This presentation will outline my research into fitness for purpose of tertiary algebra textbooks used in Iraq in the teaching of undergraduate algebra courses with regard to the training of pre-service teachers. The project draws on work done in textbook analysis, and work done into the teaching and learning of abstract algebra and the nature of proof.

It is well recognised that for many students learning abstract algebra and the nature of proof is difficult (Selden, 2010). Courses in abstract algebra are central to many tertiary pre-service mathematics teacher programs, including in Iraq. Capaldi (2012) suggests that abstract algebra textbooks can lay the foundation for a course and greatly influence student understanding of the material. However, it has been found that there can be large differences in textbooks used, at the school level at least, in different cultures. (Alajmi A. H., 2012, Fan and Zhu, 2007, Pepin and Haggarty, 2001). For instance, Mayer and Sims, (1995) Japanese texts feature many more worked out examples than texts used in the United States for mathematics.

I will be examining the textbooks in light of theories by Harel and Sowder, and Stacey and Vincent, regarding types and proof and modes of reasoning (Stacey and Vincent, 2009) and Capaldi (2012) regarding reader's relationships with books.

The textbooks will also be examined to try to infer the underlying assumptions about pedagogies and knowledge made by the author(s). Baxter-Magolda's theory, linking forms of assessment to underlying theories of knowledge (Baxter-Magolda, 1992) will be helpful in this pursuit.