Data-driven accountability in Australia : an unfolding story with lessons for leaders

Throughout the world, state and nation standardised testing of children, has become a "huge industry" (English, 2002). Although English is referring to the American system which has been involved in standardised testing for over half a century, the same could be said of many other countries, including Australia. It has been only in recent years that Australia has embraced national testing as part of a wider reform effort to bring about increased accountability in schooling. The results of high-stakes tests in Australia are now published in newspapers and electronically on the Australian federal government's MySchool website (www.myschoold.edu.au). MySchool provides results on the National Assessment Program - Literacy and Numeracy (NAPLAN) for students in Years 3,5, 7 and 9. Data are available that compare schools to statistically similar schools. This more recent publication of national testing results in Australia is a visible example of "contractual accountability", described by Mulford, Edmunds, Kendall, Kendall and Bishop (2008) as " the degree to which [actors] are fulfilling the expectations of particular audiences in terms of standards, outcomes and results" (p.20).

A case for addressing the literacy demands of student assessment

The development and implementation of the Australian Curriculum together with national testing of students and the publication of school results place new demands on teachers. In this article we address the importance of teachers becoming attuned to the silent assessors in assessment generally and in the National Literacy and Numeracy Program (NAPLAN) more specifically. Using the concept of literacies, we develop a method to conduct a literacy audit of assessment tasks that teachers can use to help both themselves and their students. Providing assistance to students as a consequence of such an audit is imperative to improve the outcomes for students and to address issues of equity.

Indigenous mathematics : creating an equitable learning environment

This chapter examines how a change in school leadership can successfully address competencies in complex situations and thus create a positive learning environment in which Indigenous students can excel in their learning rather than accept a culture that inhibits school improvement. Mathematics has long been an area that has failed to assist Indigenous students in improving their learning outcomes, as it is a Eurocentric subject (Rothbaum, Weisz, Pott, Miyake & Morelli, 2000, De Plevitz, 2007) and does not contextualize pedagogy with Indigenous culture and perspectives (Matthews, Cooper & Baturo, 2007). The chapter explores the work of a team of Indigenous and non-Indigenous academics from the YuMi Deadly Centre who are turning the tide on improving Indigenous mathematical outcomes in schools and in communities with high numbers of Aboriginal and Torres Strait Islander students.

Primary students' performance on map tasks : the role of context

This study investigated the longitudinal performance of 583 students on six map items that were represented in various graphic forms. Specifically, this study compared the performance of 7-9-year-olds (across Grades 2 and 3) from metropolitan and non-metropolitan locations. The results of the study revealed significant performance differences in favour of metropolitan students on two of six map tasks. Implications include the need for teachers in non-metropolitan locations to ensure that their students do not overly fixate on landmarks represented on maps but rather consider the arrangement of all elements encompassed within the graphic.

Recognising Torres Strait Islander women’s knowledges in their children’s mathematics education

This paper discusses women’s involvement in their children’s mathematics education. It does, where possible, focus Torres Strait Islander women who share the aspirations of Aborginal communities around Australia. That is, they are keen for their children to receive an education that provides them with opportunities for their present and future lives. They are also keen to have their cultures’ child learning practices recognised and respected within mainstream education. This recognition has some way to go with the language of instruction in schools written to English conventions, decontextualised and disconnected to the students’ culture, Community and home language.

Teachers’ and parents’ perspectives of digital technology in the lives of young children

The pervasiveness of technology in the 21st Century has meant that adults and children live in a society where digital devices are integral to their everyday lives and participation in society. How we communicate, learn, work, entertain ourselves, and even shop is influenced by technology. Therefore, before children begin school they are potentially exposed to a range of learning opportunities mediated by digital devices. These devices include microwaves, mobile phones, computers, and console games such as Playstations® and iPods®. In Queensland preparatory classrooms and in the homes of these children, teachers and parents support and scaffold young children’s experiences, providing them with access to a range of tools that promote learning and provide entertainment. This paper examines teachers’ and parents’ perspectives and considers whether they are techno-optimists who advocate for and promote the inclusion of digital technology, or whether they are they techno-pessimists, who prefer to exclude digital devices from young children’s everyday experiences. An exploratory, single case study design was utilised to gather data from three teachers and ten parents of children in the preparatory year. Teacher data was collected through interviews and email correspondence. Parent data was collected from questionnaires and focus groups. All parents who responded to the research invitation were mothers. The results of data analysis identified a misalignment among adults’ perspectives. Teachers were identified as techno-optimists and parents were identified as techno-pessimists with further emergent themes particular to each category being established. This is concerning because both teachers and mothers influence young children’s experiences and numeracy knowledge, thus, a shared understanding and a common commitment to supporting young children’s use of technology would be beneficial. Further research must investigate fathers’ perspectives of digital devices and the beneficial and detrimental roles that a range of digital devices, tools, and entertainment gadgets play in 21st Century children’s lives.

Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

A visual description of early-number counting, addition and subtraction knowledge

Early-number is a rich fabric of interconnected ideas that is often misunderstood and thus taught in ways that do not lead to rich understanding. In this presentation, a visual language is used to describe the organisation of this domain of knowledge. This visual language is based upon Piaget’s notion of reflective abstraction (Dubinsky, 1991; Piaget, 1977/2001), and thus captures the epistemological associations that link the problems, concepts and representations of the domain. The constructs of this visual language are introduced and then applied to the early-number domain. The introduction to this visual language may prompt reflection upon its suitability and significance to the description of other domains of knowledge. Through such a process of analysis and description, the visual language may serve as a scaffold for enhancing pedagogical content knowledge and thus ultimately improve learning outcomes.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

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.

Data modelling in the beginning school years

This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling. Some of the core components of data modelling are addressed. A selection of results from the first data modelling activity implemented during the second year (2010; second grade) of a current longitudinal study are reported. Data modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Reported here are children's abilities to identify diverse and complex attributes, sort and classify data in different ways, and create and interpret models to represent their data.

Data modeling in elementary and middle school classes : a shared experience

This paper argues for a renewed focus on statistical reasoning in the elementary school years, with opportunities for children to engage in data modeling. Data modeling involves investigations of meaningful phenomena, deciding what is worthy of attention, and then progressing to organizing, structuring, visualizing, and representing data. Reported here are some findings from a two-part activity (Baxter Brown’s Picnic and Planning a Picnic) implemented at the end of the second year of a current three-year longitudinal study (grade levels 1-3). Planning a Picnic was also implemented in a grade 7 class to provide an opportunity for the different age groups to share their products. Addressed here are the grade 2 children’s predictions for missing data in Baxter Brown’s Picnic, the questions posed and representations created by both grade levels in Planning a Picnic, and the metarepresentational competence displayed in the grade levels’ sharing of their products for Planning a Picnic.