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Is there any research supporting the idea that a single professor should teach the entire calculus sequence as opposed to splitting the duty amongst multiple professors? What are the pros and cons of having the same professor teach all the calculus classes?

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    $\begingroup$ I have no idea about research, but, I can attest that the students I taught back-to-back calculus I, II and III formed the deepest and most worthwhile calculus I have ever taught. In the usual situation I don't get them more than a semester and I'm always implicitly adjusting for the unknown variable of what they have covered elsewhere... $\endgroup$ – James S. Cook Nov 21 '14 at 5:45
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    $\begingroup$ Even if there were research showing this, wouldn't it be applicable only to the smallest schools? At any decent-sized schools, you have many sections of calculus, and students are just taking a section that fits their schedule. $\endgroup$ – Ben Crowell Nov 21 '14 at 14:50
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    $\begingroup$ I don't have the time to pursue this deeper at the moment, but I might check some of the literature about non-Western countries, where this is sometimes the norm, especially at the high school level (where Calculus may be covered). Relatedly: Would you be opposed to an answer about material that isn't explicitly on professors/Calculus? E.g., the same secondary school teacher for Algebra I and Algebra II. $\endgroup$ – Benjamin Dickman Nov 21 '14 at 22:37
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    $\begingroup$ This practice appears to be called looping (see, for instance, youaretheproblem.com/10-pros-cons-looping-education and files.eric.ed.gov/fulltext/ED490548.pdf). $\endgroup$ – J W Dec 24 '14 at 18:23
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    $\begingroup$ @BenCrowell No, in Germany all universities I know only have a single calculus course, sometimes with several hundreds of students. Moreover, usually it is just one professor teaching the entire sequence. $\endgroup$ – Dirk Feb 5 '15 at 16:13
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Let me start with mentioning this now well-known experiment: Improved Learning in a Large-Enrollment Physics Class. I highlight part of which that is related to your question.

During week 12, we studied two sections whose instructors agreed to participate. For the 11 weeks preceding the study, both sections were taught in a similar manner by two instructors (A and B), both with above average student teaching evaluations and many years experience teaching this course and many others.

More or less, both lecturers used the same way to teach. And a variety of different data showed that both groups of students were similar in many different aspects (including learning) at the end of week 11. What happened at week 12?

The control section was taught by instructor A as before. But the experiment section was taught by two instructors with a very limited teaching experience using a more active teaching method as designed. What happened? The abstract tells it all:

We compared the amounts of learning achieved using two different instructional approaches
under controlled conditions. We measured the learning of a specific set of topics and
objectives when taught by 3 hours of traditional lecture given by an experienced highly rated
instructor and 3 hours of instruction given by a trained but inexperienced instructor using
instruction based on research in cognitive psychology and physics education. The comparison
was made between two large sections (N = 267 and N = 271) of an introductory undergraduate
physics course. We found increased student attendance, higher engagement, and more than
twice the learning in the section taught using research-based instruction.

But, How all these is related to your question. Let us do a thought experiment. Suppose we want to design a research to compare what you are interested in. These are the variables that we should take the same: the materials covered and the order in which they are covered, the instructional methods used, the values (instructors' views of mathematics) and so on. Having kept all these the same, what remains to compare? Basically, nothing but some social aspects.

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  • $\begingroup$ I understand the post, but I don't think it really answers the question. Here is a thought experiment: Suppose you are in charge of a high school and are deciding whether teachers should stay with one cohort of students throughout a sequence of math courses or whether they should stay with the same courses and have the students change through each year. Which do you advocate for and why? (Actual question: Is there any literature that addresses such a question?) $\endgroup$ – Benjamin Dickman Feb 15 '15 at 2:56
  • $\begingroup$ @BenjaminDickman I got the question and indeed I answered that by predicting how such a research might look like. As a result, as the headteacher of your thought experiment, I am not wasting my time to search for an answer in literature, rather I would decide based on the human resources at hand. Indeed, as a school teacher and later on, as a university lecturer, I experienced both sides of your scenarios, and now that I am the headteacher of your thought experience, I know what I am doing :) $\endgroup$ – Amir Asghari Feb 15 '15 at 8:44
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It is often recommended to attend a different university for graduate work than the institution where one did the Bachelor's degree. Why? To get a different perspective.

Extrapolating from that, I would expect variety to be helpful in the calculus sequence too.

Here's another point. Consider that different strokes work for different folks, but that not all math teachers know how to teach to a variety of learning styles. A student would therefore do well to hedge his bets and try someone different each semester (unless he finds someone he's remarkably well matched with, and decides to take whatever that instructor has to offer in a particular semester).

Finally, note that math is a bit like a foreign language. Those learning a language will do best in the long run if they are exposed to a variety of speaking styles. This would make sense in the math context as well.

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