Didactic contract and secondary-tertiary transition: a focus on resources and their use

International audienceIn this article we claim that the concept of didactic contract can help to develop a deeper understanding of the secondary-tertiary transition, in particular by showing changes at three different levels: at the general, institutional level; at the level of the discipline concerning mathematical practices; and at the level of a given mathematical content. In fact, we argue that the didactic contract is linked to the use of and interaction with different resources, by teachers and students, in the sense that their use is shaped by the contract; and at the same time the available resources shape the mathematics taught. We draw here on two studies, one in the UK and one in France, to illustrate how a focus on resources can inform us about contract rules at the different levels

Students' work in mathematics and resources mediation at university

International audienceIn this paper we study the use of resources by students in their mathematical work at the beginning of university. The institution offers a variety of resources: lecture notes, books, exercises, websites, to name but a few. Leaning on a theoretical framework by Rabardel, we argue that the university teachers expected an epistemic mediation of these resources, as they supported student learning of (higher level) mathematics. However, analysing two case studies (one in the UK and one in France) we observe that the actual use of resources by novice mathematics students corresponded to a pragmatic mediation, as they searched for worked examples and “reproduction techniques”, all very similar to their use of resources at secondary school.</p

Mathematics Teachers’ Interaction with Digital Curriculum Resources: opportunities to develop teachers’ mathematics-didactical design capacity

International audienceThis particular paper reports on the investigation of (selected) French mathematics teachers' interactions with and use of a commonly used mathematics e-textbook (Sesamath), individually and collectively. Using three recent studies on teachers' work with Sesamath, and leaning on theoretical frames from the area of curriculum design and instructional design with technology, we identify several dimensions of " design " , that is mathematics teachers working as designers. Moreover, we claim that the affordances of digital resources are related to the opportunities for " design " by mathematics teachers, of their own curriculum materials in/for instruction; and for the development of teachers' mathematics-didactical design capacity. This paper is one of four in the AERA 2016 symposium on digital resources/curriculum materials, including e-textbooks, in mathematics education. The focus is on the resources' design and analysis; and teachers' and students' interaction with them. As digital resources are increasingly present in classrooms around the world, it is important to investigate their features, and in which ways they influence, afford, or indeed may transform, particular educational processes and practices. The underlying questions of the symposium are: What are the " new " digital curriculum resources, and what are the features of those resources, that influence mathematics teachers' instructional design? What are students' interactions and modes of engagement with those resources? In which ways do these resources stimulate new educational dynamics? This particular paper reports on the investigation of (selected) French mathematics teachers' interactions with and use of a commonly used mathematics e-textbook, individually and collectively

Manuels scolaires et ressources numériques: vers de nouvelles conceptualisations

International audienceIn many countries textbooks remain to be the main resources for mathematics teachers. However, textbooks have changed over time, likely due to deveopments in information technology. In this paper we report on an investigation of how two French mathematics textbooks are conceived by their authors, analysing the effects of different conceptualisations reflected in the books. For the analysis we chose two commonly used French textbooks at grade 6 (topic of “area”): one authored by a small group of experts (Helice); and one by a large group of mathematics teachers (Sesamath). In addition, we drew evidence from interviews with the textbook authors. Using the documentational approach, we analysed the textbooks with respect to quality and their usages (instrumentation-instrumentalisation). In particular, we propose to re-conceptualise the notion of quality of textbooks by introducing two dimensions for analysis: connectivity; and coherence of textbooks. Based on our analysis, we argue that (1) the “expert book” is of “didactic quality”, albeit static and oriented towards an “instrumentation usage”; whereas (2) the “teacher collective book” was of “dynamic quality” oriented towards processes of “instrumentalisation”.Dans de nombreux pays, les manuels scolaires restent en mathématiques des ressources centrales pour les professeur ; toutefois ils connaissent d’importantes évolutions liées au numérique. Nous étudions ces évolutions et leurs conséquences, en ce qui concerne la conception de manuels, avec une perspective d’approche documentaire. Nous proposons de re-conceptualiser la notion de qualité des manuels, en introduisant deux dimensions : la connectivité et la cohérence des manuels. Nous avons retenu deux manuels français pour la classe de 6e, l’un conçu par un petit groupe d’experts (Hélice) et l’autre par une large équipe de professeurs (Sésamath). Nous appliquons à ces manuels nos propositions théoriques, et illustrons par leur analyse (en retenant en particulier le thème de « l’aire ») le type de phénomènes que l’on peut identifier en termes d’instrumentalisation et d’instrumentation ; de connectivité, de cohérence et de qualité des manuels. Nous montrons que le manuel conçu par des experts est d’une plus grande qualité didactique, mais statique, et tourné vers l’instrumentation pour les utilisateurs, tandis que le manuel conçu par un collectif de professeurs est d’une qualité dynamique et tourné vers l’instrumentalisation.Em numerosos países os livros didáticos são, em Matemática, recursos centrais para os professores; todavia esses têm sofrido importantes evoluções ligadas ao digital. Nós estudamos estas evoluções e suas consequências em relação ao processo de designer de livros didáticos, pautados em uma perspectiva de abordagem documental. Nós propomos re-conceitualizar a noção de qualidade dos livros didáticos, introduzindo duas dimensões: a conectividade e a coerência dos livros. Analisamos dois livros didáticos franceses destinados ao sexto ano do ensino fundamental, um criado por um pequeno grupo de especialistas (Hélice) e outro por uma grande equipe de professores (Sésamath). Aplicamos a estes livros nossas proposições teóricas e ilustramos para sua análise (em particular o tema área) o tipo de fenômenos que podemos identificar em termos de instrumentalização e instrumentação, a conectividade, a coerência e a qualidade dos livros. Mostramos que o livro produzido pelos especialistas é de uma grande qualidade didática, mas estática, voltada para a instrumentação dos usuários, enquanto que o livro produzido pelo coletivo de professores é de uma qualidade dinâmica, voltada para a instrumentalização

Teachers’ use of resources in and for mathematics teaching

Over the past decades the amount of available resources for mathematics teaching has vastly increased, in particular the availability of resources on the web. However, we know very little about how teachers select and use the available resources. In this paper we investigate how four primary school teachers used curriculum resources in and for their mathematics teaching. Grounded in a case study approach, we have analysed lessons, teacher interviews, and documents they used for their lesson preparation and instruction. Subsequently, we identified five ”usage categories”: (1) resources to manage the teaching objectives; (2) resources to ”inspire” teaching; (3) resources for student work; (4) resources to adapt the teaching to indivi-dual students’ needs (differentiation); and (5) resources to organize the teaching. In this article we explain and discuss these five categories, and argue that the ”lens of resources” offers an opportune window into teachers’ work, in particular their work as mathematics teachers