'You do the math': Mathletics and the play of online learning

The New Zealand Annual Review of Education, 2021

Internet access and the availability of digital devices in the classroom have grown exponentially. Correspondingly, we have online platforms for learning mathematics that are subscription-based and available for schools or individuals to purchase. Research in mathematics education tends to focus on the benefits to teaching and learning afforded by digital technology, while less attention is given to the implications of having commercial applications in our mathematics classrooms, and their considerable cost. This paper reports on a study of online mathematics instructional programmes in primary schools of New Zealand. Data sources include a survey sent to mathematics leaders of all primary schools, and a discursive analysis of the websites of the most commonly used instructional programmes. There was an obvious similarity found between the promises of the websites and the rationales expressed by school leaders for using the programmes, suggesting that schools are succumbing to the seductive promises of these commercial programmes. It is argued that we need to further examine the implications of using such programmes in our mathematics classrooms, especially in the context of profit-making inside public education.

International Group for the Psychology of Mathematics Education, 2013

This paper details a framework for evaluating the potential of particular forms of technology for supporting student engagement with mathematics. I propose that, focusing on the strength of affordances to engage in particular ways allows us to begin to build an analytic frame that serves two purposes: (1) to begin to document learning as an interaction with larger bodies of data; and (2) to make and evaluate conjectures about the potential of different technologies for supporting high quality engagement with mathematics. I describe design iterations from previous work that leveraged this framework as an example of how this framework could be used and why it has proven to be valuable.

Learning technologies are commonly viewed as assisting student learning within a traditional educational context without considering vital elements such as student engagement, motivation, enjoyment and their informal, free-time learning. The name "learning technology" is therefore often something of a misnomer. This paper proposes a different way of thinking about learning technologies in the context of mathematics at the school-university transition by focusing on environments which facilitate curriculum-based learning from the perspective of student enjoyment and free-time activity. Two such "innate" learning technologies are described, namely robotics combined with an integrated computer algebra and dynamic geometry software package, and an internet-based mathematical gaming website. The evaluation of learning experiences with these technologies is explored. Conclusions are drawn about the design and deployment of innate learning technologies.

Springer eBooks, 2012

In this chapter we offer a case study of an online Mathematics for Teachers course through the lens of four affordances of new media: democratization, multimodality, collaboration and performance. Mathematics, perhaps more so than other school subjects, has traditionally been a subject that people do not talk about outside of classroom settings. However, we demonstrate through the case of the Mathematics for Teachers course that this does not have to be the case. Mathematics, even mathematics that traditionally has been seen as abstract or inaccessible, can be talked about in ways that can engage not only adults but also young children. The affordances of new media can help us rethink and disrupt our existing views of mathematics (for teachers and for students) and of how it might be taught and learned, by (1) blurring teacher/student distinctions and crossing hierarchical curriculum boundaries; (2) communicating mathematics in multimodal ways; (3) seeing mathematics as a collaborative enterprise; and (4) helping us learn how to relate good math stories to classmates and family when asked "What did you do in math today?"

Mathematics Education Research Group of Australasia, 2018

This paper reports on an aspect of a research project that examined the use of apps in primary school mathematics programmes. It reports teacher and student perspectives on how they used a range of digital tools within the apps to solve problems. We consider the interplay between the affordances of the mobile technologies, including multirepresentation and haptic, with other social and pedagogical aspects, and how the assemblage of social and technological entities influences the ways that teachers might integrate apps into their mathematics programmes.

Human Arenas

The COVID-19 pandemic has led us to an unanticipated and challenging world. In educational settings, one of the ways to respond to this crisis has been the online delivery of content. One of the valid critiques of these online delivery models is the passive role of the participants. The challenge is we still know very little about how technology could support children's active participation in their learning. This challenge exacerbates with children in early years and in their home setting, which is the focus of our research at Monash University's Conceptual PlayLab. This paper reports on solving the theoretical problem of digital design that can create a relational space for children's STEM concept formation. The paper argues that engagement with digital tools demands clear design principles that could support both robust concept formation and also development of learning motives in children. Drawing on Wartofsky's work on artefacts and tool-use and (Fleer 2017a, 2019), conceptualisation of "digital coadjuvant", we make a case that technology offers a transformative potential for children to imagine and explore together with their caregivers in the Conceptual PlayWorld. We have showed through a practice example on how person and digital technologies become mutually constituted in a pop-up Conceptual PlayWorld. The design principle highlighted in the paper argues for transcending the binary of digital and non-digital. The paper concludes that Conceptual PlayWorld offers a design model that uses digital tools to sustain and amplify children's exploration in their imaginary play situation.

Cognition and Instruction, 2019

This article analyzes an episode of classroom mathematics activity mediated by graphing technology from 3 different theoretical perspectives. An important line of research in the learning sciences focuses on graphs as inscriptions, foregrounding learners' interactions with and around the material properties of graphical displays. Several recent studies in mathematics education have emphasized the utility of an instrumental genesis approach for conceptualizing mathematics learning and teaching with graphing calculators and other tools. A third perspective, influential in science and technology studies but less widely used in education research, calls for attention to material agency, considering the ways both learners and tools might be conceptualized as actors in a classroom activity system. This article explores the potential of this alternate approach for extending insights into technology-supported mathematics teaching and learning. It is argued that a material agency account can complement and enrich theoretical frameworks for analyzing technology-mediated classroom activity. Collectively, drawing these perspectives together to examine a classroom episode in which a digital device played a pivotal role provides a framework for considering the complexities and the tradeoffs involved in cultivating proficient tool use and conceptual understanding in contemporary mathematics classrooms.

Xiv Conferencia Interamericana De Educacion Matematica, 2015

There is widespread acceptance that mathematics is important, for an individual and for society. However there are still those who disagree arguing that the subject is boring and irrelevant. It is therefore crucial that mathematics teaching strives to engage all learners at all levels, without of course sacrificing the rigour and 'essence' of the subject. In this talk, I will argue that one way to achieve both rigour and broader access to mathematics lies with using appropriately designed digital technology. I will illustrate my argument with examples from research and practice.

International Journal of Computers for Mathematical Learning, 2004

presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche's discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student's emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics.

Using Mobile Technologies in the Teaching and Learning of Mathematics, 2018

This chapter reports on how the use of mathematics apps has the potential to reshape the learning experience, a particular aspect of learning with apps that emerged from a research project examining the ways mobile technologies are used in primary-school mathematics. The chapter will consider a number of key themes related to student learning that have emerged through the research. When using some of the apps in the study, students used different digital tools within the app to solve word problems, while the affordances, including multi-representation, dynamic and haptic, made the learning experience different from when using pencil-and-paper technology. Other themes that were identified included: collaboration, socio-material assemblages, and personalisation. All of these appeared influential in the development of mathematical thinking. While the affordances of the mobile technologies are important, the teacher's pedagogical approach and the dialogue that the apps evoked were central in the learning.