Developing Teaching for Mastery in mathematics: The case of the beginning secondary teacher

Abstract

This study reports on beginning mathematics teachers’ perceptions and understanding of mastery learning (Guskey 2015; Boylan et al. 2018) and the extent to which they recognise aspects of mastery learning in practice. The study also seeks to interrogate how beginning teachers align their beliefs with their practice when they justify their responses to classroom situations. Currently, interest in mastery learning is reflected in English mathematics education policy (Department for Education and Gibb 2016; NCETM no date) and influenced by approaches to mathematics teaching in Shanghai and Singapore. However, many of the pedagogical principles taught in ITE programmes in England and Wales over decades (The Joint Mathematical Council for the United Kingdom 2017) are reflected in current conceptions of teaching for mastery and mastery. These suggest that aspects of learning mathematics such as reasoning from known facts and connecting multiple representations of concepts are fundamental to teaching and learning mathematics (Marton 2015), irrespective of whether these principles are taught as mastery learning or not. The study is of further interest given the concerns expressed by Ofsted that school focus on examination results at ‘the expense of adequate understanding and mastery of mathematics’ (2012, p.4) and the impact of a culture of performativity limiting teachers’ ability to act upon their beliefs (Ball 2003). The study focuses on the following three research questions: What aspects of mastery pedagogy do beginning secondary mathematics teachers recognise in their own practice and that of others? How do beginning teachers align and justify their beliefs with their practice? To what extent might their teaching reflect a mastery-type pedagogy? In the first part of this mixed-methods study, the TEDS-M Future Teachers questionnaire (Tatto et al. 2012) was used to collect quantitative data from 134 pre-service teachers at the beginning of their one year secondary mathematics HEI-led Post Graduate Certificate (PGCE) programme. The survey indicated that their beliefs largely support conceptual and cognitive constructivist views of learning, in line with the TEDS-M study (Tatto et al. 2012) findings. Such views support a range of pedagogies, including mastery. However, teacher beliefs are not necessarily congruent with practice (Smith 2001) and that the relationship between the two is complex (Handal 2003). Smith also identifies the difficulty pre-service teachers have regarding ‘a clash of culture and beliefs about the nature of teaching and of mathematics’ (2001, p.118) and having to respond to conflicting demands from their placement schools and the university. They also face the difficult task of learning to teach in action whilst learning the professional knowledge to inform their actions on the classroom (Darling-Hammond, 2017). The second phase of this study draws on qualitative data from six semi-structured interviews designed to interrogate and capture beginning mathematics teachers’ understanding of the features of mastery learning within their own practice. The interviews used vignettes, defined as ‘written …. stimuli… reflecting realistic and identifiable settings that resonate with participants for the purpose of provoking responses, including but not limited to beliefs, perceptions…’ (Skilling & Styliandes 2020, 542-3). Thus, the data collection included opportunities for beginning teachers to articulate their beliefs about mathematics teaching and learning in relation to their classroom practice and share their understanding of mastery approaches to teaching mathematics following Skilling & Stylianides’ assertion that the vignette approach ‘can help capture participants’ beliefs leading to a more nuanced understanding of the phenomena’ (2020, 541). The analytical framework used draws on Guskey’s (2015) interpretation of Bloom’s theory of mastery learning together with features of mastery learning in mathematics articulated by Drury (2018) and Boylan (2018). This in itself poses a research design challenge given the variation in interpretation of mastery learning as it is understood in practice. Capturing the full complexity of beginning mathematics teachers’ perception and understanding of learning to teach mathematics is beyond the scope of this study. However, interrogating their perception and understanding of some aspects of mastery learning may serve to provide insight into these teachers’ experiences at a time when mastery learning discourse is prominent (Boylan 2018). The study demonstrates that beginning mathematics teachers’ beliefs about mathematics pedagogy are aligned with the principles of mastery learning within a framework that is also informed by constructivist and cognitivist principles of teaching and learning mathematics inherent to the connectionist teacher orientation (Bruner 2006; Tatto et al. 2012). This exposes differences in the interpretation of the principles of mastery learning in the settings where they learn to teach as well as tensions that arise between beginning teachers’ beliefs, practice, professional knowledge and sense of agency in their developing classroom roles.

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ORCID for Rosalyn Hyde: orcid.org/0000-0001-8208-2983

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