The Utility of Verbs in the Determination of Cognitive Complexity

I have often sat in meetings where Standards based instruction is being discussed. You cannot discuss learning objectives without discussing Bloom’s Taxonomy. Currently the discussion is all about the revised taxonomy (2001).

Let me start by saying that this approach to a cognitive taxonomy is very useful in many disciplines. However, like any other theory it has its limitations, particularly in the application to writing objectives and analyzing assessment items for the depth of knowledge (DOK) an item assesses. This limitation is particularly obvious in the field of mathematics.

The point of this article is to caution those who evaluate teachers’ learning objectives by focusing solely on the verbs that the teachers use. The verb alone without some context of the embedded tasks required is not sufficient to determine if teachers are teaching recall, understanding, application, analysis, evaluation, or creative thinking.

Let us look at the word ‘solve.’ In the list of verbs commonly associated with tasks related to Bloom’s taxonomy solve is listed under ‘apply.’ However, the word may actually be related to tasks from almost any level of the taxonomy, and one cannot determine this without some understanding of the requirements of the tasks involved in the discipline.

In the context of: Solve x + 3 = 10 we would be justified in saying this is simply recall and at the lowest level of Bloom’s taxonomy.

In the context of: Solve 2x -6 = 17, we would argue that this rises to some level of understanding and possibly application of the principles of solving linear equations.

In the context of: Solve, using completing the square, f(x) = x2 + 12 x - 27 and determine the roots, and maximum or minimum value of the function. This certainly requires analysis.

In the context of: Solve sin x – 3cos x = √2 for 0< x< 2π. This requires all of the above plus evaluation and some creativity of choice.

The point I am making is that the same verb, solve, could be representative of tasks from any level of Blooms’ taxonomy. Just a caution.