Page History

Understanding vs. Memorizing

Imagine that you had to solve a novel physics problem today, either in real life or on a test, and that you had a physics text that contained the relevant physics as well as a selection of solved problems. Even if you had a search engine to aid your retrieval of this material, would you feel confident that you could solve your problem?

...

Please take a moment to reflect on what you have been trained to do when you study physics or review your physics homework. Very likely it is to memorize the formulae in the textbook and the solutions to the problems you’ve done. But the above example should show you that this is not sufficient – somehow you need to understand the material as well. Understanding involves being able to visualize the problem and to see the deep regularities (e.g. conservation of energy) that underlie the solution to many of these example problems. Paradoxically, if your understanding is at this level, you only need to remember the typical schema (plan of attack) involving each concept in order to be able to solve many problems – you don’t need to know the detailed solution of many different example problems involving that concept.

Constructing Understanding

Education experts agree that understanding must be constructed in your mind by your own thought processes. Passive memorization is not enough – rather you must place new knowledge within the context of what you already know and understand. For example, you probably understand intuitively that if your opponent in a snowball (or water balloon) fight is crouching behind a low fence, then you must lob your projectile slowly so that it descends at a steep angle, allowing it to pass over the fence and land on the target. Obviously this intuitive understanding should be transferred to the artillery problem discussed above.

The quick iimportant lesson here is that Newtonian Mechanics is about the everyday motion of things around you, the energy crisis, and the additional distance it takes to stop your car when the road is wet going downhill vs. uphill – all subjects about which you have some intuitive/experiential knowledge already. You must insist to yourself that as you learn learning Newtonian mechanics , requires you will to connect it with your intuition. If you don’t, you ignore a rich source of existing understanding and greatly reduces reduce your ability to usefully apply your new learning to new problems.

An example of this struggle for intuitive connection of Newtonian mechanics and real world experience is evident from this poetic summary of Newton’s First Law from the middle school student's perspectiveperspective of a student studying physics for the first time:

Objects in motion remain in motion in the classroom and come to rest on the playground.

If she thinks about this until she realizes that the difference is that the air track in class has been designed to reduce friction to insignificance but that there is considerably more friction even on a rolling ball on the playground, then her physics class can enrich her view of the everyday world, and vice versa. On the other hand, if her mental model is that what happens in the classroom is according to one set of rules while the real world operates according to another, then Newtonian mechanics will be a foreign set of concepts and equations that describe only the teacher’s reality and which will soon be forgotten.

Constructing Your Understanding

In order to construct your own knowledge, you must think about what you are reading in the text or hearing in lecture, and you must learn to step back from a problem both while beginning to solve it and also after you have finished.

Text and Lecture: How does the material at hand fit into your overall mental outline of the course? What formulae are simply special cases of others? For example, a = F/m is the same relationship as F=ma. Similarly, both are special cases of F=dp/dt, the fundamental law of change for momentum (as this text will emphasize in teaching you the Momentum Model.)

ProblemsProblem Solving: When approaching a problem the most important thing is to change your objective from “Find the Answer” to Plan the Solution. That is, concentrate on the process of solving it – what principles did you apply and why? Very valuable is a retrospective look at : ask yourself what one or two sentences of advice would have enabled you to solve the problem more quickly – this is what you really learned by doing the problem.