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I am a new calculus teacher in a high school for gifted students. I am the youngest teacher, I am not in my home country, and this country particularly values age and experience, so I have little room to discuss syllabi and homework assignments.

The level of maths is quite high (senior students deal with vector calculus and Stokes' theorem) and the class requires a large amount of weekly homework (to give an idea: about 15 exercises for each section in Stewart's Calculus, about 3 sections a week). Deadlines for these homework assignments are very strict (new assignment every week, none accepted after the deadline).

I know that practice is important, especially in calculus, but this leads to unintended outcomes:

  1. Grading takes a lot of time, so many teachers don't grade seriously (little feedback; just checking that students did the homework) and instead distribute a solutions printout from the textbook to the students.

  2. Students don't spend a lot of time thinking about or engaged with the problems; they just rephrase the solutions. Good students will try to understand the solutions, but other will not really care.

  3. Even if I don't give them the solutions printout, then they will find the answers online.

  4. Many students don't enjoy calculus and few of them would take an optional class related to calculus (say analysis or differential geometry). Freshmen are really afraid of their future calculus class.

  5. I have seen this with a couple of students: they believe that they will be successful if they copy the solutions for all homework problems (including non-assigned ones) from the textbook (at least 60 per section!). This has led to very poor results.

What can I do? I like teaching in the school, but the general philosophy of education in this country is:

If a student has unsatisfying grades, give him more homework and extra classes.

So far, I have just decided to relax the deadlines, and not to care too much about late homework, but the outcome is still not satisfying. I am also not comfortable with having different rules for homework than other classes.

My questions:

  1. Is there an efficient way to manage a huge load of homework?

  2. What are the alternatives to the "practice, practice, practice" method to gain good skills in computations?

  3. The ideal solution would be to completely change the homework list in accordance with the philosophy of "less but better," but my colleagues will be hurt if I change the school's habits. How can I discuss this problem with them without hurting their sense of hierarchy?

Thank you in advance, and sorry if my questions are imprecise. To sum up, it could be changed to "What are the most efficient methods to teach Calculus, with respect to the ratio (computation skills)/(homework load)?"

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  • $\begingroup$ Mentioning the country, if the asker is comfortable with that, might give useful context to the question. $\endgroup$ – Tommi Brander Dec 30 '17 at 9:55
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One way of reducing the load of grading is to use an online answer checker. There are several that are free and open-source, including Webwork, Lon-Capa, and Spotter (which I wrote). Webwork seems very popular among math teachers, and there is a huge body of problems set up in Webwork.

The only work you really have to grade by hand is work that involves writing, critical thinking, and higher-level reasoning. If you assign a lot of that and feel that it's too much to grade, then one option is to grade a random sample of the problems.

The overarching issue is that at some point you're going to have to make a decision as to whether your perceived lack of academic freedom is a real lack of academic freedom, and how to deal with that. It's possible that not all of your colleagues are as rigid or conservative as you imagine.

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    $\begingroup$ Online homework was one of my ideas to cope with the situation. The free open source resources will probably be very useful. $\endgroup$ – Taladris Jun 1 '14 at 15:06
  • $\begingroup$ Adding a plagiarism tool just increases the workload. Doesn't help the main dynamic of the catch 22. $\endgroup$ – guest Jul 7 '18 at 18:06
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In addition to having an online homework system if possible, you might also consider asking the students present a few problems in class. This would make the students at the very least care more about the homework and the subsequent class discussion would help you identify some of the difficulties with the assignment. Often this helps a great deal with the computational practice many calc students seem to need. Doing algebra in front of your classmates will certainly inspire to get every step right and will ensure that you are able to explain the validity of each step.

Online homework combined with presentations seems ideal. Lots of practice, instantaneous feedback on all problems, detailed feedback on several problems.

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If you are worried about student overload (I would), try to select few problems that show different aspects for homework. Try to make sure they learn, not just practice. Complement with a selection of lots of practice problems, to be done voluntarily (and not graded). It does help if solutions are available, or even better if they are checked on-line.

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In addition to recitation (excellent suggestion by ncr), I would do more pop quizzes (graded in class by paper passing), in class drill (ungraded), and more period-long tests.

I would not bother grading homework other than to verify it was done/not done. Just not worth the effort. I would stick with the no late work policy. In addition to not bucking the system, it is also really sending a better message to the students that REGULAR practice and KEEPING UP are the ways to learn rather than cramming.

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Switching to online marking for mechanical and repetitive practice is a very good idea.

What are the alternatives to the "practice, practice, practice" method to gain good skills in computations?

Though I still recommend large amounts of repetition, you can dramatically increase the quality of those repetitions in a variety of ways.

  1. For a given exercise that requires a multi-step solution, generate five "answers" of varying quality from five fictitious students. Have your actual students individually rank them by quality, then discuss their rankings in groups, with the aim of establishing criteria of assessment. This is called "Assessment as learning".

  2. Instead of grading large volumes of students' work, switch toward grading a much smaller amount of it and giving them extremely concrete comments on how they should improve next. This is "Assessment for learning".

  3. Use retrieval practice. A typical task might be "From memory, create examples and solutions for the ten most likely types of questions you expect on the test." Let them try first try this from memory, i.e. just pencil and paper and nothing else. Then they can pull out a pen, open their textbooks, and mark their work and/or their peers' work. They might form a consensus on those top 10 exercises. You can provide feedback. Then they can go through the cycle again. Of course, you'll get a better handle on whether your students are aware of what the big concepts even are, how difficult they expect the test to be, if they can distinguish among all the skills, etc. Read more at Learning Scientists and The Effortful Educator.

  4. Check out this homework policy.

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