Webbing and orchestration. Two interrelated views on digital tools in mathematics education

The integration of digital tools in mathematics education is considered both promising and problematic. To deal with this issue, notions of webbing and instrumental orchestration are developed. However, the two seemed to be disconnected, and having different cultural and theoretical roots. In this article, we investigate the distinct and joint journeys of these two theoretical perspectives. Taking some key moments in recent history as points of de- parture, we conclude that the two perspectives share an importance attributed to digital tools, and that initial differences, such as different views on the role of digital tools and the role of the teacher, have become more nuances. The two approaches share future chal- lenges to the organization of teachers'collaborative work and their use of digital resources.Comment: Teaching Mathematics and its Applications (2014) to be complete

Mathematics teacher educators’ work to foster an inquiry community

For several years, the study of mathematics teacher educators (MTEs) has been considered central in research. The present study is focused, in particular, on MTE expertise in generating documents for the work with teachers, during a professional development (PD) program. We aim to analyse how MTEs generate documents coherently with the goal they have set for the PD program itself. In the case study presented in this paper, MTEs’ goal is building an inquiry community with the teachers. The results illustrate what kind of resources are involved in MTEs’ documentational genesis and how MTEs’ choices in their documentation work are connected with their goal for the PD program

Reflections on the Documentational Work of Two Teachers in a Remote Collaborative Environment for Compound Interest Teaching

Background:  Documentational Approach to Didactics was adopted, this way considers a continuous process in which resources, associated with the utilisation schemes, are transformed into documents.  Objectives: Characterize the Documentational Genesis of two High School Mathematics teachers in remote collaborative work for teaching Compound Interest articulated with the GeoGebra software. Design: As a methodological framework, the reflective investigation methodology was used, in which the teachers contribute to data collection and analysis. The paper was structured in four professional situations: reflection situation, training situation, implementation situation, and confrontational situation. Settings and participants: Teachers worked from March to June 2021, and resources were developed through the Google Docs and Google Meet virtual platforms and later made available on Classroom. Data Collection and Analysis: Data obtained through the recordings of the meetings and the proposals of the participants, analysed according to documentational trajectory concept, the instrumentation and instrumentalisation dialectics, productive and constructive activity dialectics, and the self-efficacy concept. Results: Based on our analyses, it was possible to characterise the teachers’ Documentational Genesis. Conclusions: The Documentational Approach to Didactics was relevant to the study because it was possibly identified the resources in individual and collective utilisation schemes, mobilised in the documentational work and in class implementation by the teachers and the instrumentation and instrumentalisation dimensions in document construction for teaching Compound Interest, i.e., the Documentational Genesis process. In addition, we have identified the teachers’ self-efficacy during the documentational work and implementation of classes on Compound Interest

Developing teaching of mathematics to engineering students: teacher research, student epistemology and mathematical competence

A research project “Engineering Students Understanding Mathematics” (ESUM) has shown tensions between teachers’ theoretical perspectives and design of teaching and students strategic approach to learning. In my research team we seek to improve our teaching of engineering students and to develop their conceptual understandings of mathematics. Given our findings on student perspectives, and the institutional affordances and constraints, we are exploring a range of resources and teaching approaches using theoretical perspectives of inquiry community, documentational genesis and activity theory

Becoming Aware Of Mathematical Gaps In New Curricular Materials: A Resource-Based Analysis Of Teaching Practice

The study featured in this article, with its central focus on resources-in-use, draws upon salient aspects of the documentational approach of didactics. It includes an a priori analysis of the curricular resources being used by a teacher for the first time, followed by detailed in situ observations of the unfolding of her teaching practice involving these resources. The central mathematical problem of the lesson being analyzed deals with families of polynomial functions. The analysis highlights the teacher’s growing awareness of the mathematical gaps in the resources she is using, which we conjecture to be a first step for her in the evolutionary transformation of resource to document, as well as an essential constituent of her ongoing professional development

“One of the beauties of Autograph is … that you don’t really have to think”: Integration of resources in mathematics teaching

This paper introduces part of a larger study on the use of technology, specifically mathematics education software, by secondary mathematics teachers. It presents some of the data collected with the aim of investigating teachers’ use of mathematics-education software: why are certain settings used, or underused, how are they used, and what are the reasons behind such use? The findings will be discussed by drawing on the documentational approach (Gueudet & Trouche, 2009) and teaching triad (Jaworski, 1994). The data collected is for one interview and one lesson observation with a secondary mathematics teacher. While the documentational approach provides an overview of the set of resources being integrated to achieve a specific goal, the teaching triad presents a lens to observe teachers’ considerations when implementing a task in a mathematics lesson

Mathematic e-textbooks in different didactic configurations

The e-textbook is one of the main resources that distance learning institutions make available in the virtual learning environment (VLE) for teachers and students. According to the Brazilian References for Distance Learning, the authors should follow some methodological, epistemological and political principles for its production: to allow students and teachers (educator and tutor) to construct knowledge through interaction with peers. In this paper we seek to map the enrichment of the content in DE carried out by teachers’ educator, from the use of e-textbook, in the light of the analysis of the teacher’s instrumental orchestrations. The theoretical framework comprised Luc Trouche\u27s Instrumental Orchestration, focused on understanding the didactic configuration. Three trainers of Analytical Geometry from two courses of Mathematics teachers’ initial education of Brazilian Open University composed our subjects. As for the method, we adopted some techniques used in the documentational approach to didactics, introduced by Ghislaine Gueudet and Luc Trouche. We made a virtual visit to the teachers\u27 virtual classroom protocols in VLE, and then an interview with each teacher was undertaken. Finally, we asked them to draw a map of the resources they use in class. Our results revealed the need to add other content resources, during didactic mediation forcing the teacher to change his didactic configurations, and the need to think about a collective construction of the e-textbook, discussing in parallel with the main authors of distance learning, teachers and tutors of the performers

Teaching Resources and teachers professional development: toward a documentational approach of didactics

We propose in this paper a theoretical approach of teachers' professional development, focusing on teachers' interactions with resources, digital resources in particular. Documents, entailing resources and schemes of utilization of these resources, are developed throughout documentational geneses occurring along teachers' documentation work (selecting resources, adapting, combining, refining them). The study of teachers' documentation systems permits to seize the changes brought by digital resources; it also constitutes a way to embrace teachers' professional change