Newton's Laws are cast in terms of forces, masses and accelerations. Such things don't appear on physics tests. What you get on physics tests are pulleys, ramps, blocks, rockets, skiers, race cars, trains, planes and automobiles. The secret art behind physics that is necessary for the tests is how to go from the race cars and blocks of real life to the forces, masses and accelerations of Newtonian theory. Once you've made that translation, the application of Newton's laws is straightforward and usually little more than routine. But in my experience, physics instruction stumbled just where it was needed most - a clear, methodical way to make the translation from real beings like blocks and pulleys to the physical abstractions. This isn't to say that such translations weren't extensively practiced; they were, but the practice was an end in itself. You either "got it" from extensive practice and examples of successful solutions, or you didn't. The critical skill involved in performing physics was just the one instructors couldn't say much about.
It wasn't until I read Kant that I understood why this was so. The relevant passage is in the Critique of Pure Reason, The Transcendental Analytic, Second Book, The Analytic Principles, Introduction - On the transcendental power of judgment in general.
If the understanding in general is explained as the faculty of rules, then the power of judgment is the faculty of subsuming under rules. i.e. of determining whether something stands under a given rule (casus datae legis) or not. General logic contains no precepts at all for the power of judgment, and moreover cannot contain them. For since it abstracts from all content of cognition, nothing remains to it but the business of analytically dividing the mere form of cognition into concepts, judgments and inferences, and thereby achieving formal rules for all use of the understanding. Now if it wanted to show generally how one ought to subsume under these rules, i.e., distinguish whether something stands under them or not, this could not happen except once again through a rule. But just because this is a rule, it would demand another instruction for the power of judgment, and it becomes clear that although the understanding is certainly capable of being instructed and equipped through rules, the power of judgment is a special talent that cannot be taught but only practiced. Thus this is also what is specific to so-called mother-wit, the lack of which cannot be made good by any school; for, although such a school can provide a limited understanding with plenty of rules borrowed from the insight of others and as it were graft these onto it, nevertheless the faculty of making use of them correctly must belong to the student himself, and in the absence of such a natural gift no rule that one might prescribe to him for this aim is safe from misuse. A physician therefore, a judge, or a statesmen, can have many fine pathological, juridical, or political rules in his head, of which he can even be a thorough teacher, and yet can easily stumble in their application, either because he is lacking in natural power of judgment (though not in understanding), and to be sure understand the universal in abstracto but cannot distinguish whether a case in concreto belongs under it, or also because he has not received adequate training for this judgement through examples and actual business.
The secret art I sensed behind physics is what Kant calls judgment; the faculty of subsuming the concrete particular under general rules. In the case of physics, the general rules are Newton's Three Laws, the concrete particular are the blocks and pulleys of any given problem. Kant explains why instructors can't do much more than provide examples in developing the faculty of judgment. Using an argument to infinity, he notes that were instructors able to formulate a rule to apply the rules, that would only push the difficulty back one step, because it would still require an act of judgment to apply the meta-rule.
Kant recognized the deep mystery behind modern empirical science. That science is so powerful and exact, Kant saw, because it is formulated in terms that the mind itself creates. Chet Raymo notes this in Ch. 1 of Skeptics and True Believers, but he doesn't follow through on its deep implications:
"No scientist will dispute that 'atom' is a made-up concept; however, the concept 'atom' is the most concise way - perhaps the only way - to make sense of our detailed, quantitative experience of the material world."
Raymo doesn't mention the linkage Kant saw in the Critique: "atom" is the most concise way to make sense of experience because it is a "made-up" concept. Kant further saw that because science conducts itself in terms of "made-up" concepts, there will always be an unfathomable mystery at the bottom of both science and the mind that conducts it. On the objective side, that mystery is captured in the distinction between the phenomenal (things as they appear to us through our scientific concepts) and the noumenal (things as they are in themselves.) We know reality through our "made-up" concept of "atom." This is the human mind's "take" on reality; it surely reflects something true about reality, but it is reality filtered through the concepts the mind makes up to make reality intelligible. We can be confident that the concept "atom" reflects something true about reality, and even that it is our best way of getting at that truth, but we have no way of accessing the "pre-filtered" reality (the noumena) prior to its interpretation through the concept "atom."
On the subjective side, the mystery is reflected in the act of judgment, which is the act of the mind subsuming particular reality under the general rules of science, including general scientific concepts. The act of judgment is prior to science itself, since science only works with its own concepts, and can have nothing to say about how the mind captures reality in the concepts that make science itself possible. Newtonian physics gets rolling with forces, masses and accelerations; these are the only things it "knows." How the mind subsumes reality under Newtonian concepts is a question Newtonian science, or any other science, can say nothing about. This is why physics instructors can provide practice in the act of judgment, but can do no more than that.
An immediate conclusion from Kant's Critique is that a "science of the mind" of the kind being hotly pursued today, is an exercise in futility. The mind that "makes-up" the concepts that make science itself possible will always be invisible to that science, since it is always prior to it. As soon as science starts, it has left behind the mind that made science possible. What the mind can know at this point is only the mind as it appears on the far side of its scientific concepts; in other words, the mind only insofar as the act of scientific judgment has already occurred.
This explains why contemporary scientists and philosophers of the mind seem so often to talk past each other. None of them have really understood Kant and taken him to heart. They all start their philo-scientific investigations the way Kant says they must start, with a pre-scientific rendering of reality under scientific concepts through an act of judgment. This rendering is the most crucial and decisive part of their investigation, but is generally the part least talked about and the most taken for granted. It usually happens in an introduction or a couple of paragraphs, followed by hundreds and hundreds of pages of conclusions from the mind science that results from that initial pre-scientific judgment. Since there is no guarantee that everyone's pre-scientific judgments will be the same, there is no guarantee that all the mind researchers will make the same acts of judgment, and so no guarantee that they will arrive at the same conclusions, or even that they will conduct science in a way that others researchers find legitimate. But there is no recognition that the reason the results are different isn't because the science is different, but because the pre-science is different, and no amount of scientific research can ever resolve the difference.
The acrimony results because every mind researcher senses that his rivals are "stealing a base", but he is at a loss as to say how. Everyone is right that everyone else is stealing a base, of course, because the base stolen is the pre-scientific act of judgment that makes science possible. We've lost the philosophical self-awareness of a great philosopher like Immanuel Kant, who recognized that his own subjective act of judgment is not absolute and is not binding on everyone else. The Critique is truly a philosophical work, because it invites the reader's mind to know itself through itself, relying on its own insight and acts of judgment, not taking Kant's judgments to be absolute. Instead, the mind researcher of today takes his own act of judgment to be absolute, although not self-consciously, and implicitly demands that everyone else submit to it. Of course, all the other researchers want to start their research with their own absolute acts of judgment, and the fight is on.
Daniel Dennett, inadvertently, provides a window into this phenomenon with his concept of "heterophenomenology", his take on how mind science should be conducted, as described in Consciousness Explained. Under heterophenomenology, the mind researcher interviews a subject and gets the subject's account and interpretation of his own experience. He claims to see trees and birds, to experience emotions, feel pain, and even - Dennett's ultimate target - to experience a sense of self. During the interview, the researcher withholds judgment concerning the truth of the subject's experience; although it may seem to the subject that he saw trees or birds, or seem to him that he has a self, this all may in fact be an illusion. This is something that will be decided in the course of the researcher's later scientific investigations of the mind, which will follow on the collection of a set of interviews and lab work.
With his interviews in hand, the researcher begins his investigations. How does he do it? By beginning with acts of pre-scientific judgment of the kind he denied to his interview subjects. He decides that the "mind" or the "self" is something shadowy and possibly unreal, and that the "brain" is a hard, metaphysical fact, the reality of which is unchallengeable. What about the birds and trees the subject claims to have seen? Those may or may not be real, pending the outcome of the investigation, but the investigator's own sense that he was a real interviewer interviewing a real subject is not subject to any doubt, in fact being a prerequisite to get the scientific investigation under way. What has happened is very simple: The investigator has simply assumed that his own act of judgment is absolute with respect to his subject's acts of judgment. This is what separates Dennett, and the general run of mind researchers, from Immanuel Kant, whom they are still way behind even if they think they are miles in front of him.