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I've got a student in my introductory calculus course. They're failing because they lack algebra skills. They understand the concepts just fine, and can articulate their understanding fine, but get hung up on algebraic mechanics — factoring quadratic polynomials, manipulating rational expressions, conventions of exponent notation, etc — which then manifests poorly on exams. The natural advice to give them is to "take a semester of pre-cal to buff your algebra skills". However they are unwilling to do this; they've already taken and failed this class once (at least?) and feel committed to this calculus class now. Okay. Then how do I advise them?

I seem to be having students year-after-year in the same situation: they lack algebra proficiency but otherwise appear to be mathematically capable, and have already failed calculus at least once and are now unwilling to enroll in a "lower" course instead. I suppose the root cause of this is out of my control, but the advise I give to such students in my class now is in my control. These students usually understand that their algebra skills need attention, so my advice has been to work though a free online algebra or pre-cal course in tandem with my calculus course. But I don't know which online course to point them towards, or if there is a better idea I'm not considering.

What resources would you point these students towards? How would you advise these students?

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I know this doesn't directly answer your question which is about helping one student. But I would be wanting to see my institution implement sections of calculus with support. This blog addresses that situation.

My students liked Khan Academy, but I'm not sure how well it would do with helping them shift their mindset. (I just went and looked at it. First time ever, because I have a bias against it.) I guess I'd recommend the Algebra 1 and 2, and the Precalculus, if this was their preference. Free, friendly, and they get to watch their progress.

I like the workbook style of AOPS textbooks. But they aren't cheap. I wonder if the student would find their free site useful. It's called Alcumus. They have algebra and intermediate algebra levels. They are meant to be challenging, but they do have good explanations.

I'm not satisfied with my own answer. I hope other people can offer even better resources. This is such a common problem.

I will add that most students like this that I've encountered also have problems with some of their arithmetic skills, especially fractions and negative numbers. It's not just algebra skills, usually.

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  • $\begingroup$ Thank you. Yeah I've been stuck between recommending either Khan Academy too, or something from Coursera, but am worried that those courses, though they'll provide more practice and exposure, won't address whatever "disconnect" these students are having with algebra/arithmetic. I think I worry about remedial courses or courses with support for the same reason (maybe this reason?), but yeah I have no rank in my department and have no pull towards implementing such a thing. $\endgroup$ Commented Feb 22 at 15:06
  • $\begingroup$ A lot of the research on how bad remediation is for students has come from California, and a lot of the just-in-time support also comes from here. The blog I posted is for support during a calculus course, which is supposed to be the most effective way to do this. $\endgroup$
    – Sue VanHattum
    Commented Feb 22 at 16:17
  • $\begingroup$ To me, remediation courses and support while taking a course are very different things. $\endgroup$
    – Sue VanHattum
    Commented Feb 22 at 16:18
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My (paradoxical and politically incorrect) advice is to stick with the class they are accelerated into. but to do every single problem. Yes, even when the soft Millenials complain. Do every single problem AND lots of the "easy" ones. They will teach you algebra en passant. Tell him (or her...or it) to Drill, baby, drill!

http://theoildrum.com/files/Slide20.jpg

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