Dimarco, Silvia (2010) Mathematics in the middle: shaping the proficiency footprint. PhD thesis, James Cook University.

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Abstract

There is an undercurrent of unease seeping across Australia about sustaining a critical mass of human capital with the mathematical proficiency to successfully take up careers in mathematics, science, technology and engineering (McPhan, Morony, Pegg, Cooksey & Lynch, 2008). A key aspect of this challenge is the lack of academic rigour in the middle school mathematics classroom and the resulting impact on students’ mathematical proficiency and mathematical dispositions to successfully pursue higher level mathematics courses (Prosser, 2006). It could be argued that the middle school years are the cornerstone in the provision of the mathematical proficiency that empowers students to pursue higher level mathematics courses since mathematical experiences in the middle school underpin the strategic decisions students make when considering further education involving mathematics. This research accepted the challenge of recent research (Carrington, 2002; Department of Education, Employment and Workplace Relations (DEEWR), 2008; McPhan et al., 2008; Prosser, 2006) to further explore how teachers can deepen intellectual engagement in the middle school context. The formation of a productive proficiency footprint for Australia’s global well being depends upon students who are intellectually autonomous, proficient and predisposed to do and use mathematics.

This research investigated how the students and the teacher worked together in the middle school mathematics classroom and how this influenced students’ mathematical proficiency and mathematical dispositions. This qualitative case study explored the question, “How do middle school mathematics teachers empower students to be proficient doers and users of mathematics?”. Specifically this involved delving into how students were guided and supported by the teacher to work and think mathematically in order to construct their mathematical knowledge. Two grade 9 mathematics classrooms were observed at Amethyst College, a high school in North Queensland, over one semester in 2009. The socio-cultural and psychological perspectives within the classroom learning community provided the theoretical framework for this study. The socio-mathematical norms of mathematical difference and mathematical argumentation comprised a lens through which classroom interactions were critically analysed. Qualitative case study methods were chosen for this research since they provided an ideal opportunity to gain an emic understanding of the uniqueness of people and programs within the realities of an educational setting (Bassey, 1999; Merriam, 1998; Stake, 1995; Tellis, 1997).

The research data reveal the reflexivity of the socio-cultural and psychological perspectives. Several core issues impacted on how teachers used their professionalism and pedagogical content knowledge to establish norms that potentially empower students into being proficient doers and users of mathematics; broadly defined these issues included: the knowledge gaps and mathematical dispositions that students brought with them to the grade 9 classroom; the teachers’ epistemological beliefs, pedagogical dispositions and exhaustion and cynicism brought on by constant education reform. Streaming in the middle school and the omnipotence of the mathematics test also arose as key issues affecting students’ participation in learning at Amethyst College.

The implications of the data analysis suggest that if teachers and students continue to participate as passive recipients in their respective socio-cultural domains, Australia’s mathematical proficiency footprint will epitomise a largely cosmetic understanding over energised and mobilised participation. Research recommendations focus on how a re-configuration of Australia’s mathematical proficiency footprint might be precipitated, and how this would enhance Australia’s intellectual and social sustainability. Salient themes are building the capacity for high powered intellectual engagement in the classroom learning community and the professional learning community. Indeed the recommendations proffer the view that genuine opportunities for empowered and active participation in knowledge construction for teachers and students are what may sustain the ongoing revitalisation of middle school mathematics.

The thick description of this case study does not attempt to claim formal truths. Instead it strives to stimulate thought and reflection from the reader. In this way, the aim is to invite the reader to gain an insight into phenomenological issues, adding insight into experience and understanding.

Item ID:	17217
Item Type:	Thesis (PhD)
Keywords:	mathematical proficiency, middle school, mathematics classroom, learning communities, qualititative case studies, mathematical experience, student empowerment, student-teacher interaction, classroom practices, guidance, support, socio-cultural perspective, psychological perspective
Copyright Information:	Copyright © 2010 Silvia Demarco
Date Deposited:	31 May 2011 04:13
FoR Codes:	13 EDUCATION > 1302 Curriculum and Pedagogy > 130208 Mathematics and Numeracy Curriculum and Pedagogy @ 100%
SEO Codes:	93 EDUCATION AND TRAINING > 9302 Teaching and Instruction > 930201 Pedagogy @ 50% 93 EDUCATION AND TRAINING > 9301 Learner and Learning > 930102 Learner and Learning Processes @ 50%
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