Boundary objects and boundary crossing for numeracy teaching

In this paper, we share analysis of an episode of a pre-service teacher’s handling of a map artefact within his practicum teaching of ‘Mathematical Literacy’ in South Africa. Mathematical Literacy, as a post-compulsory phase subject in the South African curriculum, shares many of the aims of numeracy as described in the international literature— including approaches based on the inclusion of real life contexts and a trajectory geared towards work, life and citizenship. Our attention in this paper is focused specifically on artefacts at the boundary of mathematical and contextual activities. We use analysis of the empirical handling of artefacts cast as ‘boundary objects’ to argue the need for ‘boundary crossing’ between mathematical and contextual activities as a critical feature of numeracy teaching. We pay particular attention to the differing conventions and extents of applicability of rules associated with boundary artefacts when working with mathematical or contextual perspectives. Our findings suggest the need to consider boundary objects more seriously within numeracy teacher education, with specific attention to the ways in which they are configured on both sides of the boundary in order to deal effectively with explanations and interactions in classrooms aiming to promote numeracy

A Multisite Preregistered Paradigmatic Test of the Ego-Depletion Effect

We conducted a preregistered multilaboratory project (k = 36; N = 3,531) to assess the size and robustness of ego-depletion effects using a novel replication method, termed the paradigmatic replication approach. Each laboratory implemented one of two procedures that was intended to manipulate self-control and tested performance on a subsequent measure of self-control. Confirmatory tests found a nonsignificant result (d = 0.06). Confirmatory Bayesian meta-analyses using an informed-prior hypothesis (δ = 0.30, SD = 0.15) found that the data were 4 times more likely under the null than the alternative hypothesis. Hence, preregistered analyses did not find evidence for a depletion effect. Exploratory analyses on the full sample (i.e., ignoring exclusion criteria) found a statistically significant effect (d = 0.08); Bayesian analyses showed that the data were about equally likely under the null and informed-prior hypotheses. Exploratory moderator tests suggested that the depletion effect was larger for participants who reported more fatigue but was not moderated by trait self-control, willpower beliefs, or action orientation

Uses of technology in lower secondary mathematics education : a concise topical survey

This topical survey provides an overview of the current state of the art in technology use in mathematics education, including both practice-oriented experiences and research-based evidence, as seen from an international perspective. Three core themes are discussed: Evidence of effectiveness; Digital assessment; and Communication and collaboration. The survey’s final section offers suggestions for future trends in technology-rich mathematics education and provides a research agenda reflecting those trends. Predicting what lower secondary mathematics education might look like in 2025 with respect to the role of digital tools in curricula, teaching and learning, it examines the question of how teachers can integrate physical and virtual experiences to promote a deeper understanding of mathematics. The issues and findings presented here provide an overview of current research and offer a glimpse into a potential future characterized by the effective integration of technology to support mathematics teaching and learning at the lower secondary level

Research on the teaching and learning of geometry

The chapter provides a comprehensive review of recent research in geometry education, covering geometric and spatial thinking, geometric measurement, and visualization related to geometry, as well as encompassing theoretical developments and research into teaching and teacher development. Studies examining the uses of forms of digital technology are addressed in every section. The content of the chapter reflects the main emphases of research in geometry education as presented at PME conferences over the period 2005–2015. The synthesis is presented in the form of the following sections: spatial reasoning, geometric visualization, geometric measurement, geometric reasoning and proving, students’ knowledge, teachers’ knowledge and development, and teaching geometry and the design and use of geometric tasks. While some topics of research are under-represented (including the topics of congruency and similarity, transformation geometry, analytic/ coordinate geometry, vector geometry), research in geometry education is embracing the use of more recent discursive, embodied and eco-cultural perspectives, and is also employing new methods such as eye-tracking. As research develops further, the affordance of digital technologies is enriching approaches to geometric and spatial teaching and learning by providing new ways of apprehension and representation, new manipulation and processes, wider and deeper conceptual understanding and linking of different meanings and treatments