An exploration of young students' ability to generalise function tasks

The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focusing on the identifications, prediction and justification of function rules. It reports on students' attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture that there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.

An evaluation of the pattern and structure mathematics awareness program in the early school years

This paper reports a 2-year longitudinal study on the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on students’ mathematical development. The study involved 316 Kindergarten students in 17 classes from four schools in Sydney and Brisbane. The development of the PASA assessment interview and scale are presented. The intervention program provided explicit instruction in mathematical pattern and structure that enhanced the development of students’ spatial structuring, multiplicative reasoning, and emergent generalisations. This paper presents the initial findings of the impact of the PASMAP and illustrates students’ structural development.

Developing the Pattern and Structure Assessment (PASA) interview to inform early mathematics learning

The Pattern and Structure Mathematical Awareness Program(PASMAP) stems from a 2-year longitudinal study on students’ early mathematical development. The paper outlines the interview assessment the Pattern and Structure Assessment(PASA) designed to describe students’ awareness of mathematical pattern and structure across a range of concepts. An overview of students’ performance across items and descriptions of their structural development are described.

Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

Career decision making among gifted students : the mediation of teachers

There is international concern about falling enrollments in higher education, particularly the sciences, by gifted students. In this mixed method study, the top performing 200 students (approximately 1%) within a particular education jurisdiction at the beginning of their first year at university were surveyed and 20 interviewed about their school experiences using a biographical interpretive design. This study focussed on identifying those characteristics of teachers which supported students’ interests. Participants identified seven characteristics of teachers that students identified as supportive of their potential career pathways. These included connecting pedagogical practices with student interests, being passionate about their subject matter, having good content knowledge, making learning experiences relevant, setting high expectations of students, being a good explainer of complex ideas, and being a good classroom manager. This study extends our knowledge of how teachers influence gifted students and has implications for both pre-service and in-service teacher education and career counselling.

Stepping Stones A world-Class Mathematics program for the Australian Curriculum Year 1 (Student Journal)

ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals. This uniquely interactive program allows students to participate in exciting learning activites whilst still allowing the teacher to maintain control of learning outcomes. It is the first program in Australia to give teachers activities to differentiate instruction within each lesson and across school years. Written by a team of Australia's leading mathematics educators, this program integrates key research findings in a practical sequence of modules and lessons providing schools with a step-by-step approach to the new curriculum. Click links on the right to explore the program.

Communities of practice : building organisational capability through an undergraduate assurance of learning program

This study explores academic perceptions of organizational capability and culture following a project to develop a quality assurance of learning program in a business school. In the project a community of practice structure was established to include academics in the development of an embedded, direct assurance of learning program affecting more than 5000 undergraduate students and 250 academics from nine different disciplines across four discipline based departments. The primary outcome from the newly developed and implemented assurance of learning program was the five year accreditation of the business school’s programs by two international accrediting bodies, EQUIS and AACSB. This study explores a different outcome, namely perceptions of organizational culture and individual capabilities as academics worked together in teaching teams and communities. This study uses a survey and interviews with academics involved, through a retrospective panel design consisting of an experimental group and a control group. Results offer insights into communities of practice as a means of encouraging new individual and organizational capability and strategic culture adaptation.

Data modelling with first-grade students

This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling. Results are reported from the first year of a 3-year longitudinal study in which three classes of first-grade children (6-year-olds) and their teachers engaged in data modelling activities. The theme of Looking after our Environment, part of the children’s science curriculum, provided the task context. The goals for the two activities addressed here included engaging children in core components of data modelling, namely, selecting attributes, structuring and representing data, identifying variation in data, and making predictions from given data. Results include the various ways in which children represented and re represented collected data, including attribute selection, and the metarepresentational competence they displayed in doing so. The “data lenses” through which the children dealt with informal inference (variation and prediction) are also reported.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

Teachers' conceptions of how to engage students through inquiry learning : foundations for STEM

The advocacy for inquiry-based learning in contemporary curricula assumes the principle that students learn in their own way by drawing on direct experience fostered by the teacher. That students should be able to discover answers themselves through active engagement with new experiences was central to the thinking of eminent educators such as Pestalozzi, Dewey and Montessori. However, even after many years of research and practice, inquiry learning as a referent for teaching still struggles to find expression in the average teachers' pedagogy. This study drew on interview data from 20 primary teachers. A phenomenographic analysis revealed three conceptions of teaching that support inquiry learning in science in the primary years of schooling: (a) The Experience-centred conception where teachers focused on providing interesting sensory experiences to students; (b) The Problem-centred conception where teachers focused on challenging students with engaging problems; and (c) The Question-centred conception where teachers focused on helping students to ask and answer their own questions. Understanding teachers' conceptions of teaching has implications for both the enactment of inquiry teaching in the classroom as well as the uptake of new teaching behaviours during professional development, with enhanced outcomes for engaging students in STEM.

Reading students’ representations

Students’ text, symbols, and graphics give teachers a glimpse into mathematical thinking associated with investigating the Peas problem.

Work-integrated learning as a component of the capstone experience in undergraduate law

There is currently little guidance in the Australian literature in relation to how to design an effective capstone experience. As a result, universities often fail to provide students with a genuine culminating experience in the final year of their degree. This paper will consider the key objectives of capstone experiences – closure and transition – and will examine how these objectives can be met by a work-integrated learning (WIL) experience. This paper presents an argument for the inclusion of WIL as a component of a capstone experience. WIL is consistent with capstone objectives in focusing on the transition to professional practice. However, the capacity of WIL to meet all of the objectives of capstones may be limited. The paper posits that while WIL should be considered as a potential component of a capstone experience, educators should ensure that WIL is not equated with a capstone experience unless it is carefully designed to ensure that all the objectives of capstones are met.

On becoming an undergraduate : transition to university

This paper investigates the first year experience of undergraduates with a view to discovering some of the factors which determine a successful negotiation of the transitional phase. The paper begins with a theoretical framework of transition based on the three models of Van Gennep (1960), Viney (1980) and Tinto (1987) and applied to the educational transition from school to University. A new model of transition is presented which looks at the relationship between social and academic adjustment of students to university over time.

Supporting exceptional students to thrive mathematically

Providing an appropriate education for exceptional students in mathematics is mandated in educational policy in Australasia (Australian Curriculum, Assessment and Reporting Agency (ACARA), 2010; Ministry of Education, 2009, 2011) but a challenge for teachers and schools. ‘Exceptional students’ refer to two distinct populations, namely those who are gifted in mathematics and have the capability to perform very highly compared to age peers and those who experience learning difficulties in mathematics and may underperform (Diezmann, Lowrie, Bicknell, Faragher, & Putt, 2004).