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I'm planning a course on advanced calculus. Some of my topics align quite well with entire chapters of the textbook, so it makes sense for me to teach the entire topic, link it to a textbook chapter and additional resources, and assign homework from the end of the chapter. However, some of my topics take material from several chapters of the textbook and other resources, either because it's a very quick review or because the textbook presents things in a way I don't like.

What is happening is that some topics are getting a disproportionate amount of suggested practice, given how much time we spend on them in lecture. For example, I'm dedicating only one 50-minute lecture to the four topics of vectors, lines, planes, and distance, since they've already seen this stuff 3 times. However, that's 5 textbook chapters, and it's looking to be about 40 suggested practice problems. On the other hand, I'm dedicating the exact same amount of time to a single topic, parametric equations in space, and they will only get about 20 suggested practice problems. For the course itself, parametric equations are a more important topic and should be practiced a lot more. However, I don't want to assign just one question per topic for the review stuff, since practice and review is important.

Is there a nice way to communicate to students that a particular topic is more important for their understanding of the course, but that another topic should be reviewed until they are comfortable so that the important topics are simpler?

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A few options are open to you here.

  1. Simply highlight a proportion of the questions. So out of the 40 you have for vectors, lines, planes and distance just highlight or set half of them for homework. Pick and choose problems that give a good overview of the entire section so that they get a taste of different types of problems. Of course if students feel the need then there are plenty more questions in these sections that they may attempt in the text book which is no harm.

  2. Make up new parametric equation questions. Have a look at the questions that are there. Are there any styles of questions that are left out? If so create some based on that style. If there are not simply modify the questions that are there already. Try to come up with corner cases to test their understanding (or at least show them there is a bit more to the topic). Cases that display certain tricks or potentially weird (from your students point of view) answers. You will have to make the judgement call as to what is missing to the current set of questions yourself.

  3. A combination of the above. Highlight a selection of the vector questions while adding in a few parametric equation questions.

Finally in addition to the above you can explicitly mention that these topics are more important for the course. While a bit of a blunt force object if they are expecting trickier/more parametric equations they will spend more time studying it. You can also explicitly state that studying the other topics will help them with the parametric stuff.

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If you feel all 40 exercises are necessary, then just spread them out, sprinkling a few into each of the next few assignments.

Another approach would be to give the students a self-evaluation at the beginning, with a subset of the 40 exercises. For any students having difficulty with these, assign the rest of the 40 (but perhaps spread out over a week so they're not all in a lump).

There is really no reason education has to be one-size-fits-all. You can build some differentiation into your course.

If this material is review, then it is important to detect any deficiencies early on, and then help the individual students with deficiencies remedy them, so they will do well in the rest of the course.

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