This paper discusses the competency space approach to diagnosing misconceptions, skill, and knowledge acquisition. In some approaches that combine misconceptions, skill, and knowledge acquisition, the latent ability theta is used more or less as an insignificant element, but in the competency space approach, a multidimensional latent space is used. The competency space approach is explained and an example is given of its use. It is necessary to expand the acceleration model to the multidimensional space if it is to be used effectively in the competency space approach. A slow and patient approach that attempts to identify the subspace of theta that deals with attribute mastery (domain knowledge) (theta b) of a relatively small dimensionality first may be productive. Once a unidimensional theta b has been identified, the acceleration model can be tested. The example given uses data from a trigonometry test for high school students in Japan. The competency approach can be effectively used in research in which an appropriate software is developed and used for intensive observation of an individual's problem-solving behavior. Two tables and seven figures illustrate the analysis. An appendix contains the test answers. (Contains 24 references.) (SLD)