesn't work well with a certain fraction of the class. The more they apply themselves in "teaching well" (optimizing for their own profile) the less the class will work out. In fact, for a general class, there is no universally good way of teaching. The best one can do is to "jump around" over different teaching styles: some days a bit more abstract, some days, highly practical, some days, a lot of social interaction, other days more reading etc... as such, you give the opportunity to everyone to at least grab a part of the course according to their favorite teaching method, which might motivate them to make up for the parts that are less suited to their profile.

The totally different learning profiles are at the origin of a lot of religious wars in educational sciences, and the sad point is that for a general public, there is no single method that works perfectly.

 

[DavidWhitbeck]

I agree with what you said about how we learn and how the general student learns. I disagree with the jumping around strategy. Arons ("Teaching Introductory Physics") and Knight ("Five Easy Lessons") say that physics education research has found that the learning process that starts concrete and gradually abstracts the theory is the most successful.

I agree that there should be a diversity of activities, I'm just saying that there is a preferred teaching direction that will help the most students and it's not random.

I also strongly, strongly disagree on the social interaction. My students are all way too chatty, I have to keep them on task, confiscate their cell phones etc they really have absolutely no problem socializing. I'm in favor of giving them specific roles when they are doing group based activities to keep them on task and only talk about the activity at hand.

 

[Count Iblis]

Is it really necessary to have lectures at all? From my experience almost no learning takes place during lectures, so why not get rid of them? You just hand out lecture notes, and have problem sessions were student can ask and discuss problems. This should also be done in high school.

Instead of the lectures you could let the students watch videos about interesting physics topics. That would be much more fun for the students. The students would then also have more energy left after school to do some serious hard work on their physics problems.

 

[BioCore]

@Iblis,

Although I do agree, I have sometimes and have had friends tell me the same that they just fully understood a certain point after hearing it from a Professor. The problem is that some people prefer to listen to others tell them about concepts and proofs and then work on their own.