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Wednesday, February 28, 2007

What should college freshmen know?

Rudbeckia Hirta reports that she has a “freakishly competent” college calculus class:
They come to class; most of them do the assigned work; they earn high scores on the assessments.
Whether that situation should be so surprising is another story, but here I want to comment on the real import of RH’s post. She goes on to describe the computational weaknesses of this otherwise admirable class:
Over the past few days several students have come to my office to ask me questions about computations that I did in class. We'd been working with the geometric series, and we've been applying algebraic manipulations to the general term so that it's of the form arn-1 (our indexing starts with n=1). We had a problem where the general term is of the form 3n/4n+1. To get it to match the form in the book, I used rules of exponents to rewrite it at 3/16 (3/4)n-1.

Mass confusion. Totally lost. My very successful and accomplished calculus students were unable to follow the algebra. They couldn't see why those two expressions were equal. Working through the problem, slowly, in my office they would ask, "When you multiply, do you add the exponents?" Another student asked, "Is 3n/4n the same as (3/4)n?"
I would like to think that college freshmen who do their work and earn high grades on assessments would understand exponents and fractions as a result of their high-school math, but I guess I’m naive. Or maybe it’s a difference between public high schools in the South and those in the Northeast. Or maybe I’m being naive about the Northeast, and our students wouldn’t be any better.

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