Vincent Geiger

Transforming Professional Practice in Numeracy Teaching

The development of numeracy, sometimes known as quantitative literacy or mathematical literacy, requires students to experience using mathematics in a range of real-world contexts and in all school subjects. This chapter reports on a research study that aimed to help teachers in ten schools plan and implement numeracy strategies across the middle school curriculum. Teachers were introduced to a rich model of numeracy that gives attention to real-life contexts; application of mathematical knowledge; use of representational, physical, and digital tools; and positive dispositions towards mathematics. These elements are grounded in a critical orientation to the use of mathematics. Over one school year, the teachers worked through two action research cycles of numeracy curriculum implementation. The professional development approach included three whole-day workshops that supported teachers’ planning and evaluation and two rounds of school visits for lesson observations, teacher and student interviews, and collection of student work samples. During workshops, teachers also completed written tasks that sought information about their confidence for numeracy teaching and how they were using the numeracy model for planning. Drawing on data collected during workshops and school visits, we demonstrate how teachers’ instructional practices changed over time as they progressively engaged with the numeracy model.

A reflection on mathematical modelling and applications as a field of research : theoretical orientation and diversity

This chapter explores the nature of theoretical approaches used in research literature focusing on mathematical applications and modelling, in particular, the orientation and diversity of theoretic ...

Designing for Mathematical Applications and Modelling Tasks in Technology Rich Environments

Mathematical modelling and applications is a well-established field within mathematics education. Research in mathematical modelling and applications has maintained a focus on how to enhance students’ capabilities in using mathematics learnt in school to solve problems identified in, or derived from, the real world. While significant progress has been made in understanding the processes that underpin the successful applications of mathematics in real world contexts, there has been limited research into how to design tasks that are authentic reflections of the role of digital technologies in solving problems situated in the work place or daily life. This chapter draws on data sourced from a research and development project that investigated the use of digital technologies in teaching and learning mathematical modelling and applications to identify principles of effective task design. The instantiation of these principles within classroom practice is illustrated through a classroom vignette. This chapter concludes with a reflection on the research needed to further develop understanding of the role of technology as an enabler of principles of design for mathematical modelling tasks.

The Role of Social Aspects of Teaching and Learning in Transforming Mathematical Activity: Tools, Tasks, Individuals and Learning Communities

The purpose of this chapter is to explore how the reflexive interaction between resources, especially digital technologies and mathematical tasks and the users of these resources can lead to different types of transformation. In this exploration, Strasser’s (2009) tetrahedral model for teaching and learning mathematics, which incorporates students, teachers, mathematical knowledge and resources, will be extended by considering the social aspects of coming to know and do mathematics. Research data collected from secondary mathematics classrooms will be used to illustrate how such transformations are played out in authentic classroom settings. Finally, selected types of small-group and whole-class social interactions, as they relate to Strasser (2009) model, will be theorised.

Taking advantage of incidental school events to engage with the applications of mathematics: the case of surviving the reconstruction

This paper reports on one aspect of a 2 year research and development project aimed at enhancing primary and secondary teachers’ instructional practices in numeracy. The project made use of Goos’ model of numeracy as a basis for assisting teachers to plan for teaching and also to reflect upon the effectiveness of their practice. As part of the project, teachers were challenged to develop learning experiences which were relevant to their own students’ lived-in worlds. One teacher took advantage of a major, potentially disruptive, building development within her school to design a sequence of lessons in which students were challenged to adapt to the changes that were associated with the construction. The chapter concludes by discussing the changes to the teacher’s disposition towards incorporating events from the students’ lived-in worlds into her teaching practice.

Strässer’s Didactic Tetrahedron as a Basis for Theorising Mathematical Modelling Activity Within Social Contexts

This chapter considers the potential of Strasser’s tetrahedral model for teaching and learning mathematics as a means for examining the activity and/or roles of students, teachers, mathematical knowledge and artefacts during engagement with mathematical applications and modelling. Research data, collected from mathematics classrooms, will be used to illustrate how the interactions and transformations that are part of this activity are played out in authentic classroom settings.

Transformations of teaching and learning through digital technologies

This chapter is a critical synthesis of research related to the transformations that take place when digital technologies are incorporated into teaching and learning practices. In developing this synthesis, research from all levels of education was reviewed with a focus on the opportunities digital technologies offer for cognitive, pedagogical, affective and professional change. The chapter is structured in alignment with Pierce and Stacey’s (Pierce and Stacey, Int J Comput Math Learn 15(1):1–20 2010) map of pedagogical opportunities in which three dimensions for educational transformation were identified: tasks, classroom, and subject. A discussion of future directions for research into technology enhanced mathematics education concludes the review.

Early Shared Reading, Socioeconomic Status, and Children’s Cognitive and School Competencies: Six Years of Longitudinal Evidence

ABSTRACT This study explored longitudinal associations between early shared reading at 2 to 3 years of age and children’s later academic achievement. It examined the mediating role of children’s vocabulary and early academic skills, and the moderating effects of family’s socioeconomic status. Data were drawn from the Longitudinal Study of Australian Children (n = 4,768). Academic achievement was assessed at 8 to 9 years of age via standardized national test scores of literacy and mathematics achievement. Results indicated that early shared reading was associated with children’s academic achievement directly and indirectly through receptive vocabulary and early academic skills. Also, the frequency of early shared reading predicted the outcome measures, over and above other home learning activities. Associations were stronger among low and middle socioeconomic status groups compared to the high socioeconomic status group. We conclude that shared reading offers unique opportunities for adults to teach young children new words and concepts.

Exploring the Notion of Mathematical Literacy in Curricula Documents

The notion of mathematical literacy has gained momentum internationally recently through the influence of international assessment regimes such as the Programme of International Student Assessment (PISA) and national concerns about the ability of citizens to use mathematics effectively in personal, civic and work life. Accordingly, it is to be expected that these concerns should be reflected in relevant curriculum documents. This chapter presents a content analysis of a sample of 12 national curriculum documents in relation to mathematical literacy. The analysis shows that there does not appear to be general agreement about the definition of mathematical literacy within the analysed documents and that the idea of mathematical literacy is represented in a limited fashion.

Teacher Professional Development on Mathematical Modelling: Initial Perspectives from Singapore

In this chapter, I will provide commentary on the symposium dedicated to teacher professional development on mathematical modelling in Singapore which was based on papers by: Chan, Teacher professional development on mathematical modelling: Conceptions of mathematical modelling; Lee, Initial perspectives from Singapore: Problem posing and task design; and Ng, Teacher professional development on mathematical modelling: Facilitation and scaffolding. Across these three themes emerge – the importance for teachers to understand the nature of mathematical modelling; the need to acknowledge the interconnection between teaching, learning and assessment; and the influence of teacher dispositions toward designing modelling tasks. I conclude this commentary by offering observations on the research designs employed in these studies.