I am relatively new to the teaching profession, so the first time I heard about Bloom's Taxonomy, it made sense to me. But I knew little about its origins. Like many things in education, there are strong feelings both for and against many educational concepts. There are those educators who are true believers and avid users of Bloom's Taxonomy and those who abandoned its use years ago.
One proponent of Bloom's Taxonomy states that it is the first idea taught in educational classes and the root of most ideas in education. One commenter to this blog notes a "love-hate" relationship with Bloom, as every lesson plan had to be written with elements of Bloom's.
One opposing view of Bloom's Taxonomy by Dr. Brenda Sugrue argues that Bloom's taxonomy is not supported by any research on learning. Sugrue also argues that the six levels in Bloom's taxonomy cannot be consistently applied to learning objectives. As an alternative to Bloom's, Sugrue presents a Content-Performance Matrix.
I believe that utilizing Bloom's taxonomy in algebra and calculus tasks can be very beneficial. When students come out of these classes, the ultimate goal is that the mathematics that they learn will be applicable to their lives in the "real" world. So, students should not only be able to recall and repeat algebra and calculus formulas, but they should be able to apply them. So once students have basic definitions and comprehension (Bloom's levels 1 and 2), they should be able to move to the higher levels of thinking. For example, in Algebra, once we finished the three different methods of solving linear systems, I engaged my classes in a discussion as to which of the three methods they liked best. For most students, it amounted to "I like method X because it's the fastest / easiest". Even with that type of statement, these students have moved to the Analysis level of Bloom's Taxonomy. As one moves to more complex mathematics such as Calculus, the thought processes can become more abstract and much of the work will be in the upper levels of Bloom's taxonomy.
So, overall, I believe that Bloom's taxonomy has as much usefulness in any level of mathematics as it does in other subject areas.