Capitalizing on advances in mathematics and k-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations

This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students’ beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the instructional design theory of Realistic Mathematics Education and the social negotiation of meaning. The main results of the comparison study found no significant difference between project students and comparison students on an assessment of routine skills and a significant difference in favor of project students on an assessment of conceptual understanding. Given these encouraging results, the theoretical underpinnings of the innovative approach may be useful more broadly for undergraduate mathematics education reform.     

Roles of assessment in secondary education: Participant perspectives

Performance pressure at both the institutional and individual level of secondary education has been identified as a pressure that is acknowledged all over Europe and raises questions about the extent to which agents in lower and upper secondary education interpret assessment in terms of either control or learning, or perhaps both. Drawing on empirical findings from two case studies in Denmark, the article focuses on the social roles of educational evaluation and assessment, and discusses the ways in which the local level interpretations of policy demands influence teaching and learning in secondary education. To enable an analysis of the understanding of different agents in the field, the article combines important sociological thinking with the basic distinction between assessment of programmes and assessment of individuals. Presuming that assessment practices bear the traces of the social structure that they both express and reproduce, the aim of this paper is to interrogate how the agents view and interpret such practices.     

Course Coordinator Orientations Toward their Work and Opportunities for Professional Development

Innovative Higher Education - One way that university mathematics departments across the United States are making efforts to improve their introductory mathematics courses is by implementing or...     

Some issues about the introduction of first concepts in linear algebra during tutorial sessions at the beginning of university

Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many types of difficulties as formal ones and far away from the actual knowledge of the students. The purpose of this paper is to propose a methodology for studying the introduction of such concepts in linear algebra during tutorial sessions at the beginning of university, the wording of the concepts being yet presented during lectures. For this purpose, we amend a general methodology of Pariès, Robert and Rogalski inside the general framework of Activity Theory. This methodology lets us take into account several specificities of these concepts and studies the mathematical activity the teacher organises for students and the way he manages the relationship between students’ actual activities and mathematical tasks. We also present an implementation of this methodology based on a French university course to illustrate our approach and discuss its possibilities.     

La réception des travaux scouts de Pierre Bovet en France (1912–décennie 1930)

Le scoutisme français n’a pas toujours vu Baden-Powell comme un modèle. A leur fondation en 1911, les Eclaireurs de France refusent de traduire Scouting for boys. Mais, le philosophe genevois Pierre Bovet le traduit dès 1912 pour l’éditeur neuchâtelois Delachaux et Niestlé. Le texte anglais arrive en France malgré le nationalisme des Eclaireurs qui le maintient dans un purgatoire sévère. La traduction est saluée par un réformateur social comme Georges Bertier, directeur de l’Ecole des Roches. Dès 1921, celui-ci préside les Eclaireurs et les ancre dans l’Education nouvelle. En 1919, l’éditeur Delachaux et Niestlé a ouvert une succursale dans la capitale française. L’essor des traductions scoutes est contemporain, notamment par des cadres suisses, tels Ketty Jentzer, commissaire genevoise ou Jean Carrard, chef à Lausanne. Mais, alors qu’en 1920, Bovet écrit son livre-maître Le Génie de Baden-Powell où il analyse cette pédagogie au prisme de l’Education nouvelle, d’autres frontières émergent. Les Français qui possèdent leurs propres travaux, ont moins besoin des traductions suisses. La frontière se recompose selon une autre ligne, l’étude savante. Les Français travaillent avec des philosophes comme Edmond Goblot et Pierre Mendousse autour de la question sociale, objet absent chez Bovet. Les Français défendent le merveilleux pédagogique au détriment de l’analyse savante pouvant le mettre en cause. Bovet demeure un simple passeur. Le scoutisme ouvre et ferme les frontières, recombinées selon les modalités propres à chaque époque.     

Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations

The objective of the teaching experiment reported in this article was to overcome the cognitive gap, that is, students' inability to spontaneously operate with or on the unknown. Following an analysis of the cognitive obstacles involved, this paper reports the results of an alternative approach. We designed an individualized teaching experiment which was tested in six case studies. In the first part the students' natural tendency to group singletons in the unknown within the equations was expanded to a process of grouping like terms. In the second part we introduced a reverse process to grouping like terms, that of decomposition of a term into a sum. This process, combined with the cancellation of identical terms, provides a procedure for the solution of first degree equations with the unknown on both sides of the equality sign. The last part of the teaching experiment involved the decomposition of an additive term into a difference. The first two parts proved very successful and the students developed procedures on their own that were more efficient than the initial ones. The results of the third part, however, revealed the limits of this approach. The students experienced difficulties in choosing the required decomposition. It seems that some of these obstacles are rather robust and perhaps should not be dealt with incidentally but should be addressed as part of a pre-algebra course.This research was funded by the Quebec Ministry of Education (Founds FCAR 92-ER-1032).