A case study of an expert in computational thinking in the context of mathematics education research

We conducted semi-structured interviews with three experienced mathematics education researchers with great expertise in the design and use of digital technologies, including programming skills, to investigate their views and perceptions on computational thinking (CT) and its impact on mathematical learning. In this paper we report on our findings from one of them, Mark, and we suggest ways for adapting the very recent Mathematical Digital Competency (MDC) framework to encompass CT practices and dispositions. Our aim is to offer insights into how CT is perceived and understood by him, by prompting him to reflect on his own CT practices and competencies. We offer suggestions for an MDC framework for mathematics teacher educators that encompasses CT

An Analysis of Interactive Learning Environments for Arithmetic and Algebra Through an Integrative Perspective

International audienceThe analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE) dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software is given and a short description of ten ILEs concerned by the study is provided as a kind of a state-of-the-art. Then the methodology of ILEs analysis developed in the TELMA project is explained consisting in the design and the refinement of an analysis grid and its use on the ten ILEs is mentioned. Next, a first level analysis of results leading to a compiled, analytic and synthetic view of the ILEs available and/or missing functionalities is given. A second level of the analysis is also proposed, with two concise representations of the ILEs, composed of graphical representations of the previous results, leading to a 3D map of ILEs dedicated to arithmetic and algebra. This map provides, as promised, a global view of the field and permits to define five sorts of ILEs according to two criteria: the first one is teacher-oriented and concerns usages enabled by the ILE; the second one is student-oriented and concerns control provided by the ILE to accomplish such usages

An Analysis of Interactive Learning Environments for Arithmetic and Algebra Through an Integrative Perspective

International audienceThe analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE) dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software is given and a short description of ten ILEs concerned by the study is provided as a kind of a state-of-the-art. Then the methodology of ILEs analysis developed in the TELMA project is explained consisting in the design and the refinement of an analysis grid and its use on the ten ILEs is mentioned. Next, a first level analysis of results leading to a compiled, analytic and synthetic view of the ILEs available and/or missing functionalities is given. A second level of the analysis is also proposed, with two concise representations of the ILEs, composed of graphical representations of the previous results, leading to a 3D map of ILEs dedicated to arithmetic and algebra. This map provides, as promised, a global view of the field and permits to define five sorts of ILEs according to two criteria: the first one is teacher-oriented and concerns usages enabled by the ILE; the second one is student-oriented and concerns control provided by the ILE to accomplish such usages

Children challenging the design of half-baked games: Expressing values through the process of game modding

In this paper we look at the potential educational value of placing children in a dual role of identifying and changing rules and values embedded in digital games by hacking them. Children’s participation in the design of learning technologies is a difficult challenge to address, due to limitations in children’s domain-knowledge around which these technologies are developed. Their role in the design process is thus usually limited to that of a user or tester. In this paper we discuss the role of children as “hackers” of what we call ‘half-baked’ games. By hacking a pedagogically engineered half-baked game in order to improve or change it, children are expected to challenge the values, the mechanics and the rules of a fully functioning, but faulty, or inappropriate game originally designed to provoke students to modify it. This discussion uses an example of children modding such a game provocatively called ‘PerfectVille’, which was specially designed to raise problems around the issue of urban sustainability. The game itself was designed with the use of a GIS rule-based authoring tool for game design called ‘sus-x’. The children grappled with both value-laden issues and concepts embedded in the tool they used. The issue of taking children’s values into account but also of helping them to build understandings of wider contested societal values can be addressed by studying the process by which children design and change games affording such experiences. It also illuminated their own perspective and values, which they embedded in the games

Improving the Computational Thinking Pedagogical Capabilities of School Teachers

The idea of computational thinking as skills and universal competence which every child should possess emerged last decade and has been gaining traction ever since. This raises a number of questions, including how to integrate computational thinking into the curriculum, whether teachers have computational thinking pedagogical capabilities to teach children, and the important professional development and training areas for teachers. The aim of this paper is to address the strategic issues by illustrating a series of computational thinking workshops for Foundation to Year 8 teachers held at an Australian university. Data indicated that teachers\u27 computational thinking understanding, pedagogical capabilities, technological know-how and confidence can be improved in a relatively short period of time through targeted professional learning

Digital technologies and the development of the dynamic view of functional thinking

Functional thinking can be characterised by three properties, namely the assignment aspect, the covariation aspect, and the object aspect. Furthermore, static and dynamic views can be distinguished. In this article, an empirical study is presented that investigates the development of the dynamic view when working with linear functions through the use of digital technologies in the context of suitably selected tasks. The results show prerequisites and necessities for the integration of digital technologies into a constructive teaching concept for the development of functional thinking

Tracing the evolution of teachers' mathematical knowledge and pedagogy through programming: Learning from Scratch

This thesis is based on research to explore the role of primary school teachers’ mathematical and pedagogical knowledge in their engagement with computer-based microworlds that formed part of ScratchMaths (SM). SM is a two-year mathematics and computing curriculum designed for pupils aged nine to eleven years old. The aims of the research were to trace the evolution of teachers’ mathematical knowledge, as they taught SM microworlds designed for exploration and reasoning about place value, variable and angle through computer programming. The study adopted a multiple-case study approach with augmenting teacher episodes situated in the English primary school setting. The thirteen Year 6 teachers of the study were selected from national participants of the second year of the two-year SM intervention. Data collection involved video-recorded classroom observations, audio-recorded post-lesson semi-structured teacher interviews, and ‘think aloud’ while engaging with computer-based tasks. The conceptual framework for the thesis incorporated the Mathematical Pedagogical Technology Knowledge (MPTK) framework and the Instrumental Orchestration model. The findings reveal the knowledge required to teach at the intersection of programming and mathematics, and crucially, how the ideas mediate and are mediated by engagement with the SM curriculum. The findings also illustrate how teaching mathematics through computer programming requires the teacher to bridge between the computing and the mathematics domains and how some teachers managed to do this while creating new connections within and between the knowledge domains. The study contributes to the literature of teachers’ mathematical knowledge of place value, variable, and angle as well as teachers’ ability to (re-) express mathematics through computer programming. The thesis makes an original contribution to the literature with the specification of a theoretical model for analysing teachers’ knowledge for teaching mathematics through programming in the primary setting

Microworld Writing: Making Spaces for Collaboration, Construction, Creativity, and Community in the Composition Classroom

In order to create a 21st century pedagogy of learning experiences that inspire the engaged, constructive, dynamic, and empowering modes of work we see in online creative communities, we need to focus on the platforms, the environments, the microworlds that host, hold, and constitute the work. A good platform can build connections between users, allowing for the creation of a community, giving creative work an engaged and active audience. These platforms will work together to build networks of rhetorical/creative possibilities, wherein students can learn to cultivate their voices, skills, and knowledge bases as they engage across platforms and genres. I call on others to make, mod, or hack other new platforms. In applying this argument to my subject, teaching writing in a college composition class, I describe Microworld Writing as a genre that combines literary language practice with creativity, performativity, play, game mechanics, and coding. The MOO can be an example of one of these platforms and of microworld writing, in that it allows for creativity, user agency, and programmability, if it can be updated to have the needed features (virtual world, community, accessibility, narrativity, compatibility and exportability). I offer the concept of this MOO-IF as inspiration for a collaborative, community-oriented Interactive Fiction platform, and encourage people to extend, find, and build their own platforms. Until then and in addition, students can be brought into Microworld Writing in the composition classroom through interactive-fiction platforms, as part of an ecology of genre experimentation and platform exercise

They have their own thoughts : children's learning of computational ideas from a cultural perspective

Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1998.Includes bibliographical references (leaves 216-226).Paula Kay Hooper.Ph.D

Design for the Art of Learning: Defining Challenges for Maker-Driven Design Activities and Design Education in Secondary Schools

This thesis reflects on strategies used to facilitate didactic interactions between design research-creation and maker experiences in a secondary school. The author uses maker-driven design activity as a hybrid term to define educational activities that integrate critical making, sustainable action, and creative uses of technology. Two projects are described to exemplify the challenges and qualities of this didactic approach. The careful use of design constraints and observations of patterns of concern, such as process avoidance, are essential in understanding the qualities necessary for a meaningful design experience in the context of school. The author uses observations of maker-driven design activity situated in a school Fab Lab to inform guideposts for future research-creation infusing creative-technical learning with design literacy. This thesis is intended for designers, teachers, and researchers interested in creative and interdisciplinary learning experiences in what is broadly labelled as design for the art of learning