Designing digital technologies and learning activities for different geometries

This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics. In revealing these issues and challenges, the chapter examines the design of digital technologies and related forms of learning activities for a range of geometries, including Euclidean and co-ordinate geometries in two and three dimensions, and non-Euclidean geometries such as spherical, hyperbolic and fractal geometry. This analysis reveals the decisions that designers take when designing for different geometries on the flat computer screen. Such decisions are not only about the geometry but also about the learner in terms of supporting their perceptions of what are the key features of geometry

Nonviolent communication, compassion and mathematical resilience

We consider mathematics anxiety to be a result of cultural violence. We explore the possibilities offered by Marshall Rosenberg’s nonviolent (compassionate) communication (NVC), developed as a means of addressing conflict, to contribute to the existing work on mathematical resilience (MR), which seeks to address mathematics anxiety and avoidance. Nonviolent communication assumes that compassion is innate, that human behaviour comes from needs, which are indicated by feelings, and stresses the importance of empathy. This resonates with MR, and in particular validates the Growth Zone Model, an important and successful MR strategy involving the non-judgmental awareness and articulation of feelings and needs and the link between these

The interaction between task design and technology design in creating tasks with Cabri Elem

International audienceBoth the design of tasks and the design of technology have been identified as important factors in the effective use of technology-based tasks in the classroom. By analyzing both the design of a sequence of tasks (based on didactical principles from Brousseau's (1998) theory of situations) and the affordances of Cabri Elem software it will be shown that technology can be designed in such a way as to enhance the implementation of didactical principles

The mathematics resilience approach to mathematics anxiety : is this supported by self-determination theory?

One approach to the problem of mathematics anxiety, that of developing mathematical resilience (Lee & Johnston-Wilder, 2017) focuses on enabling learners to remain in the growth zone, where learners experience challenge and manage any threat. This approach, involving the use of three tools (the growth zone model, hand model of the brain and the relaxation response) has been successful in small-scale studies. We show here how the theory and practice of MR can be grounded in self-determination theory (SDT) (Deci & Ryan, 2000), with connections to SDT concepts of: autonomous motivation; the basic psychological needs of autonomy, competence and relatedness; and emotion regulation. Extensive research evidence has indicated that the satisfaction of basic psychological needs leads to well-being and that frustration of these needs leads to ill-being, indicating the potential of SDT to support research and practice in the specific area of ill-being known as mathematics anxiety

Feedback and formative assessment with Cabri

International audienceThe University of Chicago Number Stories project aims to enhance student engagement in solving real-world problems in a Cabri environment through the provision of effective feedback. The relevant literature concerning feedback and formative assessment in technology situations is hence reviewed in light of the affordances of Cabri, and issues arising in the project, such as providing feedback in open-ended situations, are discussed

Thinking in 3D with dynamic visualisation software

Thinking in 3D involves not only mental images related to external representations, but also various visualisation processes and abilities. In this workshop we explore the ways in which thinking in 3D might be supported through using 3D software applications such as Cabri 3D and small software applications developed in the DALEST project

Theory of didactical situations and instrumental genesis in a cabri elem book

International audienceThe contributions of two theoretical frameworks (Theory of Didactic Situations and Instrumental Genesis) to the design of a sequence of tasks in the Cabri Elem envi-ronment, where task and technology design are closely linked, are shown. Consider-ing the potential for instrumental genesis as a theory of technology design reveals a fundamental difficulty in dealing with representations. It is hence suggested that the role of the artefact be broadened to include environments, tools, and entities

Addressing Mathematics Anxiety through developing resilience: building on Self Determination Theory

Mathematics-specific anxiety is anxiety that impedes mathematical thinking and progress, and creates distress for many learners, or at the least a tendency to avoid mathematical thinking. Such anxiety is prevalent. The importance of mathematics to economic recovery is well-established; in order to meet the need for mathematics, the high levels of mathematics anxiety that stand in the way of individual mathematical progress should be addressed. Using a case study involving an adult learner, we use self-determination theory (Ryan and Deci, 2017) to explain why mathematical resilience (Lee and Johnston-Wilder, 2017) is a concept which can work against anxiety and for a positive stance towards mathematics. Work on mathematical resilience demonstrates that well-informed, subject-specific interventions can help people manage emotions, including anxiety, and improve progress and uptake in mathematics. We illustrate ways in which the focus of self-determination theory on meeting basic psychological needs (autonomy, competence and relatedness), to enhance wellbeing and prevent harm, provides grounding for much good practice in mathematics education and specifically for work in mathematical resilience. The tools of mathematical resilience go beyond what is currently proposed in SDT research. We illustrate ways in which these tools can specifically facilitate learners’ emotion regulation, which we propose is integral to mathematical learning competence, leading to greater mathematical wellbeing, learning, and release from mathematics anxiety

Applying Contemporary Philosophy in Mathematics and Statistics Education: The Perspective of Inferentialism

Schindler, M., Mackrell, K., Pratt, D., & Bakker, A. (2017). Applying contemporary philosophy in mathematics and statistics education: The perspective of inferentialism. In G. Kaiser (Ed.). Proceedings of the 13th International Congress on Mathematical Education, ICME-1