Subordinate and superordinate accommodations, indissociability and the case of the complex numbers

The paper deals with three notions of Ausubel’s cognitive psychology within a mathematics learning context. The notions are subordinate accommodation, superordinate accommodation and indissociability. The mathematics learning context is that of the complex numbers. There are two ways to teach complex numbers. One of them is by introducing i as a number the square of which is-1. The other one is by means of ordered pairs. It is argued that the first way requires a subordinate accommodation and the second one requires a superordinate accommodation. By means of a questionnaire which was administered to various student populations we tried to determine how people accommodated, the subordinate mode or the superordinate mode. We found that in each accommodation mode there exist several different forms. An attempt is made to use the data in order to determine which teaching method out of the two we have is preferable. It is claimed that, as long as students who do not major in mathematics are concerned, the teaching method which requires a subordinate accommodation is preferable. Even in mathematics majors superordinate accommodation might take years. It is shown that among people who accommodated, a high percentage is unaware of the process by means of which accommodation took place—this is the phenomena of indissociability.