Didactic Restrictions on the Teacher’s Practice: The Case of Limits of Functions in Spanish High Schools

The Anthropological Theory of Didactics describes mathematical activity in terms of mathematical organisations or praxeologies and considers the teacher as the director of the didactic process the students carry out, a process that is structured along six dimensions or didactic moments. This paper begins with an outline of this epistemological and didactic model, which appears as a useful tool for the analysis of mathematical and teaching practices. It is used to identify the main characteristics of the mathematical organisation around the limits of functions as it is proposed to be taught at high school level. The observation of an empirical didactic process will finally show how the internal dynamics of the didactic process is affected by certain mathematical and didactic constraints that significantly determine the teacher’s practice and ultimately the mathematical organisation actually taught.     

Umbrellas: Which Way Is the Wind Blowing?

The field of physical education/kinesiology is facing unique challenges. There are ongoing pressures for change and adaptation forcing us to look to our past as we face an uncertain future. In the past, we have been blessed with all-encompassing categories that may be called “umbrellas.” The American Alliance for Health, Physical Education, Recreation and Dance (AAHPERD) has offered us an umbrella that some of us appear to be rejecting. We do so at our peril. Disciplinary development became energized in the 1960s; we now appreciate more fully that our field entails the study of human movement particular to physical activities such as exercise, sport, games, play, aquatics, dance, and athletics. As a profession, we need the undergirding knowledge that our disciplinarians are gradually providing. This knowledge should come from both the disciplinary and professional wings of our field. There is a continuing need for the services that physical education/kinesiology can provide. We will survive if we cooperate with our colleagues in the allied professions under the overarching umbrella of AAHPERD, if we achieve consensus about what it is we do under our own umbrella, and if we devise ways and means of keeping the struts of our own umbrella strong enough to fight off the strong winds that are presently tending to tear it out of our hands.     

Learning to use learning resources during medical school and residency.

OBJECTIVES: This study (1) examined the natural history of learning to use learning resources by medical students and residents and (2) considered whether that history is consistent with the ways in which physicians approach their learning tasks. METHODS: The authors conducted and analyzed thirty-two open-ended interviews of first-year and third-year medical students and first-year and senior residents in internal medicine, family medicine, or pediatrics. RESULTS AND DISCUSSION: Learning to use learning resources occurs at the same time as learning done to address instructional and clinical problems that physicians-in-training face, with all kinds of learning following well-documented stages. Skills for using resources are developed gradually and by overcoming barriers such as time constraints and existing habits. CONCLUSIONS: Implications of the natural history of learning to use learning resources can be employed by librarians and medical teachers to facilitate self-directed learning for physicians-in-training. Specific recommendations are provided.