On the integration of digital technologies into mathematics classrooms

Trouche‘s (2003) presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche‘s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student‘s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics

Computational thinking in Denmark from an anthropological theory of the didactic perspective

In this paper, we study the external didactical transposition of programming and computational thinking (PCT) into the Danish compulsory school mathematics curriculum. Taking an anthropological theory of the didactic approach, we focus on the nature of mathematical and PCT knowledge being transposed into the new curriculum as prescribed praxeologies. Two main critiques arise. First, PCT knowledge being transposed into mathematics is broad and has no immediate relation to definitions from the literature. Second, the new competence and subject-matter areas are barely juxtaposed to those from mathematics. As a consequence, the responsibility of developing meaningful integrations in concrete teaching—the internal didactic transposition—lies entirely on teachers and material developers.This work is funded by the Novo Nordisk Foundation grant NNF19OC0058651

DevOps Didactic Transposition in IS Higher Education: A Systematic Literature Review

Information System (IS) higher education is often challenged by declining students’ academic performance and motivation. An alternative might be project-based learning (PjBL), due to its benefits for students, such as increased motivation. However, PjBL often focuses on the development phases and therefore lacks an operational vision. Against this drawback, DevOps might be seen as an advance of PjBL, arguing for a balance between the development and operational phases. Therefore, in this paper, we conducted a systematic literature review (SLR) to answer this question: What are the students’ results when DevOps is applied to the IS teaching context? We collected 339 papers and selected 22 post-filtering. The two SLR main results were: i) DevOps emerged recently in IS education; ii) DevOps is highly related to PjBL; iii) DevOps benefited students’ carrier development, scaffolds students’ grades, and communication. The main contributions of this research are: to describe the state-of-art of DevOps in IS education; to provide a theoretical foundation for IS didactic transposition from IS Industry; to detail the students’ results when utilizing DevOps is applied to the IS teaching context

What theories and methodologies are appropriate for studying phenomena related to mathematics curriculum reforms?

This chapter provides an overview of theoretical frameworks and methodologies used to analyse a range of mathematics curriculum reforms from across the globe. The means for analysis that has been developed includes linking broad theoretical frameworks and the levels within these to the lines of research and research questions; units of analysis and data considered; methodological choices; and results obtained in case studies of mathematics curriculum reform. It is proposed that the approach developed and findings presented could inform more systematic and scientific approaches to the design of reforms as well as their analysis

Task design for Engineering Mathematics: process, principles and products

International audienceWe present and analyse principles and process employed at the Danish Technical University to use authentic problems from engineering (APE) in a first year mathematics course, along with some of the products (actual student assignments)

AN EXAMINATION ABOUT THE DIDACTIC TRANSPOSITION IN THE POST-REMOTE TEACHING SCENARIO: OBSTACLES AND POSSIBILITIES

The aim of this work is to present the vision of the mathematics teacher about Didactic Transposition in the discipline of mathematics, pointing out their perceptions and various ways of working in two moments, one in the remote modality and another in the return to classroom teaching. To this end, we used a qualitative-qualitative methodology, in which fifteen mathematics teachers from the city of Sobral, Ceará, Brazil participated in the research, sharing their experiences through two virtual forms, answering some questions in two different periods – August/2021 and July/2022. The data provided us with information to reflect on the subject, verifying the main obstacles faced during and after the period of social isolation, as well as the good practices experienced and prospects for a post-pandemic scenario. Based on the answers and experiences shared by the research subjects, we understand that there were advantages in carrying out the Didactic Transposition of contents in the remote scenario, such as the possibility of using more than one technological resource during a teaching session, the dynamism that the use of different games and applications can provide, among other possibilities. However, negative aspects were also pointed out, such as difficulties in obtaining positive feedback, student participation and motivation, difficulties in handling technology in some cases or even reconciling work routine and activities in the home environment, negatively impacting teaching work. In addition, there is a perspective that face-to-face feedback brings the imperative of change, both in the format of classes and teaching methodologies, and in the professional attitude of the mathematics teacher.  Article visualizations

The co-design of scenarios for a didactic-based E-learning system viewed as an adaptive virtual document

The design and engineering of E-learning systems must be considered as a transdisciplinary problem requiring the integration of different scientific approaches. The design process of E-learning systems needs to consider several theories, models and artifacts – the e-learning system. We claim it is essential to ensure the traceability and the interpretation of phenomena related to the use of artifacts in studying precisely the relationships between theories, models and artifacts. Consequently, we develop a co-design methodology to deal with these goals. The main contribution of this paper is to describe a methodological approach enabling the co-design of problem-based learning scenarios in sciences which are based on teacher real practices acquired by means of the theory in didactic anthropology of knowledge and to show why we can formalize them in a hierarchical task model to design an adaptive E-learning system

The French Didactic Tradition in Mathematics

This chapter presents the French didactic tradition. It first describes theemergence and development of this tradition according to four key features (role ofmathematics and mathematicians, role of theories, role of design of teaching andlearning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this traditionon algebra and on line symmetry-reflection. It then questions the influence of thistradition through the contributions of four researchers from Germany, Italy, Mexicoand Tunisia, before ending with a short epilogue