Tom Lowrie’s research while affiliated with University of Canberra and other places

Although spatial reasoning is developed through interaction with the real world, many studies focus on abstract spatial skills which exhibit a moderate relationship with real-world skills. In the present study, we explore links between middle-school student performance on abstract and authentic spatial tasks. Thirty students from three geographically diverse settings demonstrated their perspective-taking skills with local landmarks and how these relate to an abstract perspective-taking task. Rural and regional students demonstrated accurate estimations for landmark locations relative to urban students. The use of spatial tools such as gesture, language, and spatial relations were analyzed to explore student processing during the task. Our findings suggest that the connection between abstract and authentic tasks is not always straight-forward. Students from rural and regional areas demonstrated robust knowledge of their local environment with evidence for meaningful connections embedded in sociocultural and geographic experiences. By contrast, more urban students were able to apply sound spatial strategies when completing the abstract task but struggled to apply these strategies without the local knowledge or awareness of their position in space. We propose that often-neglected authentic spatial tasks assess a different, but critical element of spatial skills needed for navigating the world around us.

This investigation examined the strategies students employ to solve graphic and non-graphic mathematics tasks. The students’ strategies were classified in terms of representation, specifically whether or not they used self-decoded diagrams to solve the tasks. The study involved 1187 Grade 6 students (from Singapore and Australia) solving graphic- and non-graphic mathematics tasks typically encountered in national tests. Data from these students provided solution strategies to mathematics problems; the strategies were classified as diagrammatic or analytic solutions. Data analysis was confirmatory in nature, which sought to analyze students’ solutions to understand more fully the extent to which task representation relates to task difficulty, understanding and success. There was a strong association between task success and representation for items with moderate level of difficulty—with the employment of diagrammatic solutions more likely to lead to correct solutions.

Technological pedagogical content knowledge (TPACK) has been well accepted as a framework to understand and describe types of knowledge required by teachers to teach specific content with technology effectively. However, limited studies have used the framework in analysing the complexity of technology integration in mathematics classrooms. This study investigates, through examining critical instructional events, the most influential TPACK constructs in understanding and shaping teachers’ pedagogical practices using digital technology. This case study was conducted in an early secondary mathematics classroom in Indonesia that used a web-based resource to support students’ understanding of fractions. The finding suggests that the qualitative examination of the four intersected TPACK constructs assists in understanding the challenges and the opportunities to teachers when utilising an exploratory-based technology. It demonstrates that the combination of pedagogical stances and choice of technology significantly influence the visibility of other TPACK constructs. Implications of this study include the need of thoughtful planning prior to using web-based resources and the importance to utilise critical events in developing and assessing teachers’ TPACK.

Advances in technology have blurred the boundary between representing shapes and objects in two and three dimensions. Similarly, the capacity to translate and transform shapes and objects has moved beyond static and concrete form to representations that are increasingly dynamic and animated. This chapter describes young children’s engagement with digital games as they interpret and navigate information using numeracy understandings and mathematics knowledge. In particular, the chapter highlights case studies of gamers utilising visuospatial reasoning as they solve problems in environments which require high levels of decoding. The chapter is underpinned by the notion that the embodied game space (i.e., the inside and outside space of the game environment) captures the interplay between how mathematics content is represented and the game’s architecture space. This multifaceted and multimodal access to information requires quite different demands than the mathematics encountered by students in typical classroom contexts. Games used by children in the case studies include Pokémon, Prince of Persia and The Legend of Zelda: Phantom Hourglass.

This investigation explored pre-service teachers’ mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is acquired; and (3) the applicability of mathematics. These factors were used in subsequent multivariate analyses to determine whether teachers’ mathematics competence influenced their personal mathematics viewpoints and perspectives. There was no difference between those students who had studied advanced and standard mathematics at school on the three belief and attitude measures, despite distinct differences in their MCK.

This is the first time a chapter has been dedicated solely to assessment in MERGA's four yearly review. This fact, and the emerging status of assessment in Australia's educational research domain, dictates the structure and nature of the chapter. In previous reviews, assessment (as a process) was classified within student performance in the classroom and reflections on teachers' practices. Consequently, research about assessment was distributed across content chapters. However, we anticipate that such a chapter will have prominence in reviews to come. Indeed, Callingham's (2011b) keynote paper from the 34th annual MERGA conference argued for a need to re-assess mathematics assessment "and to reconsider the purpose, nature and use of assessment information" (p. 3). Hence, a chapter in this review is timely.

This paper outlines new educational policy initiatives that have been recently introduced to Australian schooling contexts and describes the challenges of providing rich and empowering professional development opportunities for classroom teachers and educational leaders in an era of heightened accountability and change. A framework for large-scale professional learning is proposed; one that adopts a theoretical lens associated with practice architectures, situated within community- and individual-focused professional learning experiences. The theoretical component of the model has been utilised effectively in a number of countries, while the personalised learning component is drawn from an evidence-based project that established a national learning framework.

p>A survey ( n = 410) revealed statistically significant gender differences between middle school students' preference for playing particular types of games. Subsequent instrumental case studies theorised the "within-game" and "out-of-game" experiences of two middle school students as they played a digital hand-held game. These two case studies comprised stimulated recall sessions and subsequent follow-up, open-ended interviews. The analysis described the influence digital game playing can have on a participant's mathematics sense making. Findings included distinct differences in both the approach and the strategies employed by the respective participants to not only engage with the game, but contextualise it within their own knowledge and experiences. Furthermore, the study demonstrated the extent to which game playing can be a catalyst for further learning outside the game experience. <br /