Dynamic digital technologies for dynamic mathematics: Implications for teachers' knowledge and practice

This report summarises the outcomes of the Nuffi eld Foundation funded 2014–17 project ‘Developing teachers’ mathematical knowledge for teaching and classroom use of technology through engagement with key mathematical concepts using dynamic digital technology’. The Nuffi eld Foundation is an endowed charitable trust that aims to improve social well-being in the widest sense. It funds research and innovation in education and social policy and also works to build capacity in education, science and social science research

Planning to teach lower secondary mathematics with dynamic mathematical technology: Quality features of lesson plans

Set within the context of the longitudinal Cornerstone Maths project in England. we adapt Thomas and Hong’s theoretical framework (mathematical) ‘pedagogic technology knowledge’ (MPTK, Thomas & Hong, 2013) to explore teachers’ espoused knowledge to teach with dynamic mathematical technology in lower secondary mathematics. We conclude a set of eight ‘quality features’ of such plans, and highlight how each of these features can provide a dynamic insight into teachers’ MPTK development over time

A teacher’s use of dynamic digital technology to address students’ misconception about additive strategies for geometric similarity

Research has well documented that students develop a significant misconception associated with the incorrect use of additive strategies when engaging with geometric similarity (GS) tasks. Since dynamic digital technology (DDT) has the potential to support students in addressing this misconception, teachers can exploit the affordances of DDT in the classroom to accomplish it. The aim of this paper is to explore how and why a secondary mathematics teacher uses DDT in the classroom to promote students’ understanding of why additive strategies are inappropriate to use for GS tasks. Drawing on the data collected, through classroom observations and post-lesson teacher interviews, the research findings indicate that the dynamic and visual nature of DDT can be used to help students realise the inappropriateness of the use of additive strategies for GS tasks

Multi-mass solvers for lattice QCD on GPUs

Graphical Processing Units (GPUs) are more and more frequently used for lattice QCD calculations. Lattice studies often require computing the quark propagators for several masses. These systems can be solved using multi-shift inverters but these algorithms are memory intensive which limits the size of the problem that can be solved using GPUs. In this paper, we show how to efficiently use a memory-lean single-mass inverter to solve multi-mass problems. We focus on the BiCGstab algorithm for Wilson fermions and show that the single-mass inverter not only requires less memory but also outperforms the multi-shift variant by a factor of two.Comment: 27 pages, 6 figures, 3 Table

Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology

This new working group (WG) was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted; alongside the changed nature of the classroom interactions between the humans (teachers and students) and the chosen technologies. Starting with the assumption that technology resources are being used, the WG explored the nature of these tools and their affordances for the mathematical teaching and learning. The work was framed by the following three pedagogic activities, which are proving to be particularly challenging: introducing and developing understanding of new mathematical topics; managing interaction and communication in mathematics; and assessing mathematics, both formatively and summatively. Three case studies of teachers’ practices were presented to initiate discussions with respect to these challenges and to highlight some existing theoretical and methodological frames

Learning from the pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching and learning practices with and through technology

This working group (WG), which met for the second time in June 2021, was created to discuss the theoretical and methodological challenges faced by the mathematics education field when the prevailing boundaries of the classroom shifted as a result of the COVID-19 pandemic. Following a brief introduction to the aims for the WG, we offer three further case studies of teachers’ practices and an emerging synthesis of the cases according to three pedagogic activities that are proving to be particularly challenging

A research-informed web-based professional development toolkit to support technology-enhanced mathematics teaching at scale

We report a new phase of research of the scaling of Cornerstone Maths (CM), technology-enhanced curriculum units for lower secondary mathematics that embed dynamic mathematical technology (DMT). The CM curriculum units combine web-based DMT, pupil and teacher materials and teacher professional development that focus on developing the mathematical knowledge and pedagogies for teaching with technology. This paper presents the background research with teachers using CM (111 teachers from 42 London secondary schools in the period 2014-17) that suggests the need for a web-based ‘professional development toolkit’ that supports the sustainability of the innovation and ‘within-school’ scaling. It then outlines the research basis of the toolkit’s design principles and structure and its early evaluation

Dynamic Digital Technologies for Dynamic Mathematics: Executive Summary: Implications for teachers' knowledge and practice

The Executive Summary for the Nuffield Foundation funded 2014–17 project ‘Developing teachers’ mathematical knowledge for teaching and classroom use of technology through engagement with key mathematical concepts using dynamic digital technology’. The Nuffield Foundation is an endowed charitable trust that aims to improve social well-being in the widest sense. It funds research and innovation in education and social policy and also works to build capacity in education, science and social science research