Tag Archives: understanding

Reflections on Teaching Workshop

This week I’m attending a summer teaching workshop at the University of Colorado, Boulder. Today, we discussed learning objectives and student assessments. One theme that seemed to run through both of these discussions is the concept of measurability. When writing learning objectives for a demo lesson (to be given later in the week), we were instructed to make sure that the objectives could be measured in some way. Using Bloom’s Taxonomy, one may write a learning objective for a given “level” of knowledge that uses a measurable verb. For example, consider the following learning objective:

At the end of the lesson, students will be able to restate the Intermediate Value Theorem.

This learning objective is not objectionable (at least I don’t think it is!) because it uses the measurable verb restate. One can measure to what extent the learning objective has been met by measuring to what extent the theorem has been correctly restated. Often in these conversations, measurable verbs are contrasted with the paradigm example of a non-measurable verb: understanding.

I found this discussion of measurable verbs, and particularly the relegation of understanding, really striking. It reminds me of Heidegger’s distinction between exact thinking and rigorous thinking:

Exact thinking is never the most rigorous thinking, if rigor receives its essence otherwise from the mode of strenuousness with which knowledge always maintains the relation to what is essential in what is. Exact thinking ties itself down solely in calculation with what is and serves this exclusively.

In the context of learning objectives, I think what Heidegger is getting at is this: what we really care about understanding, thoughtfulness, reflection, etc.–what Heidegger calls rigorous thinking. These are qualities that separate humans from everything else (other animals, computers, and inanimate objects). But understanding is not measurable, and thus, we cannot assess whether our students actually understand anything. So, instead, we assess things that are measurable, like whether they can restate, apply, or prove a theorem–examples of what Heidegger calls exact thinking But in the switch from rigorous to exact thinking, one loses something essential. As John Searle convincingly argues, the fact that an entity (e.g., a computer program) can restate, translate, apply, or even prove a theorem is not sufficient evidence that the entity actually understands the theorem.

I wonder then, if, in stating measurable learning objectives, we are aiming at the wrong target–albeit an easier target to hit. Perhaps those who object to learning objectives are really pointing at something profound: that real thinking (rigorous thinking) can’t always be measured, and that’s OK. This raises all sorts of questions about how we might keep students accountable, how we might assign grades, etc. But these questions shouldn’t stop us from thinking clearly about what, in many cases, we really want students to do: understand!

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