Reconsidering the nature of mathematics teaching and school mathematics curriculum

This thesis contains two distinct elements. The first relates to the original intention to develop a technological tool that helps mathematics teachers become microresearchers within their own classrooms. This tool, the Real Time Feedback System, consists of a wireless network that connects a set of iPod Touch devices to a database and web server in the classroom that intermittently prompts students to respond to a set of questions written by their teacher. The responses to these questions are automatically collated into a graphical format, allowing teachers to gather live data and reflect on the progress of their lessons without the burden of manual collection and collation of student responses. The intention was that the tool would facilitate teacher reflection, resulting in improved teaching of mathematics. While the system was successful in stimulating teacher reflection, and generated enthusiastic suggestions of how it could be improved to better suit their purposes, the teachers involved in trialling the tool did not incorporate it, unaided, into their everyday practice. I took this to signify that my original aim of equipping teachers in this way was perhaps premised on an unrealistic expectation of what could be asked of teachers. This observation prompted a gestalt shift in my perspective and I began to notice unrealistic expectations embedded in the teacher reflection literature and other mathematics education research literature. I became aware of an absence of any clear sense of what constitutes reasonable expectations of mathematics teachers, and this analysis led me away from the original research aims and gave rise to the second intention of this thesis, that of seeking to reconsider the nature of mathematics teaching and school mathematics education, and the expectations that many commentators have of teachers. This reconsideration involves an exploration of aspects of teacher participation in research and professional development, how they judge their teaching practice, what implications there might be for students, and in turn what implications there might be for school mathematics. It begins with a discussion of idealism within mathematics education research centred on a detailed consideration of some ethesis-submission-form.doc May 2009; reviewed January 2010 3 researchers’ expectations of teachers and additional analysis of data relating to teachers’ willingness to be observed by researchers. Methodological issues that arise pertaining to the nature of observation are examined and it is suggested that this may be indicative of a gap existing between researcher idealism and teacher pragmatism. This analysis continues with the presentation of further survey data which indicate that teachers work long hours, are committed to their jobs, and yet despite this many seem to lack knowledge or confidence in teaching mathematics. A second group of teachers are identified who, while reporting high levels of mathematics knowledge and confidence, appear to have attitudes toward their students that could impact negatively on their ability to teach mathematics. The existence of these two groups prompts an exploration of inequity within mathematics and the proposal of a process of random inequity that could disadvantage many students. The consideration of these various forms of inequity within mathematics education prompts an analysis of the nature of school mathematics and the identification of special interest groups that seek to shape mathematics curriculum to their own ends. It is argued that pressure from these groups termed, using the categories from Ernest (1991): Industrial Trainers; Technological Pragmatists; Old Humanists; Progressive Educators; and, Public Educators, has a negative impact on the ability of teachers to teach mathematics successfully by forcing them to meet demands imposed by others that take little account of the demands inherent to being in the classroom. It is finally argued that, as a result of the success of certain groups bending mathematics curriculum to serve their own purposes, school mathematics has become disconnected from peoples’ lives. It is suggested that a different approach to the mathematics curriculum based on the realistic needs of educated adults and realistic expectations of what competent teachers can teach, could result in a mathematics better suited to the needs of society. It is argued that a curriculum based on functional numeracy, financial numeracy, citizenship numeracy, critical mathematics, and aesthetic mathematics could result in mathematics that is more teachable and more relevant to students