Making physics relevant in High School

[Gersty]

Physics is pretty easy to contextualize in a kid's everyday life, but it breaks down at a certain point. Its easy to reference the motion of cars, roller-coasters, falling objects, etc... But things like air-resistance always sort of get in the way. For example: A recent news item told of a tape measure that fell from a 50 story building and hit and killed an unfortunate worker below. My students were very interested in this story for obvious reasons, and we were in the middle of a unit on projectiles so they spent some time trying to calculate how long the tape measure was falling and how hard it must have hit the person below. What we teach in a typical high school class doesn't really get us far enough. Has anyone found success in tackling problems like this without recourse to calculus and higher level physics concepts? I feel that if we could show kids applications of physics that give us real world results that don't depend on a friction-less vacuum, we might interest a few more future physicists.

 

[ShayanJ]

I always hated this method of teaching something without actually teaching it. Because this way, you actually just swallow things given to you without understanding what's going on. So in such situations, I would teach the actual thing and if I see something is too advanced for the audience, I won't pretend that I'm teaching it, I just ignore it. Of course there is nothing wrong in giving a perspective of the subject to the audience but only given the warning that I'm not teaching it.
But there is an important obstacle in the way of teaching the full beast which is the main thing that prevents the full teaching of a subject to happen and that is the mathematical knowledge needed and if you try to teach that first, students just get bored at it because they don't understand the value and usefulness of the math.
But I think, instead of putting the subject aside, we should find a way to solve this problem. I think I have this solution. But because I have only a very little experience in teaching, I can't be sure of it and I can only suggest it as a theory. But I think this is a good theory which deserves experiment and has the potential to be successful.
I think if the audience is given a proper amount of motivation and of course there is some patience present at both sides, it is possible to teach subjects to the audience that is considered to be too advanced for them. So I think you can just present some examples that need calculus for treatment and just talk about the results without deriving them. Then just when you feel they're ready to get it, you can teach some calculus in the way of teaching the subject. Of course you're not going to teach calculus like in a calculus course. You just teach things as you come to need them.
Let me give you an example. Imagine you want to deal with linear drag force in a fall. So you write Newton's second law with the force of gravity and linear drag. Then you say this is an ordinary differential equation. So you go to tell them what is an ODE but that needs some knowledge about derivatives. So you go to teaching some minimum knowledge about derivatives. Then you say what is an ODE and you just teach the simplest method of solving that ODE and derive the results you said. But this way, you should be prepared to face an awful amount of questions coming from some confused minds. But if you know your audience well and give them enough motivation and also enough clarification(which both may vary greatly for difference audience), you can minimize the confusion.

 

[brainpushups]

Even without teaching calculus that particular problem could stimulate interesting discussion. For example, the role of approximations in physics; how close is close enough? It sounds like your class was in agreement that the free fall model did not accurately portray the speed of (or time for) the object to fall from such a height. Including air drag would give more precise approximations, but how complicated should it be? Is it enough to include just the inertial drag term? Should the viscous drag term be included? What about the fact that the air density is a function of altitude, temperature, and pressure? You could quickly work yourself into model so complicated that you would need to use numerical methods (you could teach some programming!). It would be interesting to see what the students thought about how accurate the model needs to be in order to be 'true.' Hmm. What makes something true? Another good discussion to have with students.

Even without calculus you can approximate the terminal velocity of the object easily and then use the free fall model as an approximation to determine whether or not the tape reached terminal velocity. I bet students would come to different conclusions.

Depending on the clientele you can definitely help students learn things that are not often taught at the high school level. I've offered an elective that I called 'introduction to dynamics' in which juniors and seniors in high school learned how to solve first order ODE's analytically and numerically, how to make series approximations, how complex numbers can be used to model SHO (one student even took on the driven-damped case!), and a (admittedly rudimentary) treatment of free rotations. Of course, the students did not master these topics/skills, but they certainly got something out of it and were able to analyze simple situations under each category with limited hand holding. I recently came across a paper which was a study about teaching Lagrangian mechanics to high school students in the MA school system (in Worcester, I think). The results of student learning were not that impressive (to my recollection), but they were only given 5 days! If I were to include analytic mechanics in a high school course I wouldn't be able to do it (well) in less than a semester!

 

[Astronuc]

Physics is pretty easy to contextualize in a kid's everyday life, but it breaks down at a certain point. Its easy to reference the motion of cars, roller-coasters, falling objects, etc... But things like air-resistance always sort of get in the way. For example: A recent news item told of a tape measure that fell from a 50 story building and hit and killed an unfortunate worker below. My students were very interested in this story for obvious reasons, and we were in the middle of a unit on projectiles so they spent some time trying to calculate how long the tape measure was falling and how hard it must have hit the person below. What we teach in a typical high school class doesn't really get us far enough. Has anyone found success in tackling problems like this without recourse to calculus and higher level physics concepts? I feel that if we could show kids applications of physics that give us real world results that don't depend on a friction-less vacuum, we might interest a few more future physicists.

Ultimately, physics is quantitative. One can describe physical phenomena qualitatively, but to dig deep into the physics requires mathematical models. Some models are simple, but most involve complex math.

Certainly there are simple experiments that can be performed to help students develop an understanding of physical phenomenon.

A falling object will experience air resistance. One can talk about viscous drag and terminal velocity, but applying in it an equation can be complicated.

Students can experience drag by putting their hands out the window of a moving car. As the car speed increases, the force on the hand increases.

In the first physics course I took, the professor had set up a demonstration in which a projectile was fired from a tube across the room to a falling target. As the projectile exit the launch tube, it interrupted an electric circuit that applied a current to a magnet suspending the target. With different angles and launch velocities, the projectile hit the target. The professor then lectured on the equations of motion and explained why the projectile hit the target at different initial angles and velocities. The course was taught with a blend of theory and experiment, so that the students would understand how to describe a physical system or phenomenon with mathematical equations/models.

 

[aalaniz]

Back in December I ran into the headline, "Physics is too hard for women, according to female physics students." Many of the reasons cited for "too hard" really had nothing to do with sex, like:
The notion that physics has nothing to do with the real world such as finance.

To help teachers such as yourself, I put up a Prezi fly-over presentation with 7 projects (and some YouTube videos) that could be taken up over the year connecting big physics to the real world. It's based on my experience teaching high school students and college freshmen over many years. The GPS technology in your cellphone, I tell, them in the first flyover, corresponds to roughly a $100 billion dollar industry with real world jobs made possible by the physics of general relativity. In another project I connect Brownian motion to high flying Wall Street finance...

The Prezi is at http://prezi.com/_wgcgvrj-slt/?utm_campaign=share&utm_medium=copy&rc=ex0share

My reply to the article on women and physics is at a Science 2.0 blog:
http://www.science20.com/physics_foundations/blog/physics_is_too_hard_for_women_according_to_female_physics_students-151431

 

[t--money]

Why not just get on top of your building and see how big of an effect air resistance has? My guess is "not enough" to get into the details. Drop some tape measures in a controlled (i.e., safe) environment. Time the fall multiple times at different heights and use kinematics to determine the percent error in time vs. height. If you use tape measures you already have the device for measuring height. They can even use their cell phone and a $5 Vernier app to video the fall and calculate g (http://www.vernier.com/products/software/video-physics/). The problem I see with physics is that we don't encourage students to go out and test our assumptions. At the high school level, these assumptions are easy to determine the associated errors with very little monetary investment.

 

[PFuser1232]

I recently finished high school, so I thought I could weigh in and give you a student's perspective on things. I think whether or not adding more "real life examples" increases the number of potential physicists vastly varies from student to student, depending on taste and the kind of physics or science based career they're hoping for. I always thought of solving problems based on real life occurrences as a bonus. What really appealed to me were the actual physical laws; knowing that these equations could apply to any system in the universe was mentally satisfying. Applying those equations (substituting values for the variables) to solve problems is also fun, but learning about the laws of physics with as much generality as possible is the reason I love physics. Every person likes physics in his/her own way. So I think when physics is taught there should be a balance between the abstract and the concrete; focusing on one while ignoring the other reduces the number of students interested. Whether it's an abstract general discussion about the laws of physics, or a particular application to a problem, I think math should always be there. The physics course I took in high school didn't involve much math, so I had to study how math is actually applied in physics on my own. It always seemed like the teacher avoided calculus when needed (in both deriving laws or tackling real life problems), although we did know calculus at the time. The bottom line is: keeping a balance between the abstract and the concrete, theory and experiment, and using as much mathematics as possible (since it is quite literally the heart of physics and engineering) is what makes a physics course perfect.

 

[wabbit]

Dumb question sorry - Not from the US so my idea of high school math there could well be off. But why is (basic) fall with drag that difficult math-wise if they can handle fall without drag? I mean the latter requires the students to understand the solution for ##\ddot x=g##, the former, the solution for ##\ddot x+\frac{k}{m}\dot x=g##, which is indeed more difficult - but if they get the no-drag case, they can be guided through the other one provided they know the exponential function.
I thought I remembered learning both in high school but maybe it was later, not sure.

 

[atyy]

Why is there calculus involved?

 

[ellipsis]

Dumb question sorry - Not from the US so my idea of high school math there could well be off. But why is (basic) fall with drag that difficult math-wise if they can handle fall without drag? I mean the latter requires the students to understand the solution for ##\ddot x=g##, the former, the solution for ##\ddot x+\frac{k}{m}\dot x=g##, which is indeed more difficult - but if they get the no-drag case, they can be guided through the other one provided they know the exponential function.
I thought I remembered learning both in high school but maybe it was later, not sure.

High school physics is formula-based, not calculus-based. Students learn physics by memorizing formulas, (d = (vi+vf)/2*t) - specifically, the four kinematic equations. The skills learned and required mostly consist of algebra (i.e. juggling equations around to fit a given situation) and word problem comprehension.

Furthermore, drag is quite difficult to model realistically. For one, the drag equation usually involves v^2, not v. (Even this is simplified - cross-sectional area is also relevant). Indeed, you could teach a drag equation only using v, but A: It would be wrong, and B: It would be pointless.

Finally, the very highest high school math course is only AP Calculus BC, which is equivalent to a Calculus II course in university. There is no context for differential equations, even for the brightest students. Needless to say, this all applies to the US, where I live. Also, I am only characterizing things as they are, not as they should be.

 

[wabbit]

Thanks I had no idea. And sorry about the v instead of v^2. I would not necessarily agree that a v-model would be pointless however, since I would tend to consider that any model that (a) includes a reaction increasing with speed, (b) recovers the correct result when drag=0, (c) gets terminal velocity as a feature, and (d) is tractable at the level of the students, could be a pretty good learning experience. Of course now I know (d) is wrong so it's useless in US high school context, sorry for the digression.

 

[Evanish]

Physics in high school left me with the impression that I knew more about physics then I really did. I don't think that's a good thing because it made me feel like I didn't need to learn more. Giving the youths some idea of just how vast and complex the subject is seems like a good idea to me.

 

[Stephen Tashi]

I feel that if we could show kids applications of physics that give us real world results that don't depend on a friction-less vacuum, we might interest a few more future physicists.

You can tackle mechanics problems of real life complexity without fluency in advanced mathematics by using numerical methods and simulations. However, that would require some fluency in programming or using software packages built for such purposes. How is the current generation of students equipped in that department?

 

[Yashbhatt]

Back in December I ran into the headline, "Physics is too hard for women, according to female physics students." Many of the reasons cited for "too hard" really had nothing to do with sex, like:
The notion that physics has nothing to do with the real world such as finance.

To help teachers such as yourself, I put up a Prezi fly-over presentation with 7 projects (and some YouTube videos) that could be taken up over the year connecting big physics to the real world. It's based on my experience teaching high school students and college freshmen over many years. The GPS technology in your cellphone, I tell, them in the first flyover, corresponds to roughly a $100 billion dollar industry with real world jobs made possible by the physics of general relativity. In another project I connect Brownian motion to high flying Wall Street finance...

The Prezi is at http://prezi.com/_wgcgvrj-slt/?utm_campaign=share&utm_medium=copy&rc=ex0share

My reply to the article on women and physics is at a Science 2.0 blog:
http://www.science20.com/physics_foundations/blog/physics_is_too_hard_for_women_according_to_female_physics_students-151431

Nice Prezi.