Turtle Geometry

Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates

The role of sign in students' modeling of scalar equations

We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.Comment: 5 pages, 1 figure, to be published in The Physics Teache

Some Assembly Required: How Scientific Explanations are Constructed During Clinical Interviews

This article is concerned with commonsense science knowledge, the informally-gained knowledge of the natural world that students possess prior to formal instruction in a scientific discipline. Although commonsense science has been the focus of substantial study for more than two decades, there are still profound disagreements about its nature and origin, and its role in science learning. What is the reason that it has been so difficult to reach consensus? We believe that the problems run deep; there are difficulties both with how the field has framed questions and the way that it has gone about seeking answers. In order to make progress, we believe it will be helpful to focus on one type of research instrument – the clinical interview – that is employed in the study of commonsense science. More specifically, we argue that we should seek to understand and model, on a moment-by-moment basis, student reasoning as it occurs in the interviews employed to study commonsense science. To illustrate and support this claim, we draw on a corpus of interviews with middle school students in which the students were asked questions pertaining to the seasons and climate phenomena. Our analysis of this corpus is based on what we call the mode-node framework. In this framework, student reasoning is seen as drawing on a set of knowledge elements we call nodes, and this set produces temporary explanatory structures we call dynamic mental constructs. Furthermore, the analysis of our corpus seeks to highlight certain patterns of student reasoning that occur during interviews, patterns in what we call conceptual dynamics. These include patterns in which students can be seen to search through available knowledge (nodes), in which they assemble nodes into an explanation, and in which they converge on and shift among alternative explanations

Aprendizaje orientado a la programación en economía, negocios y finanzas

[EN] As the relationship between both students (teachers) and information technology evolves, new tools are required to improve learning (teaching) in social sciences. Economics, business and finance are mainly based on data and dealing with data requires specific skills and techniques such as computer programming in order to get full potential of most quantitative models. In this paper, we propose a coding oriented learning method based on Python Notebooks which is specifically designed for students of degrees in economics, business and finance. We follow a learning-by-doing strategy that encourages students to implement economic models as a suitable way to improve the understanding of fundamental concepts. As an illustrative example, we also describe a case study in which Python Notebooks are the key tool to teach cash management in a Master in Business Administration program. Since students of today are the decision-makers of tomorrow, a further advantage of the use of a programming language as a teaching tool is the possibility to connect theory to practice by enabling students to implement their own decision support tools.[ES] La evolución entre la relación entre los estudiantes (profesores) y la tecnología de la información, requiere nuevas herramientas para mejorar el aprendizaje (enseñanza) en las ciencias sociales. La economía, los negocios y las finanzas se basan principalmente en los datos y el tratamiento de los datos requiere habilidades y técnicas específicas, como la programación informática, para aprovechar al máximo el potencial de la mayoría de los modelos cuantitativos. En este documento, proponemos un método de aprendizaje orientado a la programación basado en Python Notebooks, que está diseñado específicamente para estudiantes de títulos en economía, negocios y finanzas. Nuestra estrategia de aprendizaje es eminentemente práctica motivando a los estudiantes a implementar modelos económicos como una forma adecuada de mejorar la comprensión de los conceptos fundamentales. Como ejemplo ilustrativo, también describimos un estudio de caso en el que Python Notebooks es la herramienta clave para enseñar gestión de efectivo en un programa de Máster en Administración de Empresas. Dado que los estudiantes de hoy son los que toman las decisiones del mañana, una ventaja adicional del uso de un lenguaje de programación como herramienta de enseñanza es la posibilidad de conectar la teoría con la práctica al permitir a los estudiantes implementar sus propias herramientas de apoyo a la decisión.Salas-Molina, F.; Pla-Santamaria, D. (2018). Coding oriented learning in economics,business and finance. Modelling in Science Education and Learning. 11(1):55-64. doi:10.4995/msel.2018.9152SWORD5564111da Costa Moraes, M. B., Nagano, M. S., and Sobreiro, V. A. (2015). Stochastic cash ow management models: A literature review since the 1980s. In Decision Models in Engineering and Management, pages 11-28. Springer International Publishing.DiSessa, A. A. (2001). Changing minds: Computers, learning, and literacy. Mit Press.Guzdial, M. (2010). Why is it so hard to learn to program? In Making software: What really works, and why we believe it, pages 111-121. O'Reilly Media, Inc.Ketcheson, D. I. (2014). Teaching numerical methods with iPython notebooks and inquiry-based learning. In Proceedings of the 13th Python in Science Conference. SciPy. org.Myers, G. J., Sandler, C., and Badgett, T. (2011). The art of software testing. John Wiley & Sons.Rossant, C. (2014). IPython interactive computing and visualization cookbook. Packt Publishing Ltd.VanderPlas, J. (2016). Python Data Science Handbook: Essential Tools for Working with Data. O'Reilly

IDR : a participatory methodology for interdisciplinary design in technology enhanced learning

One of the important themes that emerged from the CAL’07 conference was the failure of technology to bring about the expected disruptive effect to learning and teaching. We identify one of the causes as an inherent weakness in prevalent development methodologies. While the problem of designing technology for learning is irreducibly multi-dimensional, design processes often lack true interdisciplinarity. To address this problem we present IDR, a participatory methodology for interdisciplinary techno-pedagogical design, drawing on the design patterns tradition (Alexander, Silverstein & Ishikawa, 1977) and the design research paradigm (DiSessa & Cobb, 2004). We discuss the iterative development and use of our methodology by a pan-European project team of educational researchers, software developers and teachers. We reflect on our experiences of the participatory nature of pattern design and discuss how, as a distributed team, we developed a set of over 120 design patterns, created using our freely available open source web toolkit. Furthermore, we detail how our methodology is applicable to the wider community through a workshop model, which has been run and iteratively refined at five major international conferences, involving over 200 participants

Une introduction accessible à la « Connaissance par Morceaux »

La Connaissance par Morceaux(CpM) est une perspective épistémologique qui a réussi à produire, dans le champ de la didactique des sciences, des explications significatives de phénomènes d’apprentissage, en particulier en ce qui concerne les conceptions préalables des élèves et les rôles de celles-ci dans l’émergence de la compétence. La CpM est nettement moins utilisée en mathématiques. Cependant, je fais l’hypothèse que les raisons de ce moindre usage relèvent principalement de différences historiques plutôt que d’écarts entre les processus d’apprentissage en mathématiques et en sciences expérimentales. L’objectif de cet article est de présenter la CpM d’une manière relativement accessible pour des chercheurs en didactique des mathématiques. Je présente les principes généraux et les caractéristiques essentielles de la CpM. Je m’appuie sur une variété d’exemples, y compris d’exemples en mathématiques, pour illustrer le fonctionnement de la CpM, son utilisation pratique et ce que l’on peut en attendre. J’espère ainsi encourager et accompagner une utilisation plus importante de la CpM dans la recherche en didactique des mathématiques.Knowledge in Pieces (KiP) is an epistemological perspective that has had significant success in explaining learning phenomena in science education, notably the phenomenon of students’ prior conceptions and their roles in emerging competence. KiP is much less used in mathematics. However, I conjecture that the reasons for relative disuse mostly concern historical differences in traditions rather than in-principle distinctions in the ways mathematics and science are learned.This article aims to explain KiP in a relatively non-technical way to mathematics educators. I explain the general principles and distinguishing characteristics of KiP. I use a range of examples, including from mathematics, to show how KiP works in practice and what one might expect to gain from using it. My hope is to encourage and help guide a greater use of KiP in mathematics education

Understanding and Affecting Student Reasoning About Sound Waves

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.Comment: 23 pages, 4 figures, 3 tables, 28 references, 7 notes. Accepted for publication in the International Journal of Science Educatio

The Schrodinger Wave Functional and Vacuum State in Curved Spacetime II. Boundaries and Foliations

In a recent paper, general solutions for the vacuum wave functionals in the Schrodinger picture were given for a variety of classes of curved spacetimes. Here, we describe a number of simple examples which illustrate how the presence of spacetime boundaries influences the vacuum wave functional and how physical quantities are independent of the choice of spacetime foliation used in the Schrodinger approach despite the foliation dependence of the wave functionals themselves.Comment: 26 pages, 4 figures, LATE