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

  1. Mar 31, 2016 #1
    So, my thread title was too long, here is the full title: Why should the kinematics equations be taught in a regular high school physics course?

    < Mentor Note -- thread title fixed (we can lengthen titles) >

    Let me explain my situation. I will teach physics in a different country next year as the only physics teacher in the school. 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. What i will do is define velocity and acceleration, and pretty much that is it. However, i am trying to convince my colleagues at the school i am at now to do the same. They do not seem to be as convinced as i am.

    What are your best reasons why the kinematics equations should be taught in a regular physics class in high school?
     
    Last edited by a moderator: Mar 31, 2016
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  3. Mar 31, 2016 #2

    Astronuc

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    Because one can. It's a rather basic subject that should be taught as early as possible. It's basic physics, like addition, subtraction and multiplication are basic mathematics. Kinematics is complementary with algebra.

    Why wait until high school. Physics should be taught as early as possible.

    These days there is so much to learn, and the earlier one starts the better.
     
  4. Apr 1, 2016 #3

    vela

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    From a conceptual standpoint, it might be better to do as you suggest and reduce the emphasis on kinematics and get to concepts like force and energy more quickly. What reasons do you have for urging your colleagues to not spend a lot of time on kinematics?
     
  5. Apr 2, 2016 #4

    symbolipoint

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    Kinematics is too fundamental a part of basic Physics, that Hlud MUST do as he says he wants. The high school Physics course would be absolutely poor without Kinematics.
     
  6. Apr 2, 2016 #5

    vela

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    Hlud is trying to convince his colleagues to not spend much time on kinematics.
     
  7. Apr 2, 2016 #6

    symbolipoint

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    Maybe that was what he meant. Let me adjust what I want to say:

    Kinematics is too fundamental a part of basic Physics,. The high school Physics course would be absolutely poor without Kinematics. How much time is given to Kinematics instruction is up to you and your department as long as the topic is covered fully enough for the best instruction at the high school level.
     
  8. Apr 2, 2016 #7

    Astronuc

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    From a pedagogical pespective, perhaps the question should be "what is the optimal approach for introducing students to classical mechanics?"

    I think the usual approach is to start with time and position/distance, then introduce velocity (v = dx/dt) and acceleration (a = dv/dt = d2x/dt2), which is kinematics. What is the proper context for teaching kinematics - when to consider mass/force, and when is it not necessary?

    Mass and momentum are then introduced, then force, and one can discuss statics and dynamics.
     
  9. Apr 2, 2016 #8

    vela

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    I agree. For a high school class, is it better to spend more time laying a good conceptual foundation while sacrificing some problem-solving aspects of physics, which they'll see in AP physics or in college anyway? Does the student get much out of knowing how to calculate how much time a ball spends in the air or how far away it lands, or would the time that's usually devoted to those aspects of intro physics be better spent on developing a better understanding of, say, modern physics?
     
  10. Apr 2, 2016 #9
    I think a worthy goal would be to ensure that every student knows how to differentiate between position, velocity and acceleration.

    Lillian McDermott has several articles on the issue of conceptual understanding.

    Investigation of student understanding of the concept of velocity in one dimension
    Investigation of student understanding of the concept of acceleration in one dimension

    A review from 1984, http://scitation.aip.org/content/aip/magazine/physicstoday/article/37/7/10.1063/1.2916318 [Broken]

    I was astonished when I learned about the fact that people mix up position and velocity. In retrospect it did explain some discussions I had over the years.
    I think that would be one motivation to treat kinematics with the caveat that the teacher should be very aware of this problem.

    A cool idea would be to incorporate questions like the one in this post to keep students motivated[1]. This isn't helpful for conceptual understanding though.

    [1] There are some things missing, like a measure for reaction speed. Then the student can argue about the (im)possibility of the answer.
     
    Last edited by a moderator: May 7, 2017
  11. Apr 3, 2016 #10
    I took high school physics in 1973 so the physics curricula may have changed but this is what I remember. We spent a lot of time understanding ballistic trajectories under constant gravity (these are not the term they used, of course). I know I (I suppose others) I say how velocity, position, acceleration related for freely falling bodies, and I (and presumably others) saw how the equations could be manipulated.
    Many other chapters in the book, stated (but did not develop or motivate the equations), and proposed homework problems that were plug and chug. I expect even today, most equations cannot be developed in a single high school course in physics for a broad audience, as completely as the ballistic equations. (How do you motivate Schrodinger's equation in high school. The best you can do in modern physics (e.g. the Bohr atom), is to present the equation). Severely reducing the ballistic equations in a course may lead one to believe, physics is not about method, but it is all plug and chug.
     
  12. Apr 4, 2016 #11

    Andy Resnick

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    Abstractly, kinematics should be taught in high school because kinematics is a foundational element of science.

    Concretely, you've left out some important information- what have your new students been prepared for already? What science and math classes have they already taken (or should have already taken)? Similarly, what are you preparing your students for- is this a senior-year college prep class? Is this a 9th grade 'physical science class'? Administratively, what are your state course content requirements?
     
  13. Apr 4, 2016 #12

    ProfuselyQuarky

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    Kinematics was covered in the first unit in my physics class--it was like the basis of everything! Physics shouldn't just be about definitions: “what is velocity?” or “what is acceleration?” That’s important, but, seriously, kinematics ties all of those things together into real applications. For one thing, learning basic kinematics helped me improve the skill of manipulating equations to find information needed. Additionally, how can you possibly go about teaching velocity and acceleration problems without kinematic equations? How to find initial and final velocities, height of projectiles, distance, range, speed, and acceleration of objects all have something to do with kinematics!
     
  14. Apr 4, 2016 #13

    SteamKing

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    It's a mistake IMO to just cover a few definitions in kinematics and then skip to some other topic in physics. Don't be surprised if your students are confused by the lack of a complete development of a topic. You don't have to make complex kinematic calculations to illustrate the topic, but you should show some work on the basics, otherwise physics just becomes another vocabulary-building course.
     
  15. Apr 4, 2016 #14
    I'll echo SteamKing here. I think depth is often desirable over breadth if you are aiming for understanding.
     
  16. Apr 4, 2016 #15

    Astronuc

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    Ostensibly, there is some exposure to science from earlier grades, and possibly some chemistry, and requisite math possibly up through Algebra II.

    I don't think anyone has suggested providing formulas and teaching students to 'plug and chug', but rather, it is helpful to understand the concepts/definitions of position/distance (in 1, 2 and 3 dimensions), time, and then velocity/speed, and acceleration, . . . and so on.

    Of course, one could use an approach like Feynman did with The Feynman Lectures on Physics, Volume I (mainly mechanics, radiation, and heat).
    http://www.feynmanlectures.caltech.edu/I_toc.html

    I'd be curious to know if Feynman's approach would inspire students, or turn them off.
     
  17. Apr 5, 2016 #16
    Yes, i agree that kinematics is too fundamental to ignore. I plan on teaching kinematics without ever teaching one of the four kinematics equations that we usually teach. I can teach kinematics in three or four blocks without doing the graphing or algebra. I am trying to convince my colleagues to do the same. They will argue that the equations are really important. I am just trying to see why you all think it is important to teach the algebra and graphing.
     
  18. Apr 5, 2016 #17
    I fail to see how this would be the case. My first year teaching, i adopted the course that the school (and pretty much the county) had taught for umpteen years. My students hated the course, because it was only plug and chug. You go from the kinematics equations, and plug and chug there. Then you move onto force, and plug and chug there. Then momentum, and energy, and so on and so forth. Sure, there was a method: the method leading you to be able to plug and chug.
     
  19. Apr 5, 2016 #18
    Sorry, i did leave off information. This is a regular physics course that i am talking about. My AP courses will continue to do the kinematics equations. My regular kids are either in algebra or precalculus for the most part. Regardless, their algebra skills are lacking (so we take a lot of time not doing physics, but just manipulating equations). While they will all have taken chemistry and biology, they do not have sufficient lab skills either (because those are not explicitly written in the standards in my state).

    This is the first year i personally sacrificed more time just doing the 'method' in favor of definitions and concepts. Personally, because of the improvements i see with my students, i am convinced on sacrificing more time doing the 'method'.

    I might add the purpose for doing as i am suggesting. When you spend so much time doing the method (which no teacher believes to be just plug and chug, but it really is not more than just isolation of a single variable), as we do in my school, then you cannot branch into much other than mechanics. Traditionally, we spend 3 quarters teaching mechanics (kinematics, forces, momentum, and energy, with no rotation or waves), and that last quarter teaching electrostatics and circuits. If i were to be honest with myself, we are spending about 3 quarters teaching isolation of a variable in equations that look different, and 1/2 quarter teaching graphing, and the last 1/2 teaching the concepts associated with those equations. If they were to reduce their teaching of algebra in equations that look different, they will be able to discuss briefly (which is fine in a regular physics course) topics such as optics.
     
    Last edited: Apr 5, 2016
  20. Apr 5, 2016 #19

    Andy Resnick

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    Thanks, that was very helpful. For what it's worth, my colleagues and I struggle with exactly the same issues you do- the students lag in math facility, so we often face the choice of spending class time teaching math instead of teaching physics. Some of us have rebelled: it goes by a lot of names, the current label is 'flipped classroom'. I now require students to learn whatever math they need- I'm talking about prerequisite-type stuff- on their own.

    One idea for you to consider: work with the math teacher(s) to better synchronize the content. For example, we created a 'problem-based learning' module for precalc students that treats kinematics as an application of quadratic functions- the module is based on a double-play in baseball. Similarly, we created a module presenting sound and music as an application of trigonometry. There are tons of pre-developed modules out there:

    http://bie.org/project_search/resul...category=330&&338&ps_first=330&ps_second=338/
    http://archive.pbl-online.org/

    One of the (unsurprising) results we have learned is that the more time students spend engaged with the material: not homework, but groupwork outside of class, peer teaching outside of class, etc. etc., the more material they learn. Sounds simple, but very difficult to implement.
     
  21. Apr 5, 2016 #20

    Andy Resnick

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    In my experience with the intro courses (non-physics majors), that approach turns most students off. For whatever reason, in the context of a intro physics class, most students equate successful plug-n-chug with learning.
     
  22. Apr 5, 2016 #21

    vela

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    Paul Hewitt (the conceptual physics guy) recommends downplaying kinematics exactly for this reason, saying it's 10% physics and 90% math. The time spent on kinematics is time not spent on other concepts.
     
    Last edited: Apr 5, 2016
  23. Apr 5, 2016 #22

    SteamKing

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    The quote below came from the OP in Post #18, not me:
    As far as what Hewitt is complaining about, everything in physics is a time suck. The time spent discussing topic A is time which can't be used to discuss topic B. That's still an insufficient reason to neglect topic A in favor of topic B.

    From looking at the problems submitted to the Intro Physics HW forum on this website, it is apparent that some students have trouble with basic kinematics. I think for that reason the topic should be taught as completely as time permits.
     
  24. Apr 5, 2016 #23

    Andy Resnick

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    I agree, but would go further- kinematics (and any other foundational concept) should not only be taught once, "as time permits". It should be discussed again and again- Arons's phrase is 'spiral back'.

    https://www.amazon.com/Teaching-Introductory-Physics-Arnold-Arons/dp/0471137073

    Another example he uses is linear graphs: a foundational concept that is used again and again, not just in x = vt and F = ma but also for many other seemingly unconnected relationships that occur in intro physics. This gives students multiple interactions with the material and over time (one hopes) the student gains mastery.

    Even better if the student can draw content links between different classes: math and physics is perhaps the easiest to consider, but regardless, the more exposure a student has to the material the better they will understand it.

    This is true for learning anything, really- we rarely understand something upon first exposure. One good aspect about Common Core is that it brings some overall coherence and narrative to the K-12 curriculum.
     
    Last edited by a moderator: May 7, 2017
  25. Apr 7, 2016 #24
    In the week before i first started teaching, we discussed Hewitt's book and ultimately decided not to use it because it did not "have enough math." I'll definitely look over his book and his philosophy again, especially since i have been teaching, i have come to realize that math is not synonymous with computation, as most of my early physics courses have led me to believe. Perhaps my colleagues will be more sympathetic to this approach. Their biggest concern is that we would be abandoning what is tried and true (the true part being debatable).

    But that is not his argument. He is arguing that learning how to isolate a variable is not doing enough physics, and hence not worth doing in physics (at least for the time we do in regular, high school physics).

    After reading Paul Lockhart's A Mathematician's Lament, i completely disagree that they are having trouble with basic kinematics. What they are doing is rather advanced kinematics, just taught earlier than it should be for these students. Yes, we pretty much teach 'basic kinematics' first universally. However, we also live in a society where its perfectly acceptable to have zero proficiency in math. Clearly there is a disconnect.

    What makes the kinematics equations more fundamental than basic optics? Or how sound works? Or why a simple machine works? If anything, because of the specific condition in which these equations apply, it is not fundamental at all.

    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. I hate the front-loaded nature of how i teach physics. My colleagues seem to be okay with it.

    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.

    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?
     
  26. Apr 7, 2016 #25
    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). Or, try flipping it around and asking about slamming on the breaks. I would be surprised if students that struggle with the mathematics of kinematics could answer this correctly. I would say that if someone can't answer this question that they don't really understand what acceleration is or what the characteristics of motion with constant acceleration are.

    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. Kinematics is the most fundamental aspect of understanding motion and mechanics which is usually the next topic. Historically, kinematics was the first aspect of terrestrial motion that was well understood (see the work of Nicole Oresme, and Thomas Bradwardine).

    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. They see excerpts of the (translations of) original treatises like those of Archimedes, Huygens, and Newton. We translate the meanings into more modern language.

    Only parts: definitions, axioms (laws), and his rules of reasoning in natural philosophy. If you've read parts of the Principia before you'd know that doing more than this is not a good idea for probably anyone that isn't absolutely gung-ho about the history of mechanics. I am, and I haven't yet made it through more than about 70 pages.
     
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