Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

A sociocultural analysis of learning to teach

This paper addresses the question of how teachers learn from experience during their pre-service course and early years of teaching. It outlines a theoretical framework that may help us better understand how teachers' professional identities emerge in practice. The framework adapts Vygotsky's Zone of Proximal Development, and Valsiner's Zone of Free Movement and Zone of Promoted Action, to the field of teacher education. The framework is used to analyse the pre-service and initial professional experiences of a novice secondary mathematics teacher in integrating computer and graphics calculator technologies into his classroom practice. (Contains 1 figure.) [For complete proceedings, see ED496848.]

Bridging the gap between tertiary education and work : a model of situated learning in accountancy

In professions such as teaching, health sciences (medicine, nursing, allied health), and built environment (engineering), significant work-based learning through practica is an essential element before graduation. However, there is no such requirement in Accountancy. This thesis reports the findings of a qualitative case study of the development and implementation of a Workplace Learning Experience Program in Accountancy at the Queensland University of Technology (QUT) in Australia. The case study of this intervention, based on sociocultural learning theory, provides the grounds for the development of a new model of teaching and learning for accounting education. The survey and interview-based study documents the responses of two cohorts of university students and a group of employers to a work placement program. The study demonstrates that a 100 hour work placement in Accountancy has elements that enhance student learning. It demonstrates the potential value of the application of sociocultural theories of learning, especially the concept of situated learning involving legitimate peripheral participation (Lave & Wenger, 1991). This research establishes the theoretical base for a paradigm shift for the Accountancy profession to acknowledge work placements prior to graduation as a major element of learning. It is argued that the current model of accounting education requires reform to better align university and workplace learning.

Building bridges to participation : sociocultural case studies of AfL

Assessment for Learning(AfL) case studies in a North Queensland school highlight the significance of the teacher-student relationship in creating a supportive culture within which students can negotiate new learner identities. AfL practices are school based evaluative practices that occur within the regular flow of teaching and learning with the purpose of informing and improving student learning to enhance learner autonomy. The identity of an autonomous learner is socially negotiated through participation in the community of practice of the class. Underpinned by a sociocultural perspective this research shows how AfL is manifested in action in its complexity and how positive teacher-student interactions can build bridges for students to move towards full participation.

An exploratory investigation of the practice of assessment for learning in Vietnamese higher education: Three case studies of lecturers' practice

In response to limited research conducted on the practice of assessment for learning (AfL) in higher education and in Asian educational settings, this qualitative study, using sociocultural theories of learning and a multiple case study approach, investigates how AfL was implemented by three lecturers in one Vietnamese university. Findings revealed that the lecturers engaged with AfL principles and practices to some extent. However, despite the lecturers' significant efforts, Vietnamese sociocultural factors such as respect for harmony, hierarchy, and examination-oriented learning, impacted on their practice of AfL. This study therefore argues that AfL requires adaptation for it to be effective in the Vietnamese tertiary context.

Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.

Building learning communities to support beginning teachers use of technology

This paper reports on the early stages of a three year study that is investigating the impact of a technology-enriched teacher education program on beginning teachers' integration of computers, graphics calculators, and the internet into secondary school mathematics classrooms. Whereas much of the existing research on the role of technology in mathematics learning has been concerned with effects on curriculum content or student learning, less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers' professional learning in the context of specific classroom and school environments. Our research applies sociocultural theories of learning to consider how beginning teachers are initiated into a collaborative professional community featuring both web-based and face to face interaction, and how participation in such a community shapes their pedagogical beliefs and practices. The aim of this paper is to analyse processes through which the emerging community was established and sustained during the first year of the study. We examine features of this community in terms of identity formation, shifts in values and beliefs, and interaction patterns revealed in bulletin board discussion between students and lecturers.

Learning in the third space : a sociocultural perspective on learning with analogies

Research on analogies in science education has focussed on student interpretation of teacher and textbook analogies, psychological aspects of learning with analogies and structured approaches for teaching with analogies. Few studies have investigated how analogies might be pivotal in students’ growing participation in chemical discourse. To study analogies in this way requires a sociocultural perspective on learning that focuses on ways in which language, signs, symbols and practices mediate participation in chemical discourse. This study reports research findings from a teacher-research study of two analogy-writing activities in a chemistry class. The study began with a theoretical model, Third Space, which informed analyses and interpretation of data. Third Space was operationalized into two sub-constructs called Dialogical Interactions and Hybrid Discourses. The aims of this study were to investigate sociocultural aspects of learning chemistry with analogies in order to identify classroom activities where students generate Dialogical Interactions and Hybrid Discourses, and to refine the operationalization of Third Space. These aims were addressed through three research questions. The research questions were studied through an instrumental case study design. The study was conducted in my Year 11 chemistry class at City State High School for the duration of one Semester. Data were generated through a range of data collection methods and analysed through discourse analysis using the Dialogical Interactions and Hybrid Discourse sub-constructs as coding categories. Results indicated that student interactions differed between analogical activities and mathematical problem-solving activities. Specifically, students drew on discourses other than school chemical discourse to construct analogies and their growing participation in chemical discourse was tracked using the Third Space model as an interpretive lens. Results of this study led to modification of the theoretical model adopted at the beginning of the study to a new model called Merged Discourse. Merged Discourse represents the mutual relationship that formed during analogical activities between the Analog Discourse and the Target Discourse. This model can be used for interpreting and analysing classroom discourse centred on analogical activities from sociocultural perspectives. That is, it can be used to code classroom discourse to reveal students’ growing participation with chemical (or scientific) discourse consistent with sociocultural perspectives on learning.

Developing shared understandings of standards-based assessment : online moderation practices across geographically diverse contexts

This thesis investigates the place of online moderation in supporting teachers to work in a system of standards-based assessment. The participants of the study were fifty middle school teachers who met online with the aim of developing consistency in their judgement decisions. Data were gathered through observation of the online meetings, interviews, surveys and the collection of artefacts. The data were viewed and analysed through sociocultural theories of learning and sociocultural theories of technology, and demonstrates how utilising these theories can add depth to understanding the added complexity of developing shared meaning of standards in an online context. The findings contribute to current understanding of standards-based assessment by examining the social moderation process as it acts to increase the reliability of judgements that are made within a standards framework. Specifically, the study investigates the opportunities afforded by conducting social moderation practices in a synchronous online context. The study explicates how the technology affects the negotiation of judgements and the development of shared meanings of assessment standards, while demonstrating how involvement in online moderation discussions can support teachers to become and belong within a practice of standards-based assessment. This research responds to a growing international interest in standards-based assessment and the use of social moderation to develop consistency in judgement decisions. Online moderation is a new practice to address these concerns on a systemic basis.

The development of teacher assessment identity through participation in online moderation

Teachers’ professional conversations regarding the qualities evidenced in student work provide opportunities to develop a shared understanding of achievement standards. This research investigates social moderation conducted in a synchronous online mode as a specific form of professional conversation. The discussion considers the different factors that influenced these conversations which included the technologic medium of the meeting. The focus of the discussion is how participation in online moderation can support teachers to develop an assessment identity as one who works within a standards-based assessment system. Qualitative data were gathered from middle school teachers from different year levels, in different curriculum areas, in diverse geographic locations, and in a range of sociocultural contexts within Queensland, Australia. Analysis of the data through a sociocultural lens of becoming suggests that participation in online moderation, while challenging for teachers, can also provide opportunities to construct and to negotiate an identity as an assessor of student work.

Sociocultural affordances of online peer engagement

University learning increasingly includes online learning experiences embedded within teaching with the dual policy intentions of increasing flexibility and learner engagement. In this research project, three university lecturers from different teaching contexts selected technologies for online learning to enhance learner engagement by encouraging peer learning. A sociocultural view of learning was used to conceptualise the technological and social affordances that might enable student peer participation and engagement. The research explored the question: “What are the benefits and barriers experienced by students engaging in online peer collaboration?” Students reported benefits including a sense of belonging that enhanced motivation, and professional identity. This article also reports on some of the challenges for students and University academics when engaging in online learning communities.

Bridging the gap between tertiary education and work : situated learning in accountancy

In professions such as teaching, health sciences (medicine, nursing), and built environment, significant work-based learning through practica is an essential element before graduation. However, there is no such requirement in professional accounting education. This paper reports the findings of an exploratory qualitative case study of the implementation of a Workplace Learning Experience Program in Accountancy at the Queensland University of Technology (QUT) in Australia. The interview-based study documents the responses of university students and graduates to this program. The study demonstrates that a 100 hour work placement in Accountancy can enhance student learning. It highlights the potential value of the application of sociocultural theories of learning, especially the concept of situated learning involving legitimate peripheral participation (Lave and Wenger 1991). This research adds to a small body of empirical accounting education literature relating to the benefits of work placements prior to graduation. The effectiveness of this short, for credit, unpaid program should encourage other universities to implement a similar work placement program as a form of pre-graduation learning in professional accounting education.