Uncover a little or cover a lot?

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The discussion centers on the effectiveness of different teaching methods in physics and mathematics. One approach involves covering a broad range of material, allowing students to learn some concepts independently, while the other focuses on a slower, more in-depth exploration of fewer topics to ensure comprehension of key concepts. The preference leans towards the latter method, especially for introductory courses, as it emphasizes understanding over mere exposure. However, there is a recognition that achieving the right balance between too much and too little content is subjective and challenging. The effectiveness of the broad coverage approach is often hindered by teachers' inability to facilitate understanding, leading to students struggling to connect disparate ideas, ultimately resulting in a lack of comprehension.
jbrussell93
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I am an undergraduate physics major just finishing up my sophomore year. During this semester, I've gotten to see both ends of the spectrum of teaching methods. Which do you think is more efficient in teaching physics/mathematics? Cover a lot of material forcing students to learn some things on their own or taking your time going through material in order to really drive home main concepts but in the end cover less material. I think that if I were a teacher, I would take the "uncover a little" route, but I guess it really depends on if the class is a first exposure or advanced level.
 
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Like all things in life:

Don't cover too much, as it is by definition, too much.

Don't cover too little, as it is by definition, too little.

Now, judging what is too much and what is too little is subtle and subjective and IMO trying to perfect it is a waste of energy.
 
As a teacher, I would cover a lot as opposed to covering little but more in depth. My reasons for this is that understanding requires connecting similar ideas together so the more ideas are in play, the more can be connected. However, it's rare that teachers know how to teach understanding so this method does not work very well. Teachers who teach this way usually end up with a lot of disparate ideas and leave it up to the students to understand it, which requires effort on their part, which pretty much means they won't put in the effort, so the end result is that they don't understand it.
 
Sequences and series are related concepts, but they differ extremely from one another. I believe that students in integral calculus often confuse them. Part of the problem is that: Sequences are usually taught only briefly before moving on to series. The definition of a series involves two related sequences (terms and partial sums). Both have operations that take in a sequence and output a number (the limit or the sum). Both have convergence tests for convergence (monotone convergence and...
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