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Monday, February 28, 2011

A lens for assessment

Recently Stephen J. Dubner in a blog entry entitled Are You Smarter Than an Eighth Grader? Published a copy of document from 1895 that had been published in the Salina (Kansas) Journal. By all appearances, this document looks to be a final exam for eighth graders though casts some doubt on this. As with so many historical questions, we may never know the full truth here, but I would still like to use this as an opportunity to discuss assessment by using this document as a lens.

Whenever I give a test, I am assessing two things. One of these things is how well each of the students understand the material. Their scores reflect how well they have learned. This can either be done as simply an abtract exercise in discerning what percentage of the material has been absorbed or, as is more often the case, against a set of standards. Did the student pass the exam? Did they learn 70 percent of the material and get a gentlemanly C? Did they learn 90 percent and earn an A? The other thing I am assessing is how well I taught the subject. Which questions did they know the answer to? Did they do so well that I could spend less time there and more on an area that they didn't do as well on?

For this exam, we don't have this sort of information. We don't know how many people passed if any or whether anyone even took it. As of this writing, I just don't know.

I recall a conversation at a local mathematics confernence a few years back with a man who had been teaching Intermediate Algebra for many years. He had carefully tracked his how his students had done on an impressive number of student learning outcomes. One of those was arithmetic with imaginary numbers. He'd tried a number of different methods of approaching the topic. He'd spent more time, given more emphasis, but he could never the the student success above a certain threshold. And he had years of data to prove this.

Others there had questions to ask about things he'd tried. The question I wanted to ask was "You are teaching the arithmatic of complex numbers to Intermediate Algebra students? Why?" Intermediate Algebra is taught in college to students who've come to college unprepared to take College Algebra. One need not know much about the arithmetic of complex numbers to meet the challenge of College Algebra, and, indeed, the time might be better spent elsewhere.

The topic is not appropriate for the students in the class. I find the arithmetic of complex numbers to be enjoyable and fascinating; it can be a useful intellectual exercise; and there are areas in which it is actually useful. If I were this teacher, I would remove the topic from the course to spend more time on other topics. I open myself up to the charges of dumbing down the course by doing this, but quite frankly the students who need it will learn about it in Differential Equations or the Theory of Functions of a Complex Variable. The students who are trying to prepare themselves for College Algebra will be able to learn what they need to be ready for that course.

As I look at the document from 1895, I see a lot of things that I don't know about. Putting the other sections aside and concentrating on the math, which is my area of expertise, I see some things there that are good, but I don't see any algebra. We teach a little algebra in the eighth grade now. This has none. There is nothing about computers, of course.

This exam proves that things change. We as teachers can use assessment methods as a tool to attempt to change for the better.

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