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

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

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

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

Mathematics and digital technology: challenges and examples from design research

Mathematics is a ubiquitous and vital substrate on which our culture is built. Yet this fact is seldom fully exploited in educational contexts. The first step must, in our view, be to open the black box of invisible mathematics to more people, (see Hoyles, 2015). A key challenge for task design and an organising design principle is to exploit digital technology to reveal more of what mathematics actually is; first, by offering a glimpse of the mathematical models underlying a given (and carefully chosen) phenomenon; and second, by fostering an approach to mathematical tasks that transcends the purely procedural. We describe in this paper how we have attempted to address these challenges

Microworlds, Constructionism and Mathematics = Micromundos, Construccionismo y Matemáticas

En este artículo, esbozamos la idea del construccionismo y cómo puede ser puesta en práctica a través del diseño de “micromundos”, islas aisladas y accesibles de actividad, dónde se encuentren pepitas de conocimiento relevante a través de herramientas y secuencias de actividades especialmente diseñadas y con pedagogías adecuadamente orientadas. En la segunda parte del artículo, describimos el diseño, implementación y evaluación de una intervención construccionista, ScratchMaths, introducida en Inglaterra, país en el que la computación es obligatoria para todos los niveles educativos (de los 5 a los 16 años). Este estudio de caso pone de manifiesto la tensión entre la fidelidad de una innovación al implementarla y su adaptación por parte de los profesores, especialmente en el contexto de las matemáticas, la cuál es una materia muy exigente tanto para los docentes como para los alumnos

Aquatic Eddy Correlation: Quantifying the Artificial Flux Caused by Stirring-Sensitive O2 Sensors

In the last decade, the aquatic eddy correlation (EC) technique has proven to be a powerful approach for non-invasive measurements of oxygen fluxes across the sediment water interface. Fundamental to the EC approach is the correlation of turbulent velocity and oxygen concentration fluctuations measured with high frequencies in the same sampling volume. Oxygen concentrations are commonly measured with fast responding electrochemical microsensors. However, due to their own oxygen consumption, electrochemical microsensors are sensitive to changes of the diffusive boundary layer surrounding the probe and thus to changes in the ambient flow velocity. The so-called stirring sensitivity of microsensors constitutes an inherent correlation of flow velocity and oxygen sensing and thus an artificial flux which can confound the benthic flux determination. To assess the artificial flux we measured the correlation between the turbulent flow velocity and the signal of oxygen microsensors in a sealed annular flume without any oxygen sinks and sources. Experiments revealed significant correlations, even for sensors designed to have low stirring sensitivities of ~0.7%. The artificial fluxes depended on ambient flow conditions and, counter intuitively, increased at higher velocities because of the nonlinear contribution of turbulent velocity fluctuations. The measured artificial fluxes ranged from 2-70 mmol m(-2) d(-1) for weak and very strong turbulent flow, respectively. Further, the stirring sensitivity depended on the sensor orientation towards the flow. For a sensor orientation typically used in field studies, the artificial flux could be predicted using a simplified mathematical model. Optical microsensors (optodes) that should not exhibit a stirring sensitivity were tested in parallel and did not show any significant correlation between O2 signals and turbulent flow. In conclusion, EC data obtained with electrochemical sensors can be affected by artificial flux and we recommend using optical microsensors in future EC-studies