Probability and Statistics Apps for Mobile Devices

Mobile devices such as tablets and smartphones are rapidly replacing laptops and notebooks as the primary student e-learning device. This chapter discusses the needs of a Statistics app user and how these differ from the needs of users of other Mathematics apps, and then reviews some the mobile apps currently available which enable a user to either learn Statistics or to carry out the sorts of summaries and analyses encountered in an undergraduate Statistics course. Implications of these apps for both teaching and learning are discussed.

Introducing iPads into Primary Mathematics Classrooms

The fast pace of technology has meant that new technologies are often being introduced into classrooms without knowledge of how they can be used to enhance teaching and learning in mathematics. This chapter explores how a small group of teachers used a new technology, the iPad, to teach mathematics within the first six months of their implementation and without the support of professional development. Findings from two separate studies are presented to support the argument that care should be taken when introducing any new technology to teach mathematics in primary classrooms and appropriate professional development that addresses the combination of mathematical content, pedagogy and technology is critical for all teachers, regardless of teaching experience.

Learning Maths with Mobiles

This chapter presents an overview of our experiences on cross-cultural design of technology in the context of mobile learning focusing on supporting learners to study mathematics in two different countries. The aim of our study is to discuss design issues from the perspective of two different types of cultures and reflect culturally sensitive issues based on a longitudinal study, which included empirical data from altogether over 3500 learners of grades 9 and 10. As a result we outline two focus areas: content and concept for best design practices. Furthermore, we argue that cross-cultural design of technology can help to identify culturally sensitive areas such as attitudes towards informal and collaborative learning and recognizing the local context for the content. Cross-cultural design of technology supports development of good user experience of mobile learning services for different local learning contexts.

Graspable Mathematics

The goal of this chapter is to describe a process of touch screen technology development, beginning from basic cognitive research and resulting in an applied educational intervention for algebra. To that end, we introduce Graspable Mathematics (GM), a novel approach to algebra instruction that integrates strong theory and evidence from perceptual learning, cognitive science and mathematics education. We present a number of concrete examples of how this framework can be applied to technology-based interventions that aim to engage students in mathematics. This chapter will also describe many of the methodological, theoretical, and practical considerations that guided our iterative design and development, as well as address many of the challenges and lessons learned when implementing the intervention in classroom settings.

Using Smartphones for Orientation Training for the Visually Impaired

This chapter discusses the potential of Indoor Positioning and Indoor Navigation (IPIN) systems in teaching and training Orientation and Mobility (O& M) to individuals with visual impairment. In addition, an attempt is made to investigate the implications of such trainings and technology in mathematics education, with regards to the learning of concepts of orientation. For individuals with visual impairment, O&M training is of crucial importance for everyday life and safety. Furthermore, these skills are often connected to problem-solving as well as to the understanding of basic geometrical concepts related to mathematics. In this chapter the developed IPIN system is presented, followed by suggested scenarios of its use in O&M trainings and O&M activities that can be used to introduce and strengthen opportunities for exploring mathematical topics.

Microworlds

This chapter combines the well-researched area of mathematics education, linear equations, with the field of mathematical microworlds. Insights into the current knowledge of both areas are presented before focusing the discussion on a new study in which pre-secondary school learners, with no prior formal teaching on the topic, explore linear equations through an algebra-based microworld called DragonBox. DragonBox is a touch-enabled mobile application available on all major platforms and to which the author has no affiliation. Touch-enabled mobile devices have great potential as vessels for mathematical microworlds and this chapter draws conclusions regarding the influence such microworlds have on a learner's understanding. Although learners in this study demonstrated procedural fluency when working with DragonBox, it was only through encouraged reflection that a relational understanding seemed to take effect and without it the children developed inconsistent notions about the structure of the microworld.

Students' Kinaesthetic Interactions with a Touch-Enabled Virtual Mapping Tool

Recent technology advances have substantially changed the way we teach and learn mathematics providing educators with opportunities for creating novel inquiry-based learning environments by increasing the range and sophistication of possible classroom activities. The affordances provided by mobile technologies can motivate students to engage in authentic problem solving activities that can promote their mathematical learning, and the attainment of important competencies essential in modern society. This chapter reports on the main experiences gained from a study that exploited affordances of tablet devices used by young students (11-year old). Findings from the study indicate that general purpose apps such as Recce that was employed in the current study can scaffold learning of the mathematics curriculum in educationally powerful ways that engage students and promote their mathematical growth.

A Multimodal Discourse on the Use of Touch Enabled Mobile Devices for Mathematics Education

The Technological, Pedagogical and Content Knowledge (TPACK) iPads in School Project aimed to investigate how touch enabled mobile devices, iPads, were used in classrooms. This chapter shares findings from the research selected for their relevance for mathematics education. Qualitative and quantitative research was undertaken in ten West Australian classrooms from kindergarten to year ten, over two years. A community of practice model supported teacher reflection “on action” and “in action” aligned to national standards. Self-tracking video devices gathered evidence on how teachers were using iPads in teaching. Videos were analysed and tagged using multimodal discourse analysis software and a research-based checklist to identify effective pedagogical practices using iPads in mathematics education entitled the TIPs Mobile Pedagogies in Mathematics Checklist (Tips-Mobile-Maths) was developed. A series of short vignettes called “i-Stories” were developed. Social networking connected the teachers and was used for dissemination of research findings.

Off-Line Communication in Mathematics Using Mobile Devices

The chapter focuses on off-line communication using (not only) mobile devices where absence of direct communication increases the risk of misunderstanding and loss of time. Two principles that can lower this danger, the principle of charity and the principle of scaffolding, are presented first separately, and then in mutual relationship. The aim of this chapter is to show that charity and scaffolding are two (connected) stages of help to pupils. If the teacher applies the principle of charity, it enables him/her to understand pupils and/or discover their problems. Having detected the learners' misconceptions or problematic parts, he/she will be able to follow the pupils' thinking process and with the help of scaffolding advance the pupils' knowledge to a higher level. All the presented theoretical constructs are illustrated by examples from an on-line mathematical course for secondary pupils. The role of technological devices in developing the quality of pupils' participation in the course is documented.

Investigating the Mathematics of Inaccessible Objects

This chapter uses a reflective practice standpoint to discuss the use of iPad-based video production apps to conduct mathematical inquiries in a college algebra class. By using sketching apps to layer photos with grids, and capturing mathematical notation as it was written, students describe mathematical features of artwork that cannot be physically touched for measurement. We discuss the potentials and pitfalls of a video assignment to uncover the mathematics of these “inaccessible” art objects. Student math videos are described through three themes: choice of video platform; level of engagement with mathematics; and videos as a lens to perceive mathematical thinking. Our commentary suggests that touch-enabled mobile devices are especially well-suited for experiential, inquiry learning activities. As research on touch-enabled devices proceeds, mathematics education researchers may consider the ways in which non-mathematical apps can be turned towards learning mathematics.