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

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

Discovery of an extended debris disk around the F2V star HD 15745

Using the Advanced Camera for Surveys aboard the Hubble Space Telescope, we have discovered dust-scattered light from the debris disk surrounding the F2V star HD 15745. The circumstellar disk is detected between 2.0" and 7.5" radius, corresponding to 128 - 480 AU radius. The circumstellar disk morphology is asymmetric about the star, resembling a fan, and consistent with forward scattering grains in an optically thin disk with an inclination of ~67 degrees to our line of sight. The spectral energy distribution and scattered light morphology can be approximated with a model disk composed of silicate grains between 60 and 450 AU radius, with a total dust mass of 10E-7 M_sun (0.03 M_earth) representing a narrow grain size distribution (1 - 10 micron). Galactic space motions are similar to the Castor Moving Group with an age of ~10E+8 yr, although future work is required to determine the age of HD 15745 using other indicators.Comment: 7 pages, 4 figures, ApJ Letters, in pres

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

Defining Procedures in Early Computing Education

From the early years of educational programming researchers considered procedural abstraction a key instrument of computational thinking and tried to understand the cognitive difficulties encountered through this concept. Defining procedures is promoted in renewed computing curricula in several countries. And yet, it is rarely acknowledged by more recent educational research. In this paper, we consider the fact that the delayed implementation of a mechanism for building procedures (known as definitions) within Scratch, a widely used programming environment for children, may have negatively impacted the focus within curricular content on this powerful idea. In our research, which is a part of a broader ScratchMaths (SM) research project, we set out to explore which factors play a role in upper primary pupils understanding and utilizing the concept of defining procedures as a common and inherent instrument of their programming. We present our observations from the project design schools and demonstrate how they guided the development of our SM pedagogic strategy for definitions

Designing for learning mathematics through programming: A case study of pupils engaging with place value

This paper focuses on a major part of a two-year intervention, ScratchMaths (SM), which seeks to exploit programming for the learning of mathematics. The SM hypothesis is that given the right design of curriculum, pedagogy and digital tools, pupils can engage with and express important mathematical ideas through computer programming. We describe the overall design of SM and as an illustration of the approach, we elaborate a more detailed description of the specific SM activities that seek to harness the programming concept of ‘objects communicating with one another’ for the exploration of the mathematical concept of place value through a syntonic approach to learning. We report a case study of how these activities were implemented in two primary classes. Our findings constitute a kind of existence theorem: that with carefully designed and sequenced learning activities and appropriate teacher support, this approach can allow pupils to engage with difficult mathematical ideas in new, meaningful and generalisable ways. We also point to the challenges which emerged through this process in ensuring pupils encounter these mathematical ideas

ANYCaRE: a role-playing game to investigate crisis decision-making and communication challenges in weather-related hazards

This study proposes a role-playing experiment to explore the value of modern impact-based weather forecasts on the decision-making process to (i) issue warnings and manage the official emergency response under uncertainty and (ii) communicate and trigger protective action at different levels of the warning system across Europe. Here, flood or strong-wind game simulations seek to represent the players' realistic uncertainties and dilemmas embedded in the real-time forecasting-warning processes. The game was first tested in two scientific workshops in Finland and France, where European researchers, developers, forecasters and civil protection representatives played the simulations. Two other game sessions were organized afterwards (i) with undergraduate university students in France and (ii) with Finnish stakeholders involved in the management of hazardous weather emergencies. First results indicate that multi-model developments and crowdsourcing tools increase the level of confidence in the decision-making under pressure. We found that the role-playing approach facilitates interdisciplinary cooperation and argumentation on emergency response in a fun and interactive manner. The ANYCaRE experiment was proposed, therefore, as a valuable learning tool to enhance participants' understanding of the complexities and challenges met by various actors in weather-related emergency management.</p

Defining and cataloging exoplanets: The exoplanet.eu database

We describe an online database for extra-solar planetary-mass candidates, updated regularly as new data are available. We first discuss criteria for the inclusion of objects in the catalog: "definition" of a planet and several aspects of the confidence level of planet candidates. {\bf We are led to point out the conflict between sharpness of belonging or not to a catalogue and fuzziness of the confidence level.} We then describe the different tables of extra-solar planetary systems, including unconfirmed candidates (which will ultimately be confirmed, or not, by direct imaging). It also provides online tools: histogrammes of planet and host star data, cross-correlations between these parameters and some VO services. Future evolutions of the database are presented.Comment: Accepted in Astronomy and Astrophysics (revised version