This is sort of an extended comment, but I find I need space to give what I think is a possibly useful answer that addresses underlying assumptions rather than answering the question as asked.
I'll give you the summary first: Confronting misconceptions may be productive in some cases, and indeed the focus on student misconceptions in math and science was central to much research in mathematics education in the 70's and 80's. However, there are reasons that this approach is problematic for instruction. I have a research reference, and an anecdote.
Smith, diSessa, and Roschelle (1993) discussed some of what had been accomplished with understanding student learning using the model of misconceptions, and then gave some critique.
In the section "Is Confrontation an Appropriate Model of Classroom
Learning?" p. 126, they wrote:
There are both strengths and weaknesses in this conceptualization of
classroom instruction. We need energetic classroom discussions in
which students take positions, make sense of and explain problematic
phenomena, and articulate justifications for their ideas. Activities
that produce states of cognitive conflict are certainly desirable and
conducive to conceptual change. However, as judged by constructivist
standards, confrontation suffers from important deficits as either a
phase of conceptual change or a model of instruction. As cognitive
competition, it cannot explain why expert ideas win out over
misconceptions. The rational replacement of one conception with
another requires criteria for judgment. As knowledge, those criteria
must be constructed by the learner, and neither confrontation nor
replacement explains the origins of such principles for choosing
concepts, crucial data, or theories. In fact, change in how one
decides in favor of one conception over another is a complex part of
conceptual development (Kuhn & Phelps, 1982; Schauble, 1990), and
confrontation is an implausible mechanism for changing principles that
decide, for example, the relevance of data to theory.
Confrontation is also problematic as an instructional model. In
contrast to more evenhanded approaches to classroom discussions in
which students are encouraged to evaluate their conceptions relative
to the complexity of the phenomena or problem, confrontation
essentially denies the validity of students' ideas. It communicates to
students that their specific conceptions and their general efforts to
understand are fundamentally flawed. The metaphor of confrontation is
also inconsistent with the pedagogical sensitivity and care required
to negotiate new understandings in the classroom (Yaekel, Cobb, &
Wood, 1991). Finally, some misconceptions are powerful enough to
influence what students actually perceive, thereby decreasing the
chances that planned confrontation and competition will be successful
My anecdote (much abbreviated): A few years ago I was assisting a teacher in a 4th grade class by helping two students who were having difficulty comparing fractions. They thought 3/4 was greater than 4/5. A number of ways of approaching this occurred to me, and to keep the story short, I will just say that I had them construct a physical model that you and I would likely agree showed that 4/5 is greater than 3/4. However, as time ran out on us, they looked at their work and said, "yes, see? 3/4 is more than 4/5."
I'm sure you could find things to critique in the details of my approach. But two things struck me later as I was driving home. The first was that sometimes seeing depends on what you are sure you know. But the second is even more relevant: I still did not know much about why those students thought 3/4 was greater than 4/5. Spending all my time trying to help them reach a productive state of confrontation, I didn't learn about what they knew.
When students know something, it represents knowledge that somehow made some sense to them in some other context. But it's not working appropriately in the desired context.
There is research showing that a focus on student conceptions, rather than mistakes, is not only productive for student learning, it also can be a helpful model in preparing teachers for thinking about student thinking (Fennema et al., 1996).
Of course, these conceptions students have are tied to specific content knowledge. Therefore, a taxonomy of mistakes (de-contextualized from specific content) may not necessarily be useful in the action of classroom instruction. Certainly useful is knowing with some accuracy the types of ways students come into the class making sense of the content in a way that is limiting them (yet it makes some sense to them).
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A Longitudinal Study of Learning to Use Children’s Thinking in Mathematics Instruction. Journal for Research in Mathematics Education, 27(4), 403–434.
Smith, J. P., diSessa, A., & Roschelle, J. (1993). Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition. The Journal of the Learning Sciences, 3(2), 115–163.