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As there are different students with different educational and economical backgrounds in the classroom, I would like to know how a professor can deal with those differences. For example, undermotivated students or those whose knowledge is very weak on the mathematical courses - what is the best teaching style for such cases?

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    Maybe a better fit for the mathematics educators stack? Commented Jul 11, 2021 at 7:31
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    @astronat I think this OK here because it can be easily generalized to several examples of weaknesses (in fact, in the OP, there is "For example"). Commented Jul 11, 2021 at 8:19
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    @astronat Actually, it sounds like this isn't teaching math, but teaching some subject that uses math where some students aren't very strong on the math prereqs. Commented Jul 12, 2021 at 13:59

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Every teacher, course, group and situation is different but these are things that worked for me (Europe, teaching unmotivated and diverse group of undergrads):

  1. Keep external teaching material (books, software) to a minimum
  2. Give regular feedback on progress (I usually start every class with a short, very basic quiz about the lass classes (self-corrected by students and with correct answers immediately discussed with class). I tell students that below a certain % of correct answers they need to learn/practice material from previous classes/courses because their background knowledge is a bit lacking.
  3. Provide extra exercises to teach/reinforce the basics (with detailed solutions) for optional individual work.
  4. Encourage or enforce group work where students teach each other. (I taught a class where the final assignment was a group work with the worst student's score defining each group member's final score. It was a huge success but it required a lot of work and constant monitoring of group dynamics.)
  5. Praise any good answer and/or students attempting to answer. Encourage students making mistakes (it gives feedback to both of you and allows to correct misunderstandings before the exam).
  6. Make sure the exercises are relevant both for the subject matter and the students (e.g., if the majority of your students are biologists, give them examples with trees and not light bulbs)
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    I agree with most of the points. But #4 is a disaster. You are shifting responsibility of teaching and the associated risks (if they fail) to the good students. In some groups the strong members will be tempted to do the job of the rest of the group to get good marks - maybe your monitoring prevents that, but in general, this is bad and outright unfair advice. Why should strong students pay with their marks if they happen to be co-grouped with a weak or lazy student, unless they work multiple times as hard (either doing everything themselves, or spending much of their time tutoring)? Commented Jul 11, 2021 at 8:48
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    Ok, if you can choose your group members, that's better. But if people put more work into group tasks than in individual tasks, either you are very good at motivating group work, or you were lucky. I have never seen anything other than split into the doers and the fellow-travelers or capable students being dragged down. The only working group work I have seen is the one one does not want: collusion. Commented Jul 11, 2021 at 9:08
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    Having been a student once and multiple times in above situations, I detested obligatory assessed group work with a vengeance. I have less-than-ideal cases even for the "best" cases where I worked with an equally strong student. In certain topics groupwork is unavoidable as per design (as software engineering or larger programming tasks); I have done that successfully as teacher, but the situation described by OP is precisely the one where I would avoid groupwork. I am impressed that you made it work. As student I would have considered being assessed by the worst score as inexcusable. Commented Jul 11, 2021 at 14:49
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    @CaptainEmacs My group assignments allowed the group to "fire" a group member. The recommendation of the others had to be unanimous. The fired member then had to complete and be graded on the assignment individually. No group member ever got fired in any of my classes.
    – Bob Brown
    Commented Jul 11, 2021 at 15:33
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    @Buffy The question mentioned economical differences, so I thought some students may have difficulty buying expensive textbooks/course materials. Sorry if I was unclear. Also, creating own teaching materials means it can be tailored better to the group's needs.
    – Aolon
    Commented Jul 11, 2021 at 19:58
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What works for me:

Create a set of exercises that cover a wide range of skills, from elementary/introductory ones to challenging ones (some of which may require literature or even own research). The students not only get an entry point into what you wish to teach, but they also can see where it leads, and the strong/experienced ones are not bored.

What's important for students is to learn the methods of thinking, and I usually spend quite some time introducing very thoroughly the method of thinking of the field. Interestingly, even stronger students seem to appreciate that, because they usually are fast in picking up material, but often not very experienced in seeing all the underlying structure. Repetition under different perspectives helps the students to pick up the methods and beginning to see how it works rather than learning by rote.

Focus on fewer, important concepts, treated deeply, rather than a litany of shallow introduction to many different ideas. The students need to learn "how to learn" and "how to approach" a topic, rather than having seen too many different things. The latter, they can do for themselves once they have the tools.

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This isn't a complete solution, but only something to think about, depending on how free you are in course design. I think it complements the answer of Captain Emacs to some extent.

I once taught a database (CS) course to a group of very able students at a top university. Almost all were very good, but not all had the same background preparation. There were several projects in the course and (IIRC) they were group/pair based. The course leaned heavily to DB principles and the underlying theory and implementation, not just use of SQL.

One assignment was about search. I made two versions of the same assignment, one easy and one quite difficult. Students could choose to do either one and the grading would be the same, no matter which they chose, based on quality of implementation.

The easy one was to implement a binary search tree and the hard one was to build a b-tree. These are about an order of magnitude different in difficulty (rough estimate). When introducing the assignment I said that if a student had never implemented a binary search tree then I would recommend they choose that one, but if they had done so, that doing it again would bore them silly, and I'd recommend the hard one.

I had a (to me) surprising number of students choose the harder assignment and I judged the experiment successful.

Of course this implies that you are willing to give the same grade for things of different difficulty, but every student learned something of value if they were successful in their implementation and also honest (to themselves) in choosing which to do. This won't work when students are too much grade driven, or otherwise too panicked about grades, but you might consider whether it would work in your environment.

Think about learning more than about grading.

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This is a separate idea from my other answer here, and I warn that I haven't tried it in this form, but would consider doing so in the circumstance you describe. But note that I also had great freedom in course design and was always able to justify "odd" pedagogical choices to my department head and dean.

One of my tricks in teaching was to use cumulative grading where students get grades by accumulating points from projects and exams. For me, exams were a relatively small part of the total, but every student knew exactly what grade they earn by adding up the points. So, some students already had nearly enough points accumulated that the final exam was essential irrelevant, so I would excuse them from it, letting them focus on other courses. This idea grows out of that practice.

Suppose you make a deal with your students that they can either take the final exam or, starting after mid term, take on a substantial project requiring some deep learning. Emphasize that the project will be difficult and that the grade for it will substitute for the final exam grade, which they need not take.

In mathematics, a "project" might be the analysis of some paper or the application of course ideas to some specific problem.

I have no evidence, but suspect that the high achievers will be drawn toward the project if you can make it interesting enough. This might also be an opportunity to introduce group or pair work if you don't do that otherwise. You will need some communication channel for these students separate from the entire class since, for the right project, there might be a lot of questions. But the "really good" students probably value a challenge. I hope I'm not too naive about this, but it was my own experience both as a student and later as a professor.

I caution that this might not work above a certain scale. I seldom had to teach as many as 40 students in a class and usually a bit under 30.

If the better students spend a lot of effort on this, then you can focus more on the students who need more help and guidance.

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