Exploring the development of thinking in senior secondary mathematics : a focus on probability

Higher order thinking skills have been identified as desirable although elusive outcomes of many educational curricula. Through a qualitative case study, the alignment between the three levels of the curriculum: intended, implemented, and attained, was examined to determine the tensions and possibilities in the development of mathematical and thinking skills in senior secondary students in Gippsland, a large regional area of Victoria, Australia. Probability was the mathematical content area of focus. Data from document analysis of the intended curriculum, textbooks as the implemented curriculum, and assessments as the attained curriculum, was combined with qualitative data from semi-structured interviews with twenty students and fourteen senior secondary mathematics teachers. These diverse data sources scaffolded each other to identify tensions and possibilities influencing development of student thinking in senior secondary mathematics. This research demonstrated that the flow of content via the intended-implemented-attained curriculum was not adequate to describe all the influences on student learning. The lens of Activity Theory (Engeström, 2001) came closer to capturing the related complexities whereby the textbooks, calculators, bound reference books and assessments, combined with the balance of agency demonstrated by the teachers and students, were found to both support and cause tensions within the activity system. Probability was found to be a valuable topic to study in relation to the development of thinking skills due to its relevance in decision making, how it linked many areas of mathematics and the uniqueness of the classic, experimental, and subjective views of probability. This study is significant in the contribution it makes to understanding the tensions and possibilities associated with the development of mathematical thinking relating to probability through the lens of Activity Theory. While the intended curriculum encouraged a range of thinking skills, this intended curriculum could be implemented in a way that promotes memorisation rather than the intended higher order thinking. This study concludes with recommendations for the curriculum designers, textbook publishers, teachers, and students which may support the development of mathematical and thinking skills.Doctor of Philosoph