The role of affordances in children’s learning performance and efficiency when using virtual manipulative mathematics touch-screen apps

This paper focuses on understanding the role that affordances played in children’s learning performance and efficiency during clinical interviews of their interactions with mathematics apps on touch-screen devices. One hundred children, ages 3 to 8, each used six different virtual manipulative mathematics apps during 30–40-min interviews. The study used a convergent mixed methods design, in which quantitative and qualitative data were collected concurrently to answer the research questions (Creswell and Plano Clark 2011). Videos were used to capture each child’s interactions with the virtual manipulative mathematics apps, document learning performance and efficiency, and record children’s interactions with the affordances within the apps. Quantitized video data answered the research question on differences in children’s learning performance and efficiency between pre- and post-assessments. A Wilcoxon matched pairs signed-rank test was used to explore these data. Qualitative video data was used to identify affordance access by children when using each app, identifying 95 potential helping and hindering affordances among the 18 apps. The results showed that there were changes in children’s learning performance and efficiency when children accessed a helping or a hindering affordance. Helping affordances were more likely to be accessed by children who progressed between the pre- and post-assessments, and the same affordances had helping and hindering effects for different children. These results have important implications for the design of virtual manipulative mathematics learning apps

A matter of justice

The Aboriginal 'Embassy' on the lawns outside Parliament House, Canberra, was a striking symbol of the dissatisfaction many Aborigines feel with the justice they receive under the white man's law. This book demonstrates how that justice discriminates against Aboriginal Australians. Dr Rowley discusses typical situations - the plight of the Aboriginal employee on the northern cattle stations, the fringe dwellers round country towns, those living in the cities and those still on managed reserves. He examines the question of land rights, and the failure of the white institutions to offer justice to Aborigines. The book ends with a discussion of the role of bureaucracy in Aboriginal administration and of the opportunities which could be offered to Aborigines through new institutions. In A Matter of Justice the author's knowledge and understanding of Aborigines and their problems reveals a compassion and humanity towards Aboriginal people all too rare among white Australians

Applying the modification of attributes, affordances, abilities, and distance for learning framework to a child's multi-touch interactions with an idealized number line

Technologies such as touchscreen apps are increasingly popular in mathematics education. Researchers have begun to investigate children's interactions with the apps, outcomes of using apps, and the characteristics that contribute to outcomes. This study applies the Modification of Attributes, Affordances, Abilities, and Distance (MAAAD) for Learning Framework to an 11 year-old child's interactions with the mathematics app Motion Math: Zoom to evaluate the outcomes, contributors, and interactions. This framework accounts for relationships among attributes, affordance-ability relationships, and distance involved in interactions. Interacting with Motion Math: Zoom involves using multi-touch gestures to navigate an idealized number line with changeable interval scales. Findings indicate that the framework can contribute to research on the outcomes, contributors, and interactions, as well as linking the three

Virtual manipulatives and students’ counterexamples during proving

Counterexamples play a crucial role in the disciplinary practice of mathematics, and experiences with their use can enhance students’ engagement with mathematical practice and their learning of mathematical content. Although it is known that students encounter difficulties in producing and addressing counterexamples, and while there is evidence that incorporating appropriate computer technology into classroom tasks can improve the student experience, task design focusing on counterexamples is scarce in mathematics education research. In this chapter, we address such matters by employing a framework for research on computer-based virtual manipulatives to re-examine tasks that were designed using a set of design principles that included a key role for a dynamic geometry environment. Our analysis shows that the tasks, which were originally based on our theory-informed design principles, are further supported with the conceptual framework on virtual manipulatives. We also provide an empirical illustration of the affordances of the tasks with a task-based interview where undergraduate students successfully discovered and addressed counterexamples. An implication for mathematics education research is the importance of ensuring that task design is considered from various theoretical and conceptual perspectives in order to strengthen the theoretical underpinnings of the task design