Kinematics in High School Physics: Reasons to Teach Equations

[boonebr]

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]

<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.

 

[Andy Resnick]

<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.

 

[brainpushups]

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!

 

[Hlud]

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.

 

[brainpushups]

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.

 

[Andy Resnick]

<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.

 

[Hlud]

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!

 

[Andy Resnick]

I'm going to have to steal this question!

Feel free to- I stole it from Arons :)

 

[math737]

I symphatize with your students. I hated learning the kinematics, even as a math lover. I think its not the concept or plug and jug but instead the way kinematics is taught in school. I say teach it, because the capabilities that it has given humanity is vast. So teach it in a conceptual way rather than a bury your face in the numbers way. Think about it, we can make accurate predictions of location, time, velocity and acceleration, give them examples of industries this has made a difference in. Teach them that physics is meant to be a practical tool in your tool kit rather than just homework you get stuck on. Teach them that real world problems can very much be designed the same way. Like try to have a contest among your students to come up with thorough explanation for how to get a ball through a hoop from a x distance you dictate. Rather than shuffing it down their throats let them mingle, examine, reason, analyze, and come to their own conclusions about the application and limits of kinematics. good luck.