Epistemic quality for equitable access to quality education in school mathematics

This paper reports on a study that aims to address the challenges of UN Sustainable Development Goal 4 to ensure inclusive and equitable quality education for all. The study focuses on school mathematics in particular. With regard to ensuring equitable access to quality education, it is argued that there is a need to consider the epistemic quality of what students come to know, make sense of and be able to do in school mathematics. Accordingly, the aim is to maximize the chances that all pupils will have epistemic access to school mathematics of high epistemic quality. The study is based on the theoretical framework of Joint Action Theory in Didactics (JATD). Associated research questions focus on the quality of teacher-student(s) joint action and on the epistemic quality of the content. The paper draws on empirical research findings of the Developing Mathematical Thinking in the Primary Classroom (DMTPC) project (2010–12) and also on the findings of a parallel study of mathematics teachers’ assessment practices in Ghana. One teacher’s action research project is used as an exemplar to illustrate how mathematics can become more accessible and inclusive thus leading to an evolution in mathematical thinking and high-quality epistemic access for all.     

Making abstract mathematics concrete in and out of school

We adopt a neo-Vygotskian view that a fully concrete scientific concept can only emerge from engaging in practice with systems of theoretical concepts, such as when mathematics is used to make sense of outside school or vocational practices. From this perspective, the literature on mathematics outside school tends to dichotomise in- and out-of-school practice and glamorises the latter as more authentic and situated than academic mathematics. We then examine case study ethnographies of mathematics in which this picture seemed to break down in moments of mathematical problem solving and modelling in practice: (1) when amateur or professional players decided to investigate the mathematics of darts scoring to develop their “outing” strategies and (2) when a prevocational mathematics course task challenged would-be mathematics teachers’ concept of fractions. These examples are used to develop the Vygotskian framework in relation to vocational and workplace mathematics. Finally, we propose that a unified view of mathematics, outside and inside school, on the basis of Vygotsky’s approach to everyday and scientific thought, can usefully orientate further research in vocational mathematics education.     

Collaborative action research as a tool for generating formative feedback on teachers’ classroom assessment practice: the KREST project

This paper sets out to explore science teachers’ classroom assessment practices and outlines some of the tensions and synergies in changing assessment practices. It describes episodes from a collaborative action research project with science teachers designed to support the strengthening of classroom assessment practices – the King’s Researching Expertise in Science Teaching project. This paper focuses on how the collaborative action research project functioned as a tool for generating formative feedback for the teachers and how this feedback supported the teachers in making sense of and further developing their classroom assessment practices.     

Mediating creativity and performativity policy tensions in dance education-based action research partnerships: insights from a mentor's self-study

This paper will present and critique the mediation of tensions arising as a result of the collision of creativity and performativity policies in English primary education, in the context of the three-way model of creative partnership being used for professional development in certain English schools. The paper will consider these partnerships from my perspective of research mentor to classroom teachers and dance artists engaged in dance-based action research (Creativity Action Research Awards 2). The paper focuses on two tensions arising in these contexts and their relationship to the creativity/performativity policy tensions: firstly process (with inherent potential for risk-taking, and critical appraisal) versus product (with inherent potential clarity) in the context of both the wider school performativity agenda and the performance expectation within dance; secondly, the necessary depth of enquiry to achieve ownership of creative activity by teachers and learners versus a desire for initiatives to demonstrate immediate results articulated in verbal, numeric or written form. The paper draws on my self-study of my role as research mentor within the CARA 2 initiative, to consider the manifestation and mediation of these tensions within actual three-way partnership practice, and the implications for current and future practice and policy.     

Conditions for linking school mathematics and moral education: A case study

In recent years the mathematics education research community has undergone a social turn towards a greater interest in the values and broader educational purposes of mathematics education, including issues of social justice and citizenship education. Building on these developing interests, this paper presents a conceptual framework that links the teaching of school mathematics with moral education. Then, in a case study involving two countries, England and Canada, this framework is used to explore the affordances and constraints faced by mathematics teachers in those countries if they want to intentionally practice moral education in the classroom.     

Mathematics Teacher Research: Process, Practice and the Development of Teaching

This paper discusses a study of teacher researchers undertaking research into self-chosen aspects of their own mathematics teaching at the secondary level. The study used qualitative methods to explore the processes and practices of this research and the issues which it raised. Emergent theory of teachers' research activity fitted strongly with a view of action research relating to critical reflective practice. The teachers were seen as reflective practitioners, developing knowledge and awareness through enhanced metacognitive activity. Their research was characterised as evolutionary, in contrast with established patterns of action research. Despite differences in the substance of each teacher's research there were commonalities which provide insights into the conducting of research by teachers and its potential for the development of mathematics teaching. The special nature of mathematics in this research, and the role of external researchers in the project, were important considerations.     

Professional mathematics teacher identity: analysis of reflective narratives from discourses and activities

This article focuses on the methodological use of reflective narratives from discourses and activities of an experienced primary teacher as evidence of her professional identity. The teacher’s reflective narratives emerge from her participation in a 3-year developmental and research project, Learning Communities in Mathematics, conducted at the University of Agder (UiA) in Norway. As background for our study, we firstly present the teacher in action with her sixth-grade pupils in a mathematics lesson, and then analyse selected clusters of reflective narratives from different empirical situations in the project. We have identified four identity indicators, which have been elaborated and organised thematically, related to the teacher’s engagement and critical alignment in the community of participants: (1) Positioning in relation to pupils, (2) Reflecting on developing a workshop model in teaching, (3) Integrating and expanding models of teaching and (4) Challenging positioning in relation to didacticians. These indicators provide evidence of the teacher’s professional identity. We suggest that the emergence of these indicators also gives empirical evidence of professional teacher identity development.     

Navigating dilemmas in transforming assessment practices: experiences of mathematics teachers in Ontario,Canada

Current thinking encourages teachers to incorporate a range of assessment practices that are responsive to student thinking and promote student learning. At the same time, teachers are situated in a landscape of accountability, where they are often seen as technicians who implement prescribed curriculum, policies, and procedures with success measured by externally created assessments. This paper considers how teachers navigate this difficult terrain as they incorporate new assessment practices in their classrooms. We report on a two-year project undertaken with 42 teachers of mathematics (Grades 4–12) in Ontario, Canada. Using an analytic framework adapted from Windschitl (Review of Educational Research, 72(2), 131–175.2002), we explore the dilemmas these teachers identified as they met in communities of practice. Our findings highlight the need for coherence in the assessment messages communicated to teachers and provide evidence of the critical role of ongoing collaboration and dialogue to support the development of teachers’ professional judgement and enable change in their assessment practice.     

The developmental trajectories of mathematics anxiety: Cognitive,personality, and environmental correlates

Students who are highly anxious about mathematics-related activities generally exhibit lower mathematics achievement and motivation compared to their less anxious counterparts. Despite negative implications of mathematics anxiety (MA) on mathematics learning, there is a paucity of research examining how MA develops over time. Using the Longitudinal Study of American Youth dataset (N = 3116), the present study investigated two main questions regarding the development of MA in secondary school: (1) Is the development of MA characterized by a heterogeneous subset of growth trajectories? (2) How are time-varying personal and environmental factors (e.g., mathematics achievement; perceptions of math teachers) related to specific MA growth trajectories? Student MA was repeatedly assessed in six annual waves spanning across middle and high school. Using growth mixture modeling, we identified four growth trajectories of MA: (1) The non-anxious group that exhibited chronically low MA; (2) The highly anxious group which displayed moderately high MA over time; (3) The resilient group that exhibited high initial MA that steadily decreased over time; and (4) The vulnerable group that reported low initial MA that drastically increased over time. In addition, significant differences in the development of mathematics achievement, personality hardiness, and perceptions of mathematics teachers were found in these four MA groups. Findings highlight heterogeneity in the development of MA, identify middle school as a critical period for MA development, and emphasize the importance of examining developmental changes in cognitive, personality, and environmental factors to help clarify distinct MA trajectories across middle and high school.     

The development of a mathematics teacher’s professional identity during her first year teaching

This study is focused on a period that poses several challenges for the development of mathematics teachers’ professional identities and agency: their first year of teaching in schools. During this period, beginning mathematics teachers confront tensions and contradictions among the principles, ideals, and experiences encountered during pre-service education and the demands, and restrictions of their teaching practice in schools. This article approaches this topic by developing an interpretative case study centered on one novice mathematics teacher, Sol. The aim is to describe and understand the development of Sol’s professional identity and agency during her first teaching year. Considering identity development as a diachronic phenomenon, we carry out a narrative analysis of the research data. The findings show that Sol developed her professional identity and agency through a process that gathered together the teaching practices possible inside her school, the positions she could negotiate as a newcomer inside the institution, and the cultural practices and discourses embodied during pre-service education. The results bring to the forefront the profound and tense interactions between the intimate and personal terrain of mathematics teachers and the social and cultural world of the schools where they work. Sol’s case also contributes to understanding the role that a robust pre-service education can play in the development of beginning teachers’ professional identities and in the possibility they could become agents of transformation in their schools.     

Teacher tensions: expectations in a professional development institute

The purpose of this study was to better understand teacher tensions in professional development. The population under study was practicing mathematics teachers engaged in a week-long professional development institute. Data sources included observations, interviews, and teacher products (such as registration forms, surveys, journals, and notebooks). The data were analyzed to determine what tensions were evident in the institute and how those tensions arose. In this paper, we examine participants’ tensions in a professional development situation when their expectations did not match reality. We have done so by presenting a theoretical model of professional development based on an instructional rhombus that illuminates the actual and applicatory aspects of teachers’ professional development experiences. The main tensions expressed by the teachers were related to the content and pedagogy of the institute. This study points toward the importance of teachers’ expectations in professional development.     

Developing mathematical thinking in the primary classroom: liberating students and teachers as learners of mathematics

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011–2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. Particular attention is given to the epistemological positioning of the researchers as this influenced both the curriculum design process and also the theoretical framing of the research study which are both described. The project was set up within a design research framework, which aimed to promote classroom-based action research on the part of participants through the course and also research by the university researchers into the process of curriculum development. The research questions focused on the teachers’ confidence, competence, attitudes and beliefs in relation to mathematics and their expectations and experiences of the impact on pupil learning arising from this course. Empirical data were drawn from pre- and post-course surveys, interviews and observations of the discussion forums in the online environment. Findings from this study highlight the way the course had a transformational and emancipatory impact on these teachers. They also highlight ways in which the ‘framing’ of particular aspects of the curriculum had an oppressive impact on learners in the ways that suppressed creativity and limited the exercise of learner autonomy. Furthermore, they highlight the ways in which a number of these teachers had experienced mathematics as a school subject in very negative ways, involving high levels of ‘symbolic violence’ and of being ‘labelled’.     

The cosmopolitan turn in Literature education and its resulting tensions in Singapore schools

ABSTRACT

In this article, I highlight the emergence of a cosmopolitan turn in Literature education as observed in teachers’ beliefs and practices in Singapore schools. Central to the cosmopolitan turn is the view that Literature education should not be disengaged from real-world connections to others particularly those who are marginalized and oppressed in the world. In the first part of this article, I describe core principles informing a cosmopolitan approach to teaching Literature that is distinct from previous movements. In the second part, I utilize case studies of Literature teachers from four secondary schools in Singapore to discuss key tensions resulting from teachers’ attempts to foster cosmopolitan sensitivities. These tensions point to the propensity for Literature education to prioritize a form of universalism that neglects the dynamic interconnections between national and global identity; to encourage a human capital approach to education where cosmopolitanism is co-opted to strategically benefit elites and to perpetuate passive rather than active cosmopolitan engagement with justice. I suggest that awareness of these tensions can enable educators to develop more holistic and ethically grounded cosmopolitan Literature education where all students can be equipped with critical and empathetic capacities to navigate diverse and conflicting values in our global age.     

Mathematics Teachers' Positions and Practices in Discourses of Assessment

Recent curriculum reforms have led to a wider variety of methods of assessment in formal 'high stakes' assessment regimes in many countries. Morgan's study of mathematics coursework assessment in UK schools identified a number of positions adopted by teachers as they assessed student texts. Using Bernstein's theoretical framework, we revisit Morgan's study in order to construct a model for understanding teachers' assessment practices and positionings. The model consists of opposing forms, generated by modelling agencies, agents, practices and specialised forms of communication, to identify their principles of construction, displayed as changes in the strength of boundary. This helps to distinguish practices of assessment as different modalities of regulation, and to understand the tensions within and between discourses and practices. Thus, for example, by interpreting tensions between discourses of 'mathematical investigation' and of 'assessment' in terms of the contradictory demands made by different modes of pedagogic practice, we can reveal the social assumptions of the pedagogic discourse.     

Contradictions,dialectical oppositions and shifts in teaching mathematics

The study reported in this paper concerns the tensions and conflicts that teachers experience while they enact a new set of reform-oriented curricular materials into their classrooms. Our focus is οn the interactions developed in two groups of teachers in two schools for a period of a school year. We use Activity Theory to study emerging contradictions and we elaborate on the construct of dialectical opposition to understand the nature of these contradictions and their potential for teacher learning. We provide evidence that discussions about contradictions and their dialectical character in the two groups support teachers to engage differently in mathematics teaching and learning and carry potentials for shifts in the practices that evolve in their classrooms. Our study addresses empirically in the context of mathematics teaching the philosophical claim about the role of contradictions as a driving force for any dynamic system.     

STUDY ON LATVIAN MATHEMATICS TEACHERS’ ESPOUSED BELIEFS ABOUT TEACHING AND LEARNING AND REPORTED PRACTICES

The aim of the research was to compare espoused beliefs about teaching and learning and reported practices for the teachers of mathematics in Latvia. The sample consisted of 390 teachers of mathematics from different regions of Latvia. The present research is a part of an international comparative research within the NorBa project (Nordic–Baltic Comparative Research in Mathematics Education) that makes use of a quantitative questionnaire for mathematics teachers. The results show that the espoused beliefs of Latvian teachers of mathematics on efficient teaching tend more to a constructivist approach, whilst reported practices are more oriented to a traditional approach; yet, there exist statistically significant differences for teachers of different social and demographical groups. The research outcomes may be used for the improvement of teacher further education programmes.     

Theory and Practice in Mathematics Teaching Development: Critical Inquiry as a Mode of Learning in Teaching

In this paper I address the challenge of developing theory in relation to the practices of mathematics teaching and its development. I do this by exploring a notion of ‘teaching as learning in practice’ through overt use of ‘inquiry’ in mathematics learning, mathematics teaching and the development of practices of teaching in communities involving teachers and educators. The roles and goals of mathematics teachers and educators in such communities are both distinct and deeply intertwined. I see an aim of inquiry in teaching to be the ‘critical alignment’ (Wenger, 1998) of teaching within the communities in which teaching takes place. Inquiry ‘as a tool’ and inquiry ‘as a way of being’ are important concepts in reflexive developmental processes in which inquiry practice leads to better understandings and development of theory.