Transforming the mathematical practices of learners and teachers through digital technology

This paper argues that mathematical knowledge, and its related pedagogy, is inextricably linked to the tools in which the knowledge is expressed. The focus is on digital tools and the different roles they play in shaping mathematical meanings and in transforming the mathematical practices of learners and teachers. Six categories of digital tool-use that distinguish their differing potential are presented: i. dynamic and graphical tools, ii. tools that outsource processing power, iii. tools that offer new representational infrastructures for mathematics, iv. tools that help to bridge the gap between school mathematics and the students’ world; v. tools that exploit high-bandwidth connectivity to support mathematics learning; and vi. tools that offer intelligent support for the teacher when their students engage in exploratory learning with digital technologies Following exemplification of each category, the paper ends with some reflections on the progress of research in this area and identifies some remaining challenges

A computational lens on design research

In this commentary, we briefly review the collective effort of design researchers to weave theory with empirical results, in order to gain a better understanding of the processes of learning. We seek to respond to this challenging agenda by centring on the evolution of one sub-field: namely that which involves investigations within a constructionist framework of learning with carefully designed computational tools. We argue that these studies, specifically those where children were learning to program, were early adopters of the Design Research methodology and offer a useful lens through which to focus on the current field

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

Designing a programming-based approach for modelling scientific phenomena

We describe an iteratively designed sequence of activities involving the modelling of 1- dimensional collisions between moving objects based on programming in ToonTalk. Students aged 13-14 in two settings (London and Cyprus) investigated a number of collision situations, classified into six classes based on the relative velocities and masses of the colliding objects. We describe iterations of the system in which students engaged in a repeating cycle of activity for each collision class: prediction of object behaviour from given collision conditions, observation of a relevant video clip, building a model to represent the phenomena, testing, validating and refining their model, and publishing it ? together with comments ? on our web-based collaboration system, WebReports. Students were encouraged to consider the limitations of their current model, with the aim that they would eventually appreciate the benefit of constructing a general model that would work for all collision classes, rather than a different model for each class. We describe how our intention to engage students with the underlying concepts of conservation, closed systems and system states was instantiated in the activity design, and how the modelling activities afforded an alternative representational framework to traditional algebraic description

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

Techno-mathematical literacies in the workplace: a critical skills gap

There has been a radical shift in the mathematical skills required in modern workplaces. With the ubiquity of IT, employees now require Techno-mathematical Literacies, the mastery of new kinds of mathematical knowledge shaped by the systems that govern their work. The education system does not fully recognise these skills, employees often lack them, and companies struggle to improve them. This project has developed prototype learning resources to train a variety of employees in the mathematical awareness and knowledge that today?s employment require

Bridging Primary Programming and Mathematics: some findings of design research in England

In this paper we present the background, aims and methodology of the ScratchMaths (SM) project, which has designed curriculum materials and professional development (PD) to support mathematical learning through programming for pupils aged between 9 and 11 years. The project was framed by the particular context of computing in the English education system alongside the long history of research and development in programming and mathematics. In this paper, we present a “framework for action” (diSessa and Cobb 2004) following design research that looked to develop an evidence-based curriculum intervention around carefully chosen mathematical and computational concepts. As a first step in teasing out factors for successful implementation and addressing any gap between our design intentions and teacher delivery, we focus on two key foundational concepts within the SM curriculum: the concept of algorithm and of 360-degree total turn. We found that our intervention as a whole enabled teachers with different backgrounds and levels of confidence to tailor the delivery of the SM in ways that can make these challenging concepts more accessible for both themselves and their pupils

Building mathematical knowledge with programming: insights from the ScratchMaths project

The ScratchMaths (SM) project sets out to exploit the recent commitment to programming in schools in England for the benefit of mathematics learning and reasoning. This design research project aims to introduce students (age 9-11 years) to computational thinking as a medium for exploring mathematics following a constructionist approach. This paper outlines the project and then focuses on two tensions related to (i) the tool and learning, and (ii) direction and discovery, which can arise within constructionist learning environments and describes how these tensions were addressed through the design of the SM curriculum