¿Qué pueden aportar a los enseñantes los diferentes enfoques de la didáctica de las matemáticas? (segunda parte)

In the first part of this paper we raised the question of whether a customized theory of the didactics of mathematics was legitimate and presented and overview of such a theory. This second part analyses the contribution from and constraints the classical approaches and social practices on which they rely, and discusses the relationship between mathematics and its didactic

¿Qué pueden aportar a los enseñantes los diferentes enfoques de la didáctica de las Matemáticas? (primera parte)

This paper offers a general view of the relationships between Education, Mathematics Education and Mathematics

Research on classroom practice: A monograph for topic study group 24, ICME 11 - The introductory chapter

published_or_final_versionThe 11th International Congress on Mathematical Education (ICME 11), Monterrey, Mexico, 6-13 July 2008. In Quaderni di Ricerca in Didattica, 2009, n. S4, p. 1-

Alien Registration- Brousseau, Lucian G. (Fairfield, Somerset County)

https://digitalmaine.com/alien_docs/9788/thumbnail.jp

Alien Registration- Brousseau, Lucian G. (Fairfield, Somerset County)

https://digitalmaine.com/alien_docs/9788/thumbnail.jp

Bridging knowing and proving in mathematics An essay from a didactical perspective

Text of a talk at the conference "Explanation and Proof in Mathematics: Philosophical and Educational Perspective" held in Essen in November 2006International audienceThe learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which they can apply in significant problem situations, and which is amenable to falsification and argumentation. They can validate what they claim to be true but using means generally not conforming to mathematical standards. Here, I analyze how this situation underlies the epistemological and didactical complexities of teaching mathematical proof. I show that the evolution of the learners' understanding of what counts as proof in mathematics implies an evolution of their knowing of mathematical concepts. The key didactical point is not to persuade learners to accept a new formalism but to have them understand how mathematical proof and statements are tightly related within a common framework; that is, a mathematical theory. I address this aim by modeling the learners' way of knowing in terms of a dynamic, homeostatic system. I discuss the roles of different semiotic systems, of the types of actions the learners perform and of the controls they implement in constructing or validating knowledge. Particularly with modern technological aids, this model provides a basis designing didactical situations to help learners bridge the gap between pragmatics and theory

Ways to teach modelling—a 50 year study

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author’s observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was entirely focused on their learning standards models of a restricted range of phenomena, largely from Newtonian mechanics. This did not develop the numeracy/mathematical literacy that was so clearly important for future citizens. Early explorations started with modelling workshops with high school teachers and mathematics undergraduates, observed and analysed—in some case using video. The theoretical basis of this work has been essentially heuristic, though the Shell Centre studies included, for example, a detailed analysis of formulation processes that has not, as so often, been directly replicated. Recent work has focused on developing a formative assessment approach to teaching modelling that has proved both successful and popular. Finally, the system-level challenges in trying to establish modelling as an integral part of mathematics curricula are briefly discussed

‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal

Changing classroom culture, curricula, and instruction for proof and proving: how amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions?

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also critically important to knowing and doing mathematics. Although the seven papers, and the intervention studies they report, vary in many ways—student population, content domain, goals and duration of the intervention, and theoretical perspectives, to name a few—they all provide valuable insight into ways in which classroom experiences might be designed to positively influence students’ learning to prove. In our commentary, we highlight the contributions and promise of the interventions in terms of whether and how they present capacity to change the classroom culture, the curriculum, or instruction. In doing so, we distinguish between works that aim to enhance students’ preparedness for, and competence in, proof and proving and works that explicitly foster appreciation for the need and importance of proof and proving. Finally, we also discuss briefly the interventions along three dimensions: how amenable to scaling up, how practicable for curricular integration, and how capable of producing long-lasting effects these interventions are

The SURFEXv7.2 land and ocean surface platform for coupled or offline simulation of Earth surface variables and fluxes

CC Attribution 3.0 License.Final revised paper also available at http://www.geosci-model-dev.net/6/929/2013/gmd-6-929-2013.pdfInternational audienceSURFEX is a new externalized land and ocean surface platform that describes the surface fluxes and the evolution of four types of surface: nature, town, inland water and ocean. It can be run either coupled or in offline mode. It is mostly based on pre-existing, well validated scientific models. It can be used in offline mode (from point scale to global runs) or fully coupled with an atmospheric model. SURFEX is able to simulate fluxes of carbon dioxide, chemical species, continental aerosols, sea salt and snow particles. It also includes a data assimilation module. The main principles of the organization of the surface are described first. Then, a survey is made of the scientific module (including the coupling strategy). Finally the main applications of the code are summarized. The current applications are extremely diverse, ranging from surface monitoring and hydrology to numerical weather prediction and global climate simulations. The validation work undertaken shows that replacing the pre-existing surface models by SURFEX in these applications is usually associated with improved skill, as the numerous scientific developments contained in this community code are used to good advantage