How can physics and calculus be effectively taught together?

[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.

 

[DavidWhitbeck]

I have found that lecture shouldn't dominate class time, but it's still important and needs to be there. Fifteen minutes for a subject can be enough if you force the students to study the book on their own. But if you don't do any lecture, they will just not learn it at all. I know this from personal experience. Lecture in moderation, especially in conjunction with examples and demos, is an invaluable learning tool in the classroom.

 

[DeanBH]

lectures, and hard open questions that gets people involved and thinking IMO.

 

[DavidWhitbeck]

lectures, and hard open questions that gets people involved and thinking IMO.

I agree with that. Simple problems teach students to just be formula seekers and not really how to solve problems. Challenging problems that require interpretation and deep thinking, force students to develop good problem solving skills. I really like Maryland's context rich problems and their guidelines for creating them.

My approach next year in teaching physics will be--

conceptual only, worksheets and questions but not problem solving-- first pass through the material

ALPS kits-- on the second pass through the material, show them how to solve problems by practicing each step in isolation (especially constructing pictorial representations of the problem)

Problem solving-- on the third and final pass through the material, have them use the concepts and the methodology they learned before to practice solving difficult problems.

 

[lulz]

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.

Just wondering: why don't you capitalize your sentences? Is it because a sentence is more symmetrical when everything is lowercase, i.e. it looks nicer?

I'm not trying to be a prick, just genuinely curious.

 

[FrogPad]

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.

Man, you must have never had a great professor that just blew your mind. Listen to Feynman sometime... would you get rid of that?

 

[vanesch]

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 don't want to give the wrong impression that one day, one should talk about hilbert spaces, and the next day, one should show pulleys. Of course there has to be a building-up of the material. I was talking about the didactic techniques. Sometimes you can give a lecture which gives you a general treatment (that's "abstract", to pleas the intellectual profiles), say, define Newton's law and so on, and sometimes you can give a very concrete set of examples, from real life (to please the practical constructivists). Sometimes you can give individual reading assignments, and sometimes you can hand out tasks to be done in small working groups (that's the social interaction part, in the constructionist style) - I wasn't talking about social interaction in the "let's have a beer together" style! Different student profiles will have different "learning efficiencies" for the different activities, but by introducing some variability, you can preferentially reach different parts of the class "efficiently".
Sometimes you can have them do presentations (to please the "I want to be successfull" types) and sometimes you want them to be a bit more passively acquire the material.

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.

Of course, sorry if I implied that. I was talking about the techniques, not the material itself.

 

[terminator88]

I am curious too about something.

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.

Where did he see fizix?

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?

 

[Count Iblis]

Man, you must have never had a great professor that just blew your mind. Listen to Feynman sometime... would you get rid of that?

We should give all lectures like that. But that's not going to happen. So, you would then be beter off by showing a video of Feynman lecturing instead of lecturing yourself. But then you could just as well turn all your lectures into video sessions. Sometimes a lecture by e.g. Feynman, sometimes a documentary etc. etc.

You then save a lot of time that you can put to better use by writing good lecture notes and thinking of problems for the problems sessions.

 

[Count Iblis]

I am curious too about something.

Where did he see fizix?

Actually writing fizix is no problem whatsoever as most brains are able to interpret it correctly. It is amazing how the brain can do this. You can even take some text (spelled correctly), and then randomly permute the letters in all the words except the first and last letters and most of the text will still be readable. The strange thing is that the text is then better readable if you try to read in "fast reading mode". If you try to read it slowly, word for word, it is quite a bit harder to read. I've just done this for one paragraph written by someone in this thread. Just try to see if you can read this:

In many caess, fhasemrn pshycis and fsrahmen cclaulus are eetepcxd to be tkaen in pealarll. Framhesn phcyiss is aslo neisaclsrey aseibsclce to ppleoe oudtise the pciyhss drtaepmnet as mnay prorgams wlil rqrieue taking at lsaet prat of taht snuecqee; tihs asdie from sttdunes who are tikang it to filufll gaernel eioctudan renqutemries. Tuhs you get this ruslet. On top of tihs, msot pchisys depmntaerts seem to aarldey be sutck fniootg two incsnaets of tihs sieres - the "for sitesncits / mojars" ianstcne is adraley cucualls bsead to a dreege. what tihs raelly menas is taht it uess a very samll aomunt vrey late in, wilhe rnyielg lealrgy on tegionorrtmy and albegra. The ohetr vsrioen is ostueatltsoiny alebrga-bsead, but in trun deson't use that nrelay as mcuh as it cuold be.