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In a freshman course in mathematics for biology students, I have had the issue that basic algebra (e.g. simplifying $\frac{a/b}{c/d}$) is far from being mastered. On the one hand, it seems ill-suited to teach more advanced matters to student failing on the basics. On the other hand, if we take too much time to cover the material allegedly covered in high school, we can hardly hope to cover what is needed to these student, and we enforce the impression that not mastering high-school mathematics is ok.

How much effort should we spend in class for studying material that is supposed to be mastered but in practice is not?

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This is a situation where using an online homework system is particularly useful; usually there will be an early section of review material from which you can assign problems. I would advise issuing such an assignment as early as possible in the term (preferably on the first day), making sure the students realize it is for a grade and that as it covers prerequisite material for the course, no in class time (or very little) will be spent on these problems. Note that these homework systems will also give students examples and detailed instruction on how to do the assigned problems, so the students should be able to (re)learn the necessary material on their own.

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  • $\begingroup$ Often students think they understand something and only when they get to solve the first problem they realize they don't. You should provide them with a chance to realize that. Since this is a biology course, not math course, it might be helpful to let them know right away in the homework why they are going to be needing to know this. Like "In the 4th lecture, there will be this formula and you should know how to simplify it". I am not sure if it would work for you, but if matching exercises on khanacademy.org/exercisedashboard exist, you can point the students to these. $\endgroup$
    – user7610
    Apr 1, 2014 at 21:23
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In addition to other useful answers... this sort of problem will recur forever, since students (even with good attitudes) chronically misjudge the importance of background courses, and chronically misjudge the degree of facility and competence really desirable for later work. E.g., sometimes students see a passing grade (C+?) as showing they're ready to move forward... while, in reality, that's terrible from the viewpoint of competence and reliability.

But there'll be no room in your course to rant about the failings of the ambient cultural attitudes, blah-blah-blah. Nor will many students be willing to agree with the premise that they in fact do not know things they thought they know... with "know" as certified by a grade in a course in the past.

Thus, for me both in undergrad courses at all levels, and in grad courses, I "recall" things ... sometimes in gruesome detail ... pretending to be apologetic for boring people who know it all too well... to at least passively drill everyone in the absolutely critical riffs.

Yes, I am implicitly doubting that formal reviews are as effective as one would want, exactly because of the inaccurate self-perceptions of the students. It is quicker, and not toooo burdensome to "in-line" the review/recapitulation of things that... yes, we'd like to be able to assume the kids know, but they just don't.

The meta-comment is that this is a huge issue, and we can't expect any sort of "solution", but only a strategy to fight back on an on-going basis...

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I think if you notice this problem, you should briefly revise it, go on with the material, stress that it is essential that they know the basic stuff, and hand out extra exercises on the basic material which will not be graded but which you are ready to discuss in your office hour.

This way you offer a chance to learn the basics but stress that your job is to teach something more advanced.

My experience, however, is mixed. They acknowledge my goodwill to help and even recognize that they have serious problems, but it is very very rare that someone comes to my office. They are not mathematics students, they have more important things to do...

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  • $\begingroup$ Is "revise" a typo for "revisit"? $\endgroup$
    – Alex Becker
    Mar 31, 2014 at 20:10
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    $\begingroup$ @AlexBecker: en.wiktionary.org/wiki/revise I used it in the meaning 3. Maybe should choose a different word? $\endgroup$
    – András Bátkai
    Mar 31, 2014 at 20:14
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    $\begingroup$ Ah, I was unfamiliar with that meaning (I've lived in the US my whole life, where revise is not used that way). I don't think there's any reason to preference US English over UK English, so I don't see a problem with it. $\endgroup$
    – Alex Becker
    Mar 31, 2014 at 20:16
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I've previously written online algebra tutorials for 2nd year bio students, with online quizzes at the end. It seemed to help. The advantage is you can base the learning materials on the course content to some extent. Also you can let students know early that they may have a problem before its too late to pass or withdraw. Set it as an early mandatory thing to complete as an assessment of prerequisities.

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Some strategies could be useful for improving students' basic information without wasting time in the main process of the course.

  • Use a TA and ask him/her to work on students' basic information during some sessions.
  • Surely there are some students in your class who know the basics better than others. Divide the students to some groups such that each group includes an informed student as a head. Ask heads to help their friends on basic subjects in some sessions. Of course you should motivate these heads by some extra grades or something like this.
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You should give your students an assessment test to see what they have not mastered. Then you may wish to give them some basic material for practice on their own time.

Once a professor asked me "Didn't you take a course in differential equations"?

I said "Of course, twice".

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  • $\begingroup$ "Practice in their own time", for biology student in math course, needs a lot more than just saying it to become anything close to real. $\endgroup$
    – Benoît Kloeckner
    Apr 1, 2014 at 9:13

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