## Flawed and Uneasy Compromise

Karl Fisch,
The Fischbowl,
Jul 05, 2012

Karl Fisch has an interesting problem (to which I will offer a solution). "I haven't been able to figure out how to design assessments that not only test the skills that students are required to learn, but with problems that can't be solved effortlessly with Wolfram Alpha (and thereby don't give me enough information to tell what my students have learned about the Algebra)." It's a bit funny to me, because Wolfram Alpha is like a graphing calculator on steroids. So, the solution is to undertsand *what it is* when we're teaching algebra. It is *not*, I assert, how do do manipulations in algebra. It's like logic that way: you could sit there and endlessly derive theorems from axioms, or manupulate the square of opposition. But the real underlying skill being taught is *how to formalize* and *how to reason formally*. Doing the calculations constitute the mechanical bit you complete only after you have successfully formalized. So, to put the answer a bit simplistically, the answer to Fisch's dilemma is to assign word problems, preferably in contexts where the word problems arise as a natural part of trying to complete some authentic real-world task. (Photo from the video Bermuda Skype Research.)

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