DiSessa (1980) outlines the conventional way of how students learn the Newton’s law of motion and questions whether teaching novices this way is pedagogically justified.
[Quotation]
There is a rather striking asymmetry in Newton’s Laws. The first two laws have an incredibly rich and varied network of techniques, equations, important special cases, heuristic advice, etc., relating to them. The spine of the network consists in
(1) selecting the physical system(s) of interest,
(2) identifying all forces acting on it (them),
(3) using F=ma to solve.
Branching away, one could organize a great deal of what is taught in elementary mechanics by how it contributes to this general form of analysis. Free-body diagrams contribute prominently on the left-hand side of the equation. The art of selecting a system is a subproblem of free-body analysis. Kinematics provides standardized special cases like uniform acceleration and uniform circular motion as grist for the F=ma machine on the right-hand side. One should not forget such trivialities as vector decomposition and advice about how to carry out such decomposition effectively. (Can any freshman physicist look at an object moving on a flat surface without decomposing an applied force into normal and tangential components?) The list can easily be extended by thinking about special devices used in the varied domains, such as statics, rope and pulley problems, trajectories, etc., in which one conventionally learns to implant F=ma.
On the other hand, contrast the relative sparsity surrounding Newton’s Third Law, action and equal and opposite reaction. Beyond the image of a man jumping off a boat, how much more is there? Even in the form of conservation of momentum (a form which surprisingly few students recognize as identical to action-reaction) most students will think the principle as a constraint equation which will help in collision situations, but little more.
This broad asymmetry is not so much in the laws themselves but in the way that they are conventionally taught and thought about. In particular this paper aims at showing how the action-reaction notion can be enriched to come much closer to parity with F=ma as insightful way of looking at many phenomena of mechanics.
Actually, I will use a reformulation of action-reaction which emphasizes the fundamental conservation law embedded in it: Force is simply the flow of the conserved “stuff,” momentum, from one place to another. Technically speaking, force is the rate with which momentum flows.
A useful context for this paper can be set by suggesting in a little more detail what does and does not account for the fact that momentum flow is almost entirely outside the bounds of “normal physics teaching” represented in current texts. As a frame for analysis elementary mechanics, momentum flow is clearly Newtonian at its formal core. It is in that sense by no means “new physics.” The issue is more one of style than content. Moreover, the uniform dominance of one style over another is not usually so much a question of efficiency, but more one of culture. Thus, we are led to frame the issue in much the same way in which Thomas Kuhn (1970) explained certain discontinuities in the history of science: what is learned by succeeding generations of scientists is to a great extent culture, carried as much in the selection of problems posed and patterns implicit in paradigm solutions as it is carried in the explicit theory. In that light this paper begins to ask whether or not the culture of physics as experienced by novices is pedagogically justified.
[Quotation Ends]
This introduction paragraph gives a very good example of Kuhn’s idea about how science can be viewed as a culture. It also helps me have a better sense about this.
I think this paragraph also demonstrate a way of presenting philosophy of science by starting from a solid ‘scientific stuff.’
I will category this article into “momentum approach.”
Reference
diSessa, A. A. (1980). Momentum flow as alternative perspective in elementary mechanics. American Journal of Physics, 48(5), 365-369.
Kuhn, T. S. (1970). The structure of scientific revolution. Chicago, IL: University of Chicago.
[Quotation]
There is a rather striking asymmetry in Newton’s Laws. The first two laws have an incredibly rich and varied network of techniques, equations, important special cases, heuristic advice, etc., relating to them. The spine of the network consists in
(1) selecting the physical system(s) of interest,
(2) identifying all forces acting on it (them),
(3) using F=ma to solve.
Branching away, one could organize a great deal of what is taught in elementary mechanics by how it contributes to this general form of analysis. Free-body diagrams contribute prominently on the left-hand side of the equation. The art of selecting a system is a subproblem of free-body analysis. Kinematics provides standardized special cases like uniform acceleration and uniform circular motion as grist for the F=ma machine on the right-hand side. One should not forget such trivialities as vector decomposition and advice about how to carry out such decomposition effectively. (Can any freshman physicist look at an object moving on a flat surface without decomposing an applied force into normal and tangential components?) The list can easily be extended by thinking about special devices used in the varied domains, such as statics, rope and pulley problems, trajectories, etc., in which one conventionally learns to implant F=ma.
On the other hand, contrast the relative sparsity surrounding Newton’s Third Law, action and equal and opposite reaction. Beyond the image of a man jumping off a boat, how much more is there? Even in the form of conservation of momentum (a form which surprisingly few students recognize as identical to action-reaction) most students will think the principle as a constraint equation which will help in collision situations, but little more.
This broad asymmetry is not so much in the laws themselves but in the way that they are conventionally taught and thought about. In particular this paper aims at showing how the action-reaction notion can be enriched to come much closer to parity with F=ma as insightful way of looking at many phenomena of mechanics.
Actually, I will use a reformulation of action-reaction which emphasizes the fundamental conservation law embedded in it: Force is simply the flow of the conserved “stuff,” momentum, from one place to another. Technically speaking, force is the rate with which momentum flows.
A useful context for this paper can be set by suggesting in a little more detail what does and does not account for the fact that momentum flow is almost entirely outside the bounds of “normal physics teaching” represented in current texts. As a frame for analysis elementary mechanics, momentum flow is clearly Newtonian at its formal core. It is in that sense by no means “new physics.” The issue is more one of style than content. Moreover, the uniform dominance of one style over another is not usually so much a question of efficiency, but more one of culture. Thus, we are led to frame the issue in much the same way in which Thomas Kuhn (1970) explained certain discontinuities in the history of science: what is learned by succeeding generations of scientists is to a great extent culture, carried as much in the selection of problems posed and patterns implicit in paradigm solutions as it is carried in the explicit theory. In that light this paper begins to ask whether or not the culture of physics as experienced by novices is pedagogically justified.
[Quotation Ends]
This introduction paragraph gives a very good example of Kuhn’s idea about how science can be viewed as a culture. It also helps me have a better sense about this.
I think this paragraph also demonstrate a way of presenting philosophy of science by starting from a solid ‘scientific stuff.’
I will category this article into “momentum approach.”
Reference
diSessa, A. A. (1980). Momentum flow as alternative perspective in elementary mechanics. American Journal of Physics, 48(5), 365-369.
Kuhn, T. S. (1970). The structure of scientific revolution. Chicago, IL: University of Chicago.
Comments