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As was the case in the Sinclair et al. This is the fourth and final article directly related to student use of a particular mobile technology. This research has important implications for the design of such apps. Qualitative and quantitative video data is used by the authors who identify 95 potential helping and hindering affordances among the 18 apps they trialled.

As was the case in previous research on iPads Larkin ; Moyer-Packenham et al. The remaining articles in the special issue shift the focus to examinations of possible appropriate pedagogies to best utilise the affordances of the mobile technologies available to classroom and university teachers. A variety of theoretical frameworks are proposed and the educational contexts include very young children, upper primary, junior secondary and senior secondary students, and undergraduate education students.

As was the case with the first four articles, these pedagogically oriented articles encompass a range of national and international contexts. Accompanying this demographical shift are increased community expectations that such teachers can embed information communication technologies ICTs effectively into the teaching of mathematics. In this article, Attard and Orlando investigate how four early career primary school teachers use ICT in their teaching of mathematics. Two important factors, developed from the research presented in this paper, suggest that ECTs uses of technology to teach mathematics may be more complicated than first envisaged.

Ingram, Williamson-Leadley and Offen report on a qualitative investigation into the use of Show and Tell tablet technology in mathematics classrooms. A Show and Tell app allows the user to capture voice and writing or text in real time.


The article starts from the premise that teaching secondary mathematics has a number of challenges, including the expectations that teachers cover the prescribed curriculum, help students learn difficult concepts and prepare students for future studies and, increasingly, that they do so incorporating digital technologies. Their analysis indicates that the teacher and students were positive about their experiences with a flipped classroom approach, that utilised mobile technologies and that students were motivated to engage with the teacher-created online mathematics resources.

In so doing, the study adds to the limited research literature related to student and teacher perceptions of the affordances of the flipped classroom approach in secondary school mathematics. This article, by Bray and Tangney, explores how a combination of a transformative, mobile technology-mediated approach facilitated the development of mathematics learning activities in 54 Irish, secondary school students. This article proposes clear, logical connections between aspects of the activity design and their impact on student attitudes and behaviours in learning mathematics.

Relationship between the strands

Although situated in an Irish context, there are clear implications in this research for mathematics teaching in many other countries. The final article in this issue, from Handal, Campbell, Cavanagh and Petocz, reports on a survey of Australian, pre-service students studying primary school education. The technological pedagogical content knowledge TPACK model is used as the conceptual framework for the analysis of these students engagement with iPad mathematics apps. The respondents examined three different apps using a purposely designed instrument in regard to their explorative, productive or instructive instructional role.

All articles in this special issue have undertaken the normal blind, peer-review MERJ process, and we deliberately sought national and international colleagues who are both knowledgeable in the field and also not contributing authors for this special issue. Nigel and I would very much like to acknowledge the wonderful reviewing work of the following colleagues, many of whom did several reviews of an article in this special issue. Clearly, without their contributions this special issue would not have been possible.

We look forward to further editorial work with both Robyn and Peter. Finally, we would like to express our support for Ms.

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Belle Mojado Springer Press , who answered many, many emails regarding the Springer Editorial system—thank you very much Belle. The special issue identifies some themes and challenges as the mathematics education community continues to examine the usefulness of mobile technologies to enhance the learning of mathematics, either from the particular affordances of the media that allow teachers to reshape the learning experience, or from the particular pedagogy associated with the technologies. Questions arise when technology is considered in the teaching process: what is the relationship between features of the tablets, the architecture of the apps, and the learning that a reshaped environment might afford?

In terms of pedagogy, what approaches might best optimise student engagement and mathematical thinking? As well, how might the notion of scaffolding be re-envisaged to include feedback from digital sources and a greater element of self-assessment? Equity issues concerned with access both within domestic school communities and globally still remain, and require ongoing examination.

Representation of data

Some planning and management aspects also need to be considered. What comes first when planning — the mathematics, the app or the pedagogy? What are the best ways to manage the introduction of new apps? Researchers also need to continue to critically examine the influence of mobile technologies on learning across a range of contexts and the ways that they interact with other pedagogical media. The articles in this special issue reveal considerable potential for mobile technologies to enhance student engagement and mathematical thinking, but the full scope of opportunity and the relationships with other learning approaches are still to be fully unravelled.

Nevertheless, they make a considerable and very worthy contribution to further understanding in this critical endeavour. Skip to main content Skip to sections. Advertisement Hide. Download PDF. Mathematics education and mobile technologies. Article First Online: 23 December While there are a range of technologies and associated pedagogical approaches that can be incorporated into mathematics education, it is important to consider the ways that they might reshape the learning experience and influence engagement and understanding.

In this issue, the focus clearly concerns either mobile technologies themselves iPads, iPhones, Androids or pedagogies associated with the use of mobile technologies flipped classrooms, twenty-first century learning. These require skills in using digital systems; and critical and creative thinking including systems, design and computational thinking. The curriculum is designed so that students will develop and use increasingly sophisticated computational thinking skills, and processes, techniques and digital systems to create solutions to address specific problems, opportunities or needs.

Computational thinking is a process of recognising aspects of computation in the world and being able to think logically, algorithmically, recursively and abstractly. Students will also apply procedural techniques and processing skills when creating, communicating and sharing ideas and information, and managing projects. A number of key concepts underpin the Digital Technologies curriculum.

These establish a way of thinking about problems, opportunities and information systems and provide a framework for knowledge and practice. The key concepts are:. The concepts of abstraction, data collection, representation and interpretation, specification, algorithms and implementation correspond to the key elements of computational thinking. Collectively, these concepts span the key ideas about the organisation, representation and automation of digital solutions and information.

They can be explored in non-digital or digital contexts and are likely to underpin future digital systems. They provide a language and perspective that students and teachers can use when discussing digital technologies. Abstraction involves hiding details of an idea, problem or solution that are not relevant, to focus on a manageable number of aspects.

Abstraction is a natural part of communication: people rarely communicate every detail, because many details are not relevant in a given context. The idea of abstraction can be acquired from an early age. For example, when students are asked how to make toast for breakfast, they do not mention all steps explicitly, assuming that the listener is an intelligent implementer of the abstract instructions. In digital systems, everything must be broken down into simple instructions. The concepts that are about data focus on the properties of data, how they are collected and represented, and how they are interpreted in context to produce information.

These concepts in Digital Technologies build on a corresponding statistics and probability strand in the Mathematics curriculum. The Digital Technologies curriculum provides a deeper understanding of the nature of data and their representation, and computational skills for interpreting data. The data concepts provide rich opportunities for authentic data exploration in other learning areas while developing data processing and visualisation skills.

Data collection describes the numerical, categorical and textual facts measured, collected or calculated as the basis for creating information and its binary representation in digital systems. Data collection is addressed in the processes and production skills strand. Data representation describes how data are represented and structured symbolically for storage and communication, by people and in digital systems, and is addressed in the knowledge and understanding strand. Data interpretation describes the processes of extracting meaning from data and is addressed in the processes and production strand.

The concepts specification, algorithms and implementation focus on the precise definition and communication of problems and their solutions. This begins with the description of tasks and concludes in the accurate definition of computational problems and their algorithmic solutions. This concept draws from logic, algebra and the language of mathematics, and can be related to the scientific method of recording experiments in science.

Specification describes the process of defining and communicating a problem precisely and clearly.

Processing Mathematics Through Digital Technologies | Nigel Calder | Springer

For example, explaining the need to direct a robot to move in a particular way. An algorithm is a precise description of the steps and decisions needed to solve a problem.

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Algorithms will need to be tested before the final solution can be implemented. Anyone who has followed or given instructions, or navigated using directions, has used an algorithm. These generic skills can be developed without programming. For example, students can follow the steps within a recipe or describe directions to locate items.

Mathematics education and mobile technologies

Implementation describes the automation of an algorithm, typically by using appropriate software or writing a computer program. These concepts are addressed in the processes and production skills strand. The digital systems concept focuses on the components of digital systems: hardware and software computer architecture and the operating system , and networks and the internet wireless, mobile and wired networks and protocols.

This concept is addressed in both strands.