Surprises from mathematics education research: student (mis)use of mathematical definitions

The authors of this paper met at a summer institute sponsored by the Oregon Collaborative for Excellence in the Preparation of Teachers (OCEPT). Edwards is a researcher in undergraduate mathematics education. Ward, a pure mathematician teaching at an undergraduate institution, had had little exposure to mathematics education research prior to the OCEPT program. At the institute, Edwards described to Ward the results of her Ph.D. dissertation on student understanding and use of definitions in undergraduate real analysis. In that study, tasks involving the definitions of “limit” and “continuity,” for example, were problematic for some of the students. Ward’s intuitive reaction was that those words were “loaded” with connotations from their nonmathematical use and from their less than completely rigorous use in elementary calculus. He said, “I’ll bet students have less difficulty or, at least, different difficulties with definitions in abstract algebra. The words there, like ‘group’ and ‘coset,’ are not so loaded." Eventually, with OCEPT support, the authors studied student understanding and use of definitions in an introductory abstract algebra course populated by undergraduate mathematics majors and taught by Ward. The “surprises” in the title are outcomes that surprised Ward, among others. He was surprised to see his algebra students having difficulties very similar to those of Edwards’s analysis students. (So he lost his bet.) In particular, he was surprised to see difficulties arising from the students’ understanding of the very nature of mathematical definitions, not just from the content of the definitions. Upon hearing of Edwards’s dissertation work, some other mathematicians who teach undergraduates found those difficulties surprising even when restricted to real analysis. Hereafter, we present a simple two-part theoretical framework borrowed from philosophy and from mathematics education literature. Although it is not our intent to give an extensive report of either study, we next indicate the methodology used in Edwards’s dissertation and in our joint abstract algebra study so that the reader may know the context from which our observations are drawn. We then list the “surprising” difficulties of the two groups of students, documenting them with examples from the studies and using the framework to provide a possible explanation for them. We conclude with what we see as the implications for undergraduate teaching, along with some specific classroom activities that the studies and our experience as teachers suggest might be of value.Keywords: Education, Mathematical definitions, MathematicsKeywords: Education, Mathematical definitions, Mathematic

La production biologique de porcs en Europe - Gestion de la santé des porcs dans les élevages de production

Les éleveurs de porcs biologiques ont développé en Europe différents systèmes de logement qui dépendent de la disponibilité des terres, des caractéristiques du sol et du climat, des traditions et des schémas de certification. Ce guide décrit les principaux systèmes de logement des porcs biologiques. Il compare les avantages et les inconvénients de chacun et donne des recommandations aux éleveurs pour mieux agir sur la santé des animaux

On the Approach to the Equilibrium and the Equilibrium Properties of a Glass-Forming Model

In this note we apply some theoretical predictions that arise in the mean field framework for a large class of infinite range models to structural glasses and we present a first comparison of these predictions with numerical results.Comment: 22 pages, 15 figure

Managing clinical trials

Managing clinical trials, of whatever size and complexity, requires efficient trial management. Trials fail because tried and tested systems handed down through apprenticeships have not been documented, evaluated or published to guide new trialists starting out in this important field. For the past three decades, trialists have invented and reinvented the trial management wheel. We suggest that to improve the successful, timely delivery of important clinical trials for patient benefit, it is time to produce standard trial management guidelines and develop robust methods of evaluation

Effect of parasympathetic stimulation on brain activity during appraisal of fearful expressions

Autonomic nervous system activity is an important component of human emotion. Mental processes influence bodily physiology, which in turn feeds back to influence thoughts and feelings. Afferent cardiovascular signals from arterial baroreceptors in the carotid sinuses are processed within the brain and contribute to this two-way communication with the body. These carotid baroreceptors can be stimulated non-invasively by externally applying focal negative pressure bilaterally to the neck. In an experiment combining functional neuroimaging (fMRI) with carotid stimulation in healthy participants, we tested the hypothesis that manipulating afferent cardiovascular signals alters the central processing of emotional information (fearful and neutral facial expressions). Carotid stimulation, compared with sham stimulation, broadly attenuated activity across cortical and brainstem regions. Modulation of emotional processing was apparent as a significant expression-by-stimulation interaction within left amygdala, where responses during appraisal of fearful faces were selectively reduced by carotid stimulation. Moreover, activity reductions within insula, amygdala, and hippocampus correlated with the degree of stimulation-evoked change in the explicit emotional ratings of fearful faces. Across participants, individual differences in autonomic state (heart rate variability, a proxy measure of autonomic balance toward parasympathetic activity) predicted the extent to which carotid stimulation influenced neural (amygdala) responses during appraisal and subjective rating of fearful faces. Together our results provide mechanistic insight into the visceral component of emotion by identifying the neural substrates mediating cardiovascular influences on the processing of fear signals, potentially implicating central baroreflex mechanisms for anxiolytic treatment targets

Insights into the intracellular localization, protein associations and artemisinin resistance properties of Plasmodium falciparum K13

The emergence of artemisinin (ART) resistance in Plasmodium falciparum intra-erythrocytic parasites has led to increasing treatment failure rates with first-line ART-based combination therapies in Southeast Asia. Decreased parasite susceptibility is caused by K13 mutations, which are associated clinically with delayed parasite clearance in patients and in vitro with an enhanced ability of ring-stage parasites to survive brief exposure to the active ART metabolite dihydroartemisinin. Herein, we describe a panel of K13-specific monoclonal antibodies and gene-edited parasite lines co-expressing epitope-tagged versions of K13 in trans. By applying an analytical quantitative imaging pipeline, we localize K13 to the parasite endoplasmic reticulum, Rab-positive vesicles, and sites adjacent to cytostomes. These latter structures form at the parasite plasma membrane and traffic hemoglobin to the digestive vacuole wherein artemisinin-activating heme moieties are released. We also provide evidence of K13 partially localizing near the parasite mitochondria upon treatment with dihydroartemisinin. Immunoprecipitation data generated with K13-specific monoclonal antibodies identify multiple putative K13-associated proteins, including endoplasmic reticulum-resident molecules, mitochondrial proteins, and Rab GTPases, in both K13 mutant and wild-type isogenic lines. We also find that mutant K13-mediated resistance is reversed upon co-expression of wild-type or mutant K13. These data help define the biological properties of K13 and its role in mediating P. falciparum resistance to ART treatment