Glenda Anthony

The Teacher's Role in Classroom Discourse: A Review of Recent Research Into Mathematics Classrooms

Current curriculum initiatives in mathematics call for the development of classroom communities that take communication about mathematics as a central focus. In these proposals, mathematical discourse involving explanation, argumentation, and defense of mathematical ideas becomes a defining feature of a quality classroom experience. In this article, the authors provide a comprehensive and critical review of what it is that mathematics teachers actually do to deal with classroom discourse. Synthesizing the literature around a number of key themes, the authors critically assess the kinds of human infrastructure that promote mathematical discourse in the classroom and that allow students to achieve desirable outcomes. From the findings, they conclude with implications for teachers.

The Learner’s Perspective Study

Learning environments are never identical. Research findings from the Learner’s Perspective Study (LPS) affirm just how “culturally-situated are the practices of classrooms around the world and the extent to which students are collaborators with the teacher, complicit in the development and enactment of patterns of participation that reflect individual, societal and cultural priorities and associated value systems” (Clarke, Emanuelsson, Jablonka, & Mok, 2006, p. 1). In this book we attend closely to this collaboration with our focus on the voice of the student.

Mathematics education in the early years: Building bridges

Aligned with the enhanced international commitment to early childhood education, recognition of the importance of providing young children with opportunities to develop mathematical understandings and skills is increasing. While there is much research about effective mathematics pedagogy in the school sector, less research activity is evident within the early childhood sector. Focused on people, relationships and the learning environment, this article draws on a synthesis of research on effective pedagogical practices to describe effective learning communities that can enhance the development of young childrens mathematical identities and competencies. Concerned that the wider synthesis noted limited cross-sector collaboration within the mathematics education community, this article aims to act as a bridge for researchers currently working within the preschool and school sectors. The authors argue that understandings of effective pedagogies that enhance young childrens mathematics learning will benefit from more cross-sector research studies.

When mathematics students fail to use appropriate learning strategies

Both research findings and curriculum documents support and promote the use of learning strategies as a significant factor in successful mathematics learning. However, despite such promotion, it appears that presently many senior students’ learning behaviours are of a passive, dependent nature rather than an active, self-regulated nature. Without appropriate strategic learning behaviours students will be ill-equipped to cope with the high cognitive demands of a constructivist learning environment. Based on an examination of students’ awareness and applications of learning strategies this paper identifies five possible reasons for students’ failure to use appropriate learning strategies. Findings highlight the need for the learning environment to support, in active ways, the development and use of strategic learning behaviours.

Student voice in mathematics classrooms around the world

The Learner’s Perspective Study ascribes to the premise that the investigation of social practice within the mathematics classrooms must attend to the learners’ practice with at least the same priority as that accorded to the teachers’ practice. In focusing on student voice within this partnership, as enacted in many different guises across different cultures and socio-political learning environments, we hope that we will be better informed to understand the relationship between pedagogy and learning mathematics, and between pedagogy and the empowerment of diverse learners.

The professional education and development of prospective teachers of mathematics

This critical review of Australasian research on the professional education of prospective teachers of mathematics, presented or published in the period from 2008-2011, covers a period in which teacher education has undergone ‘dynamic reform’ at a global level (Tatto, Lerman, & Novotna, 2010). In Australasia, teacher education programs have experienced a range of systemic, political, social, and economic pressures that have led to modifications in program and curricula structures and increased performativity requirements. These pressures are fuelled by the widespread belief that “improvements in student learning depend on substantial, large-scale changes in how we prepare and support teachers” (Ball & Forzani, 2009, p. 497). The motivating force behind this attention is the claim that teachers are ‘key’ to students’ opportunities to learn mathematics. In creating these opportunities to learn mathematics it is clear that “what mathematics teachers know, care about, and do is a product of their experiences and socialisation both prior to and after entering teaching, together with the impact of their professional education” (Even & Ball, 2009, p. 1). It is the experiences and socialisation associated with the education of prospective teachers of mathematics—the pre- service and induction phase—that are the focus of attention in this chapter.

Challenges, Reforms, and Learning in Initial Teacher Education

This critical review of Australasian research concerns initial teacher education published in the period 2012–2015. The contribution to the field is organised into four broad areas: (a) research on teacher preparation: accountability, effectiveness, and policies; (b) research on teacher preparation for the knowledge society, which forms the bulk of the reviewed research; (c) research on teacher preparation for diversity; and (d) research focused on the work of teacher educators. Situated within educational settings that are undergoing continuous change and politicised attention, we note, in particular, research efforts to critically explore, design, and trial pedagogies, tasks, and partnerships associated with occasioning productive learning opportunities for prospective teachers to learn both the knowledge and the core practices of ambitious teaching.

The use of questions within in-the-moment coaching in initial mathematics teacher education: enhancing participation, reflection, and co-construction in rehearsals of practice

ABSTRACT Managing mathematical discussion is known to be challenging for novice teachers. Coaching within student teacher rehearsals of teaching has been shown to develop mathematics teaching practice, but can be time consuming. To examine how coaching using questions could assist novice teachers to promote mathematical thinking and discussions within time-constrained programmes, videos of rehearsals, reflective debriefs, and student teacher surveys were collected across a range of courses over 4 years. Findings included that student teacher roles in rehearsals were enhanced through coaching with questions and co-construction was enabled. Coaching questions exposed effective practice, particularly in relation to orchestrating mathematical discussion, enabling student teachers to reflect, discuss, make decisions, and immediately trial teaching strategies. Questions appeared to lengthen rehearsals but improved their effectiveness through enhancing participation and enabling co-construction of meaning. Findings indicate that questions used in coaching of rehearsals inform and empower novice teachers, essential factors within initial teacher education for equitable and ambitious mathematics teaching.

Solving Linear Equations

Concerted efforts at improving student performance in algebra demonstrate that “children throughout the elementary grades are capable of learning powerful unifying ideas of mathematics that are the foundation of both arithmetic and algebra” (Carpenter, Franke, & Levi, 2003, p. xi). In New Zealand, Britt and Irwin’s (2005) investigation of the Numeracy Development Project found that those students who acquired flexibility in using a range of general arithmetical strategies also developed the ability to express the structure of those strategies in symbolic forms.

Student Perceptions of the ‘Good’ Teacher and ‘Good’ Learner in New Zealand Classrooms

What constitutes ‘good’ teaching and ‘good’ learning is a complex and controversial issue. Educational agencies in New Zealand, like those in other western countries, have called for synthesis of research evidence (see Anthony & Walshaw, 2007; Stanley, 2008; Ingvarson, Beavis, Bishop, Peck, & Elsworth, 2004; National Mathematics Advisory Panel, 2008; Sullivan, 2011) to inform policy and professional development initiatives aimed at improving the quality of teaching and learning outcomes.