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Why should the kinematics equations be taught in a regular high school physics course?

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vela

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In my experience the concepts are often understood better by the students who understand the mathematics.
I'd say that's true for all of physics. But the question is what your goal is for the course. If the course is, as Hlud says, the only physics course many of these students will ever take, does it really benefit the students to know how to calculate how long the ball will be in the air but not understand the nature of radioactivity? I'd say that having them understand radioactivity isn't the boogeyman it's often made out to be by anti-nuclear activists or the panacea pro-nuclear forces suggest it is is more relevant in today's world.

This is the first year I've tried this, but I have gone very deeply into history and the development of science with my students this year.
How has this worked out for you? Do you find it helps keep the students more interested in the subject? I think many of us here enjoy messing around with the math and just learning physics for the sake of learning it, but most students don't. They need to see how it's really part of their culture and not something only for nerdy types.
 
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CWatters

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I have, for the past couple years, taught the kinematics equations to my regular physics classes (spending around 6-8 weeks doing so), and i will not be doing that in my new school.
I'm curious what you would use those 6-8 weeks for if not teaching kinematics? Is there another physics topic that will be covered instead or ?
 
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In my experience the concepts are often understood better by the students who understand the mathematics. It would be interesting to try asking some 'conceptual' questions like those in Hewitt's book that are based entirely on proportional reasoning like, for example 'if you step on the gas pedal and accelerate from rest and you travel a distance of 5 feet in the first second, how far will you have traveled at the third second' (assuming the acceleration is constant).
This is exactly what i am suggesting to my colleagues to eliminate. Your examples are not really conceptual, but more computational. And i actually see the opposite. My colleagues who teach AP Physics I (of which i teach a section of) don't care for my suggestion. One colleague goes as far to say that a conceptual-focused course dumbs it down. We agreed to put a conceptual question concerning the scope of those kinematics equations on a test. His students ended up missing that question far more than he ever thought. I could give more examples of students who know the math, but struggle with the physics.

I don't think it is being argued that kinematics is more fundamental than, say, the law of reflection. But now we're talking about two different branches of physics.
But, if i am to teach either kinematics or optics, i have to make a choice. My regular physics students generally don't get to see both. The same could be said of students in an intro to physics class in college.

How has this worked out for you? Do you find it helps keep the students more interested in the subject? I think many of us here enjoy messing around with the math and just learning physics for the sake of learning it, but most students don't. They need to see how it's really part of their culture and not something only for nerdy types.
I, too, am extremely curious. I have always wanted to do something like that, but have been too overwhelmed with thinking about it.

I'm curious what you would use those 6-8 weeks for if not teaching kinematics? Is there another physics topic that will be covered instead or ?
There are plenty of topics that we don't even touch in regular physics: anything in optics, thermo, rotation, waves, modern, etc... I just had a conversation suggesting that regular physics should be turned into a survey course. A lot of teachers i have talked to about this believe that mechanics is heavily focused in the county/state standards. Despite me showing them the contrary, they still seem to be hesitant.
 
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I'd say that's true for all of physics. But the question is what your goal is for the course. If the course is, as Hlud says, the only physics course many of these students will ever take, does it really benefit the students to know how to calculate how long the ball will be in the air but not understand the nature of radioactivity? I'd say that having them understand radioactivity isn't the boogeyman it's often made out to be by anti-nuclear activists or the panacea pro-nuclear forces suggest it is is more relevant in today's world.
The goal is the question indeed. One of the reasons I changed my course to involve so much history was in thinking about this very problem: what should the average high school student take away from a single course in physics? I decided that they should understand the details of how the process of science works; call it scientific literacy. I saw an opportunity for telling the story of physics as a vehicle for this. I want students to be able to learn how to make arguments, how to evaluate others' arguments, and to understand that physics has just as much aesthetic value as a great work of art (perhaps the greatest in the history IMO). I want them to think for themselves, not regurgitate someone else's thoughts. I would argue that this is a better thing to teach them than, say, the nature of radioactivity. I would hope that students could learn to look at the scientific arguments for something and perhaps arguments that aren't endorsed by the scientific community and come to their own opinion by weighing the merits of the arguments. If they understand how scientific arguments are made they can give them the appropriate weight against lofty rhetoric.

How has this worked out for you? Do you find it helps keep the students more interested in the subject? I think many of us here enjoy messing around with the math and just learning physics for the sake of learning it, but most students don't. They need to see how it's really part of their culture and not something only for nerdy types.
Its been a mixed bag. I've definitely hooked some students with the history, philosophy, and other topics related to the physics that we've discussed than if we hadn't done them. There is also enough of the detailed mathematics to satisfy the nerdy types. On the other hand, I had to eliminate a few projects to make room for the new material and I think I lost a few by doing this. Granted, the ones I've lost are the less motivated students who wouldn't have learned much physics from the projects anyway, but would have had a good time with them. Overall, I'm pretty happy with how it has worked. Next year I'm going to try using Steven Weinberg's book To Explain the World as a companion text to the course. I think this will help free up some time since I won't have to spend as much class time on the history; they can read it for themselves and I can do some additional activities or provide additional math help during class.
 
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This is exactly what i am suggesting to my colleagues to eliminate. Your examples are not really conceptual, but more computational.
Can you give me an example of what you interpret to be a conceptual question about acceleration?

And i actually see the opposite. My colleagues who teach AP Physics I (of which i teach a section of) don't care for my suggestion. One colleague goes as far to say that a conceptual-focused course dumbs it down. We agreed to put a conceptual question concerning the scope of those kinematics equations on a test. His students ended up missing that question far more than he ever thought. I could give more examples of students who know the math, but struggle with the physics.
Don't get me started on AP. What a complete waste. I went to talk with a large number of science faculty at a local ivy league college a few years ago and some of them had been keeping data on how students coming in to first year science courses faired on their introductory courses. Students who had taken AP classes in high school showed absolutely no difference from those who had not taken AP courses. The most frequent AP test score regardless of final grade for their introductory course was a 5. AP courses do not teach you how to think.

I absolutely agree that you can focus too much on the mathematics and then the concepts will escape the students. I think a balance is needed. When I first started teaching I think I was too heavy on the math also.

But, if i am to teach either kinematics or optics, i have to make a choice. My regular physics students generally don't get to see both. The same could be said of students in an intro to physics class in college.
Perhaps. This is the first year I've done any optics. Because I've followed the historical track this has let me cover more branches of physics that I ever had done before. My courses before this year were entirely classical mechanics. If you agree that science literacy is important and how science shaped our worldview then I think you should probably omit optics because, at least in the early development of optics around the time of Newton, the work in optics had very little effect on the changing world view. On the other hand, you can probably hook some students with optics because you can do a lot of cool things!

I, too, am extremely curious. I have always wanted to do something like that, but have been too overwhelmed with thinking about it.
The amount of work has been enormous and I spend a lot of free time reading about science history and developing the curriculum. Luckily, that's what I'm interested in right now. I think I've used close to 20 different texts to put material together and this does not include the translations of the original treatises that I've at least skimmed (of which there are probably also around 20, but I didn't go back to count).


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My question I guess is, what do your standards require the students to do? If conceptual understanding is the key you might consider reasearching the lecture demonstration model of physics education. Marietta College in Ohio isa big proponent of this method and it has shown to be effective in a lot of ways in my classroom.
 

Andy Resnick

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<snip>
What makes the kinematics equations more fundamental than basic optics? Or how sound works? Or why a simple machine works?
That's a fair point. One answer is that it's historical- mechanics is an older branch of science than optics. That said, hydrodynamics is older than mechanics, so why don't we start with hydrodynamics?

Another answer is that we have to start somewhere, and kinematics lends itself to quantitative experiential learning better than optics or sound. Simple machines (levers, screws, etc) can be taught prior to kinematics, and they often are, but in the end, kinematics is a common starting point to introduce mathematical modeling of the real world, because it's based purely on measurable quantities (velocity and acceleration).

Personally, I've toyed with the idea of basing a physics I class entirely on 'energy' and perhaps not even bothering with 'force.' The state of Ohio mandates otherwise, but in my head it's an interesting approach.

I do like the graphing. What i will suggest to my colleagues, as i will do this, is to do shapes of graphs only. Do not connect the graphs with equations, or put any numbers at all on the graphs.
That's fine- doing that can be termed 'ratio reasoning', and is something I wish my students had more experience with prior to intro physics.

This is not a good argument at all. I could expose the students to kinematics the whole entire year. They will better understand it, true, but will they benefit from this change? No, because the majority of students who take this course do not ever take another physics class again.
That's not exactly what I mean, because you are right- students would be perfectly happy to cover only 1 chapter for an entire year, so they don't have to come to class and will do well on the assignments. What I mean is that the underlying concepts of kinematics, for example separating vectors into components with each component independent of the other, is a theme that recurs again and again. The relations between momentum, force, and impulse make more sense when students (again) see the definition of acceleration a = dv/dt. That's what I mean by spiraling back.

Are you open for other connections throughout the year, like we do with math? I know most physics courses do a bit of history when talking about gravitation and orbits. Would you make deeper connections with history class and physics than this? Would you have your students read Newton's Principia and analyze it from both an historical and physical perspective?
No, I don't have them read Principia, but I definitely make connections with history- I talk about the controversy regarding conservation of energy and momentum in connection with radioactive decay and the subsequent postulation and discovery of the neutrino, for example. I talked about Torricelli getting in trouble with the Catholic church with his barometer, and we just analyzed the differences between Galileo's telescope and Kepler's (greatly improved) telescope. Some students like the historical context, some don't.
 

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<snip> at least in the early development of optics around the time of Newton, the work in optics had very little effect on the changing world view.
I pretty much agree with everything you have written except this point. Galileo (again) created a major controversy when he observed that the moon is not a perfect sphere- it has craters and mountains- and that Jupiter has moons. Both of these contradicted teaching of the church.

I'm sure it's no accident that his middle finger is preserved and on display in the science museum in Florence.
 
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I pretty much agree with everything you have written except this point. Galileo (again) created a major controversy when he observed that the moon is not a perfect sphere- it has craters and mountains- and that Jupiter has moons. Both of these contradicted teaching of the church.
I agree with you the telescope played a role in helping shift the world view in that respect. I had my students read Sidereus Nuncius because of the impact it had. My comment was more about the theoretical development of optics playing little role in the shift in world view. The impact of theoretical mechanics on the 'revolution' of that time period is much more significant. I think you could cover only the history of mechanics and get students to understand the impact of the scientific revolution. It would be much more challenging to do this by covering the history of optics. This was mostly a response to the OPs comment about needing to choose what to cover based on time constraints. Of course, I think its best to cover both!
 
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Can you give me an example of what you interpret to be a conceptual question about acceleration
I would say an easy conceptual would be whether or not an object moving in a circle has a linear acceleration or not. Then, a mid level question would ask in what direction is that acceleration. I would do these questions early on in the year. Off the top of my head, i can't think of a high level question to do early on in the year. Maybe one that involves changes in acceleration, and a physical description of that kind of motion.

For quantitative questions, i would lean towards more graphing, or designing a method for measuring acceleration.

My question I guess is, what do your standards require the students to do? If conceptual understanding is the key you might consider reasearching the lecture demonstration model of physics education. Marietta College in Ohio isa big proponent of this method and it has shown to be effective in a lot of ways in my classroom.
Virginia state standards are very vague in what is asked of the students. I interpret it as being more of a survey course. Most teachers in my county just ignore the latter few standards and make it a mechanics heavy course. On the topic of mathematics role in physics education, clearly any physics class would be bereft in the absence of any quantitative and logical based reasoning. However, my first year of teaching felt as if i was just doing algebra and computation 50% of the time. While algebra is a useful tool, it is given way too much priority in high school.
 
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I would say an easy conceptual would be whether or not an object moving in a circle has a linear acceleration or not. Then, a mid level question would ask in what direction is that acceleration. I would do these questions early on in the year. Off the top of my head, i can't think of a high level question to do early on in the year. Maybe one that involves changes in acceleration, and a physical description of that kind of motion.
Fair enough. My question was a little vaguely worded. Since we were talking kinematics I was looking more for what you would consider to be a conceptual question about uniformly accelerated motion.

Virginia state standards are very vague in what is asked of the students. I interpret it as being more of a survey course. Most teachers in my county just ignore the latter few standards and make it a mechanics heavy course.
I expect most states are like that. Vermont's standards were equally vague. I haven't paid much attention to standards over the past several years, but I know that the Next Generation Science Standards are less focused on content mastery and more focused on scientific practice. Historically, I believe that up until the 1970s or 1980s physics education at the high school level rarely included anything besides mechanics.
 

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<snip>
For quantitative questions, i would lean towards more graphing, or designing a method for measuring acceleration.
<snip>
One of my Physics I test questions is for students to draw the (instantaneous) acceleration and velocity vectors for a car driving around an ellipse at constant speed- I provide an ellipse and indicate the points where they should draw the vectors. The results are, shall we say, discouraging.
 
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Fair enough. My question was a little vaguely worded. Since we were talking kinematics I was looking more for what you would consider to be a conceptual question about uniformly accelerated motion.
I think that is one of the issues. Some of my colleagues 'forget' that circular motion kinematics is still kinematics.

I expect most states are like that. Vermont's standards were equally vague. I haven't paid much attention to standards over the past several years, but I know that the Next Generation Science Standards are less focused on content mastery and more focused on scientific practice. Historically, I believe that up until the 1970s or 1980s physics education at the high school level rarely included anything besides mechanics.
I'll have to look more into that. I like the sound of that ^.^

One of my Physics I test questions is for students to draw the (instantaneous) acceleration and velocity vectors for a car driving around an ellipse at constant speed- I provide an ellipse and indicate the points where they should draw the vectors. The results are, shall we say, discouraging.
I'm going to have to steal this question!
 

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