An analysis of mathematical tasks used at second-level in Ireland

This thesis is concerned with the analysis of mathematical textbook tasks at second-level in Ireland, in the context of the introduction of the revised curriculum entitled ‘Project Maths’. This work aims to gain greater insight into the mathematical tasks that students and teachers encounter on a daily basis, to attain some understanding of the teaching and learning taking place in Irish classrooms. A total of 7635 tasks on the topics of Pattern, Sequences and Series and Differential Calculus contained in three textbook series for senior cycle, in editions available before and those available after the curriculum change were analysed. The analysis was informed by the use of five frameworks: an amended version of the Project Maths problem-solving objectives, a novelty framework designed during the course of this research, Levels of Cognitive Demand (Smith and Stein, 1998), Lithner’s reasoning framework (Lithner, 2008) and Usiskin’s model of mathematical understanding (Usiskin, 2012). My findings suggest that the post-Project Maths textbook tasks offer greater opportunities in all five areas when compared to those in the older textbooks, but that there is still scope for further development. Based on my analysis, it would appear that all three textbook series have neglected important objectives of the Project Maths curriculum such as justifying conclusions and communicating mathematically. Furthermore, the findings indicate that there is a need for more attention to be paid to fostering novelty in textbook tasks, increasing the level of cognitive demand, and more opportunities should be provided for creative reasoning. Greater effort should also be made to diversify the dimensions of student understanding offered by tasks. Following this analysis, some sample tasks were designed, paying particular attention to the areas my findings indicate are in need of improvement. This was achieved by building on existing textbook tasks as well as creating completely new ones