This study explores the relationship between computational thinking, teaching programming, and Bloom's Taxonomy. Data is collected from teachers, academics, and professionals, purposively selected because of their knowledge of the topics of problem solving, computational thinking, or the teaching of programming. This data is analysed following a grounded theory approach. A computational thinking taxonomy is developed. The relationships between cognitive processes, the pedagogy of programming, and the perceived levels of difficulty of computational thinking skills are illustrated by a model. Specifically, a definition for computational thinking is presented. The skills identified are mapped to Bloom's Taxonomy: Cognitive Domain. This mapping concentrates computational skills at the application, analysis, synthesis, and evaluation levels. Analysis of the data indicates that abstraction of functionality is less difficult than abstraction of data, but both are perceived as difficult. The most difficult computational thinking skill is reported as decomposition. This ordering of difficulty for learners is a reversal of the cognitive complexity predicted by Bloom's model. The plausibility of this inconsistency is explored. The taxonomy, model, and the other results of this study may be used by educators to focus learning onto the computational thinking skills acquired by the learners, while using programming as a tool. They may also be employed in the design of curriculum subjects, such as ICT, computing, or computer science.