Proceedings of The International Conference on Research in Teaching and Education
Modelling the diversity of Tertiary Abstract Algebra Textbooks
Hassnaa Hasan Shaheed, Judy-Anne Osborn and Malcolm Roberts
This work sets about understanding and modelling differences in look and feel between tertiary Abstract Algebra texts. We present a `proof-of-concept’ stage model of this difference, in terms of a concept that we call the `terrain’ of a text. Our model is influenced by our conceptual framework, which brings together `Reader Oriented Theory’, and `Content Analysis’. We define `terrain’ to be the proportion and arrangement of functionality within a text. The particular functionality that we explore in this article relates to four categories: `Facts’, `Explanation’, `Notation’ and `Signposting’. In particular, the modelling of the type and frequency of `Facts’ in Abstract Algebra techniques appears to be novel; whereas `Explanation’ has been considered in previous literature at least in the particular instance of proof. Utilising an acronym for the four categories, we call the resulting model the `FENS’ model of Terrain. The FENS model has several different instantiations, each associated with a different type of theoretical reader, defined by a collection of reading characteristics. The differences depend on the kinds of Facts, Explanations etc. that different readers are likely to be sensitive to in their reading. For instance, a reader who is interested only in technical mathematical facts will `see’ a different book to one who is interested in big-picture ideas and historical origins. Our model indicates two results of interest: (i) different books have very different FENS even for the same reader, and (ii) different readers are likely to experience very different FENS for the same book.
Keywords: Textbook, Abstract Algebra, Reader Oriented Theory, and Content Analysis.