Vince Geiger

Reshaping teacher and student roles in technology-enriched classrooms

This paper draws on data from a three-year longitudinal study of secondary school classrooms to examine pedagogical issues in using technology resources in mathematics teaching—in particular, graphics calculators and overhead projection panels that allow screen output to be viewed by the whole class. We theorise four roles for technology in relation to such teaching and learning interactions—master, servant, partner, and extension of self—and illustrate this taxonomy with observational data from five senior secondary mathematics classrooms. Our research shows how technology can facilitate collaborative inquiry during both small group interactions and whole class discussions when students use their calculators and the overhead projection panel to share their mathematical understanding.

CAS-Enabled Technologies as "Agents Provocateurs" in Teaching and Learning Mathematical Modelling in Secondary School Classrooms

This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates that CAS enabled technologies have a role to play as provocateurs of productive student-student-teacher interaction in both small group and whole class settings. Our research indicates that technologies that incorporate CAS capabilities have the potential to mediate collaborative approaches to mathematical enquiry within life-related mathematical tasks.

Technology, Communication, and Collaboration: Re-thinking Communities of Inquiry, Learning and Practice

This chapter presents an overview of the role of technology in mathematics education within the framework of social learning theories. A review of past submissions to ICMI sponsored activities over the last 20 suggests that social perspectives on teaching and learning with technology have become increasingly prevalent. A review of recent literature, such as the proceedings of ICMI 17, as well as broader research sources, adds further support to the view that there is growing interest among the mathematics education community in how digital technologies can enhance mathematics teaching and learning through attention to social aspects of coming to know and understand. Four typologies of digital technologies and their role in collaborative practice are identified: technologies designed for both mathematics and collaboration; technologies designed for mathematics; technologies designed for collaboration; and technologies designed for neither mathematics nor collaboration. As new technologies continue to be developed and refined, they offer new ways to construe communication, collaboration, and social interaction and thus change the availability and feasibility of different kinds of communities of practice. This has implications for both research and practice.

Technology Enriched Classrooms: Some Implications for Teaching Applications and Modelling

We report on a research study that investigated interactions between students, teachers, and technologies in senior secondary mathematics classrooms. Based on data from classroom observation and lesson videotapes, student interviews and questionnaires, we propose four roles for technology in relation to such interactions: master, servant, partner, and extension of self. We illustrate the roles of technology by presenting episodes from lessons that were focused around application tasks. Our analysis shows how different technologies as utilised by individual students, mediated the students’ social interactions, and were integrated into the production of mathematical arguments. Implications for the approach to applications and modelling activities are discussed.

Developing a diagnostic framework for evaluating student approaches to applied mathematics problems

In the development of innovative programmes to enhance the application skills of students a neglected population tends to be those students who have difficulty in addressing quite basic problems, but whose educational setting is prescribed by school policies such that more innovative teaching and learning environments are not available to them. This research sets out to develop a diagnostic framework that supports teaching and learning in such situations. Based on empirical research studies and on theoretical constructs of human learning a script analysis framework was developed encompassing criteria across categories of planning, monitoring, heuristic strategies, verification, knowledge resources, and beliefs. The framework represents a synthesis and extension of previous work. Two teachers worked with 47 students throughout a year in a senior secondary mathematics course geared to students intending to study mathematics at tertiary level. Data collection was limited to the type of information available ...

Curriculum Intent, Teacher Professional Development and Student Learning in Numeracy

Numeracy, or mathematical literacy as it is also known, is a major educational goal internationally, and as such, is addressed in the curriculum documents of educational jurisdictions and in national and international testing regimes. This chapter reports on an aspect of a research study which investigated the interrelationship between curriculum intent, teacher professional learning and action, and students’ perspectives on their own learning in a 12 month long research and development project. Specifically, this chapter examines the impact upon student learning as a teacher attempted to implement the numeracy requirements of a state based curriculum in an educational jurisdiction within Australia. These attempts were structured through a rich model of numeracy and supported through regular interaction with the project researchers in a collaborative partnership aimed at improving student learning outcomes in alignment with state curriculum objectives. An emergent aspect of the project is the importance of a clear model of numeracy, which outlines essential elements, to changes in a teacher’s numeracy practice. These changes in practice led to positive student views on their mathematics learning and to greater connectedness of this learning within and outside of mathematics itself.

Facilitating Mathematisation in Modelling by Beginning Modellers in Secondary School

Based on theoretical considerations, a possible means of gaining a resolution of the long standing issues of problem formulation and specification and their successful mathematisation by relatively naive modellers is proposed. This is based on empirical evidence having been provided for paradigmatic cases of the construct of implemented anticipation as proposed by Niss, that is, foreshadowing of future action projected back onto decisions about current action during ideal mathematisation. A Foreshadowing and Feedback Framework to Engage Beginning Modellers in Implemented Anticipation and its theoretical underpinnings are outlined and illustrated using empirical data.

The Role of Textbooks in Developing a Socio-critical Perspective on Mathematical Modelling in Secondary Classrooms

One approach to teaching using mathematical modelling and applications is to take a socio-critical perspective where the goal is development of a critical understanding of the world through modelling physical and social phenomena. Several curriculum documents in Australia as well as in other countries, with a modelling and applications emphasis, promote socio-critical aspects to be developed by mathematics curricula, particularly at senior secondary level. The role of modern textbook resources in promoting this development and how teachers could use these resources to mediate such a learning goal in relation to the applications of mathematics is an under researched area. This chapter interrogates curriculum documents and textbook tasks to assess the potential role of textbooks in developing this understanding in students through mathematical modelling.

A case study of effective practice in mathematics teaching and learning informed by Valsiner’s zone theory

The characteristics that typify an effective teacher of mathematics and the environments that support effective teaching practices have been a long-term focus of educational research. In this article we report on an aspect of a larger study that investigated ‘best practice’ in mathematics teaching and learning across all Australian states and territories. A case study from one Australian state was developed from data collected via classroom observations and semi-structured interviews with school leaders and teachers and analysed using Valsiner’s zone theory. A finding of the study is that ‘successful’ practice is strongly tied to school context and the cultural practices that have been developed by school leaders and teachers to optimise student learning opportunities. We illustrate such an alignment of school culture and practice through a vignette based on a case of one ‘successful’ school.

Mathematical Applications, Modelling and Technology as Windows into Industry Based Mathematical Practice

The growing importance of mathematical skills and ICTs to the workplace and industry is placing greater demand on teachers, schools and designers of curricula to find approaches to teaching and learning that facilitate the transfer of school-based mathematical knowledge to the world outside of school. This chapter explores the potential of a synergy between research in the areas of mathematical applications and modelling, numeracy, and ICTs in mathematics education, to offer the means of designing school based activities that provide\a bridge between school mathematics and the worlds beyond school.