Hiccups within technology mediated lessons: a catalyst for mathematics teachers’ epistemological development

© 2015 British Society for Research into Learning Mathematics. The notion of the lesson ‘hiccup’, defined as the perturbation experienced by a teacher during teaching that has been triggered by the use of mathematical technology, was first proposed in Clark-Wilson. Hiccups which are both unanticipated and unplanned, emerged from a study that sought to make sense of the process of secondary mathematics teachers’ situated learning as they began to use a particular new technological tool (TI-Nspire™ handheld devices and software) in their classrooms. The high frequency of the resulting hiccups enabled a categorisation of seven hiccup types that were shown to have influenced the development of teachers’ mathematical, pedagogic and technological knowledge. This article first reports and then extends this earlier work by articulating the design principles for a professional development approach within the Cornerstone Maths (CM) project that uses hiccups to try to address professional development ‘at scale’ concerning student use of dynamic digital technologies in mathematics classrooms

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

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

Коллективизация и азербайджанское село

This chapter argues that there are contrary views regarding the mathematical needs of employees in workplaces, and this results in confusion around debate on the issue. The problem has been exacerbated by the ubiquity of information technologies and the widespread automation of routine procedures, which have resulted in little if any trace of the mathematical processes going on. Following a short survey of research in the field, we summarize recent research that has identified a particular difficulty in terms of widespread pseudo-mathematical interpretation of symbolic output in workplaces. Such interpretations are shown to impede communication, but can be challenged by developing relevant techno-mathematical literacies among employees. Effective strategies for developing techno-mathematical literacies relevant to specific work sectors are described

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

Playing Beowulf: Bridging computational thinking, arts and literature through game-making

Preparing younger generations to engage meaningfully with digital technology is often seen as one of the goals of 21st century education. JeanetteWing’s seminal work on Computational Thinking (CT) is an important landmark for this goal: CT represents a way of thinking, a set of problem-solving skills which can be valuable when interacting with digital technologies, and with different fields of knowledge, such as Arts and Humanities. Even if this cross-areas relevance has been celebrated and acknowledged in theoretical research, there has been a lack of practical projects exploring these links between CT and non-STEM fields. This research develops these links. We present a specific case – a game produced by two 14 years-old boys – within Playing Beowulf, a collaboration with the British library’s Young Researchers programme, in which students aged 13–14 from an inner-London (UK) school have developed games based on their own readings of the Anglo-Saxon poem Beowulf during an after-school club. The game was produced using MissionMaker, a software (currently under development at UCL Knowledge Lab) that allows users to create and code their own first-person 3D games in a simple way, using pre-made 3D assets, such as rooms, props, characters and weapons and a simplified programming language manipulated through drop-down lists. We argue that MissionMaker, by simplifying the development process (low floor), can be a means to foster the building of knowledge in both STEM (CT) and Arts and Humanities, building bridges between these two areas inside and outside traditional schooling

Beyond jam sandwiches and cups of tea: An exploration of primary pupils' algorithm‐evaluation strategies

The long-standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from five years old. Algorithm is introduced early in the English computing curriculum, yet, there is limited knowledge of how young pupils view this concept. This paper explores pupils’ (aged 10-11) understandings of algorithm following their engagement with one year of ScratchMaths (SM), a curriculum designed to develop computational and mathematical thinking skills through learning to program. 181 pupils from six schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils’ algorithmic thinking