Francesca Ferrara

A method for quantifying focused versus overview behavior in AOI sequences

We present a new measure for evaluating focused versus overview eye movement behavior in a stimulus divided by areas of interest. The measure can be used for overall data, as well as data over time. Using data from an ongoing project with mathematical problem solving, we describe how to calculate the measure and how to carry out a statistical evaluation of the results.

Diagrams and Tool Use: Making a Circle with WiiGraph

Using Châtelet’s perspective on the gesture/diagram interplay, we aim to contribute to the current discussion on the role of technology showing influences of tool use on some grade 9 students’ diagrammatic activity. The students have been engaged in graphing motion experiences in the context of a teaching experiment with WiiGraph, a software application modelling the movement of two controllers of the game console Nintendo Wii. In particular, we focus on the activity of making a circle and the circle emerging as a gradient of speeds and directions out of students’ movements. Telling the story from the point of view of the diagram, we focus on the new dimensions and movements that arise from, within and about the working surface, as dynamic sources and sites of mathematical thinking.

Touching Numbers and Feeling Quantities: Methodological Dimensions of Working with TouchCounts

In this chapter, we discuss a classroom-based intervention that we carried out with a group of first grade children using a multi-touch iPad application called TouchCounts , as part of a research project aimed at developing children’s number sense. We situate our work within an inclusive materialist approach to the study of mathematics education (de Freitas & Sinclair, 2014), which maps the various materialities at work in the mathematics classroom, as a way to attend to the relational entanglement of numbers, iPad and learners. Drawing on this vision, we analyse the methodological dimensions of using TouchCounts, conceptualising the application as an experimental means that allows us to better see methodological implications as they sustain mathematical encounters for learners. We investigate how event-like interventions emerge out of the material relations with the surrounding and engender new kinds of mathematical experiences with number. We focus particularly on a situation in which the number of children around a table became the variable under discussion providing the basis for emerging relational meanings of number.

The Coordinated Movements of a Learning Assemblage: Secondary School Students Exploring Wii Graphing Technology

This chapter uses assemblage theory to investigate how students engage with graphing technology to explore mathematical relationships. We use the term ‘learning assemblage’ to describe provisional dynamic physical arrangements involving humans and other bodies moving together and learning together. Emphasis on dynamic coordinated movements allows us to study how mathematics learning occurs in complex interaction with technology. We tap into the rich concept of ‘sympathy’ to understand the way that students develop a feeling for these coordinated movements as they participate collaboratively in mathematical investigations. Through sympathetic movements, a learning assemblage sustains a kind of affective agreement amongst the various bodies that participate. We show how assemblage theory helps us rethink the role of affect in technology tool use. This chapter sheds light on innovative ways of theorizing the role of Wii graphing technology in mathematical practice.

Introduction: Innovative Spaces for Mathematics Education with Technology

The idea of this book arose from research encounters occurred during a past ICTMT Conference: the International Conference on Technology in Mathematics Teaching. The ICTMT Conference, which is now moving to its 13th edition, has a strong commitment to promote technology in mathematics education for improving the quality of teaching and learning by effective use of technology. In recent years, international research in mathematics education has offered a range of theoretical perspectives that attempted to provide different and interrelated frames and viewpoints to the study of use and role of digital technologies in/for teaching and learning mathematics.