L'apprentissage de l'itération dans deux environnements informatiques

Cet article présente une étude comparée de l'apprentissage de l'itération dans deux environnements informatiques différents : Pascal et Multiplan. Cette étude a été réalisée avec des élèves de troisième (fin de la scolarité obligatoire) d'un collège français. Les AA. ont pu dégager des analogies importantes entre les deux environnements à propos de l'itération. Mais l'hypothèse consistant à prévoir un transfert des connaissances d'un logiciel à l'autre ne s'est pas trouvée confirmée, ce qui confirme la complexité cognitive du concept d'itération, déjà mise en évidence dans d'autres recherche

Design approaches in technology enhanced learning

Design is a critical to the successful development of any interactive learning environment (ILE). Moreover, in technology enhanced learning (TEL), the design process requires input from many diverse areas of expertise. As such, anyone undertaking tool development is required to directly address the design challenge from multiple perspectives. We provide a motivation and rationale for design approaches for learning technologies that draws upon Simon's seminal proposition of Design Science (Simon, 1969). We then review the application of Design Experiments (Brown, 1992) and Design Patterns (Alexander et al., 1977) and argue that a patterns approach has the potential to address many of the critical challenges faced by learning technologists

CROO: A universal infrastructure and protocol to detect identity fraud

Identity fraud (IDF) may be defined as unauthorized exploitation of credential information through the use of false identity. We propose CROO, a universal (i.e. generic) infrastructure and protocol to either prevent IDF (by detecting attempts thereof), or limit its consequences (by identifying cases of previously undetected IDF). CROO is a capture resilient one-time password scheme, whereby each user must carry a personal trusted device used to generate one-time passwords (OTPs) verified by online trusted parties. Multiple trusted parties may be used for increased scalability. OTPs can be used regardless of a transaction’s purpose (e.g. user authentication or financial payment), associated credentials, and online or on-site nature; this makes CROO a universal scheme. OTPs are not sent in cleartext; they are used as keys to compute MACs of hashed transaction information, in a manner allowing OTP-verifying parties to confirm that given user credentials (i.e. OTP-keyed MACs) correspond to claimed hashed transaction details. Hashing transaction details increases user privacy. Each OTP is generated from a PIN-encrypted non-verifiable key; this makes users’ devices resilient to off-line PIN-guessing attacks. CROO’s credentials can be formatted as existing user credentials (e.g. credit cards or driver’s licenses)

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 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

Approaching Proof in the Classroom Through the Logic of Inquiry

The paper analyses a basic gap, highlighted by most of the literature concerning the teaching of proofs, namely, the distance between students' argumentative and proving processes. The analysis is developed from both epistemological and cognitive standpoints: it critiques the Toulmin model of reasoning and introduces a new model, the Logic of Inquiry of Hintikka, more suitable for bridging this gap. An example of didactical activity within Dynamic Geometry Environments is sketched in order to present a concrete illustration of this approach and to show the pedagogical effectiveness of the model

Validation of Solutions of Construction Problems in Dynamic Geometry Environments

This paper discusses issues concerning the validation of solutions of construction problems in Dynamic Geometry Environments (DGEs) as compared to classic paper-and-pencil Euclidean geometry settings. We begin by comparing the validation criteria usually associated with solutions of construction problems in the two geometry worlds – the ‘drag test’ in DGEs and the use of only straightedge and compass in classic Euclidean geometry. We then demonstrate that the drag test criterion may permit constructions created using measurement tools to be considered valid; however, these constructions prove inconsistent with classical geometry. This inconsistency raises the question of whether dragging is an adequate test of validity, and the issue of measurement versus straightedge-and-compass. Without claiming that the inconsistency between what counts as valid solution of a construction problem in the two geometry worlds is necessarily problematic, we examine what would constitute the analogue of the straightedge-and-compass criterion in the domain of DGEs. Discovery of this analogue would enrich our understanding of DGEs with a mathematical idea that has been the distinguishing feature of Euclidean geometry since its genesis. To advance our goal, we introduce the compatibility criterion , a new but not necessarily superior criterion to the drag test criterion of validation of solutions of construction problems in DGEs. The discussion of the two criteria anatomizes the complexity characteristic of the relationship between DGEs and the paper-and-pencil Euclidean geometry environment, advances our understanding of the notion of geometrical constructions in DGEs, and raises the issue of validation practice maintaining the pace of ever-changing software.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42932/1/10758_2004_Article_6999.pd

Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Exploiting Distance Technology to Foster Experimental Design as a Neglected Learning Objective in Labwork in Chemistry

This article deals with the design process of a remote laboratory for labwork in chemistry. In particular, it focuses on the mutual dependency of theoretical conjectures about learning in the experimental sciences and technological opportunities in creating learning environments. The design process involves a detailed analysis of the expert task and knowledge, e.g., spectrophotometry as a method for the determination of the concentration of a compound in a solution. In so doing, modifications in transposing tasks and knowledge to the learning situation can be monitored. The remote laboratory is described, as well as the specific features that alter the degree of fidelity of the learning situation in comparison to the expert one. It is conjectured that these alterations might represent actual benefits for learning