Between Meaning-Making and Learning the “Rule”: The Case of a Prospective Teacher of Mathematics at the Secondary Level

This article reports on a case study intended to improve understanding of the development and characteristics of prospective mathematics teachers’ oral explanations. The teaching practices of Donna, who taught algebraic operations, were analyzed, after which she was interviewed. The presence of an important tension in how Donna explained mathematics emerged where her explanations were divided between contextualized understandings and formalized knowledge, highlighting the difficulties in teaching of transition from one to the other. The article concludes with a discussion of a plausible rationale for this tension, which emerges from an understanding of mathematics as reduced to a call for formalized procedures.Cet article présente une étude de cas visant l’amélioration des connaissances sur le développement et les caractéristiques des explications orales que fournissent les enseignants candidats en mathématiques. L’auteur a analysé les pratiques d’enseignement de Donna, qui a présenté des opérations d’algèbre, et a ensuite passé la stagiaire en entrevue. La présence d’une tension importante dans les explications mathématiques de Donna s’est fait sentir quand ses explications étaient partagées entre des connaissances contextualisées et des connaissances formelles, mettant en évidence la difficulté de passer d’une sorte de connaissances à l’autre. L’article conclut avec une discussion sur une explication plausible de cette tension en tant que résultat d’une interprétation des mathématiques comme n’étant que des procédures formalisées

MATHEMATICAL CURIOSITIES ABOUT DIVISION OF INTEGERS

As mathematics educators, our focus of attention is mainly placed on the learning and teaching of mathematics. But, as we study phenomena of mathematical learning and teaching, we often come across intriguing mathematical phenomena that capture our interest. We find ourselves often bouncing mathematical ideas back and forth, not just looking for (new/better) ways of teaching or presenting a mathematical concept, but also of uncovering and discovering potential understandings of the concept. These mathematical issues we encounter represent for us a significant aspect of our work, and are also very stimulating. One of these issues arose for us as we were tackling issues of division of numbers and of conventions relating to the remainder; issues that are, mathematically speaking, as we hope to communicate, very interesting and thought provoking. Thus, we explore four different avenues/curiosities about division, where operations with positive and negative numbers are considered, as well as the meaning one can draw out of these operations

Vésicules extracellulaires : biomarqueurs et véhicules de propagation de protéinopathies

La maladie de Parkinson (MP) est une maladie neurodégénérative invalidante pour laquelle le diagnostic ne peut être donné qu’une fois la dégénérescence neuronale bien entamée, rendant impérative la découverte d’un biomarqueur ; un outil biologique permettant de prédire l’apparition de la pathologie ou d’évaluer sa progression. Mon projet de maîtrise visait donc l’étude des vésicules extracellulaires (VE) issues du sang comme test diagnostique ou comme marqueur de la progression de la MP. La quantification des VE effectuée par cytométrie de flux à haute sensibilité a révélé une augmentation spécifique des VE dérivées d’érythrocytes (VEE) chez les parkinsoniens comparés à leurs contrôles, ainsi qu’une forte corrélation avec la progression de la maladie. L’analyse quantitative de l’alphasynucléine (α-Syn), principale protéine impliquée dans la pathologie de la maladie, a montré un niveau similaire entre les individus. Cependant, l’analyse protéomique des VEE a révélé une modulation de certaines protéines entre les patients et les donneurs sains. Nos résultats suggèrent que les VEE pourraient conduire au développement d’un marqueur pour suivre l’évolution de la maladie ainsi que l’effet de nouvelles thérapies.341812 Parkinson’s disease (PD) is a debilitating neurodegenerative disease for which the diagnosis can only be confirmed once the degeneration state is very advanced, making imperative the discovery of a biomarker: a biological tool to predict the onset of pathology or its progression. My master’s project was designed to study extracellular vesicles (EV) from the blood in order to discover if they could be used as a diagnostic test or as a marker of disease progression. Quantification of EV performed by high-sensitivity flow cytometry demonstrated an increase in PD patients compared to their controls and a strong correlation with the progression of the disease only in EV derived from erythrocytes (EEV). Quantitative analysis of α-Syn, the main protein involved into PD pathogenesis, showed a similar level between individuals. However, analysis of the EEV proteome reveals a modulation of some proteins between patients and healthy donors. Our results suggest that EEV have the potential to lead to the development of a marker abled to track disease course as well as measuring the effect of new therapies

Layering methodological tools to represent classroom collectivity

Our research is guided by the question: “How might we observe, document, display, and analyze data from a collective systems perspective?” In this research forum, we share new research tools for studying mathematics classrooms, highlight opportunities for observation and analysis by layering these tools, and then illustrate how the layering of tools allows for visual distinctions across lessons and classrooms.Research was supported by the Social Sciences and Humanities Research Council of Canada

Platelet-derived extracellular vesicles in Huntington's disease.

The production and release of extracellular vesicles (EV) is a property shared by all eukaryotic cells and a phenomenon frequently exacerbated in pathological conditions. The protein cargo of EV, their cell type signature and availability in bodily fluids make them particularly appealing as biomarkers. We recently demonstrated that platelets, among all types of blood cells, contain the highest concentrations of the mutant huntingtin protein (mHtt)-the genetic product of Huntington's disease (HD), a neurodegenerative disorder which manifests in adulthood with a complex combination of motor, cognitive and psychiatric deficits. Herein, we used a cohort of 59 HD patients at all stages of the disease, including individuals in pre-manifest stages, and 54 healthy age- and sex-matched controls, to evaluate the potential of EV derived from platelets as a biomarker. We found that platelets of pre-manifest and manifest HD patients do not release more EV even if they are activated. Importantly, mHtt was not found within EV derived from platelets, despite them containing high levels of this protein. Correlation analyses also failed to reveal an association between the number of platelet-derived EV and the age of the patients, the number of CAG repeats, the Unified Huntington Disease Rating Scale total motor score, the Total Functional Capacity score or the Burden of Disease score. Our data would, therefore, suggest that EV derived from platelets with HD is not a valuable biomarker in HD.The study was funded by an operating grant from the Merck Sharpe & Dohme to F.C. who is also a recipient of a National Researcher career award from the Fonds de Recherche du Québec en santé (FRQS) providing salary support and operating funds. I.S.-A. was supported by a CIHR-Huntington Society of Canada postdoctoral fellowship. R.A.B. and S.L.M. are supported by a National Institute for Health Research (NIHR) award of a Biomedical Research Center to the University of Cambridge and Addenbrooke’s Hospital. E.B. is supported by the Canadian Institutes of Health Research. N.D. MD-MSc. also funded by CIHR and by Canadian Consortium on Neurodegeneration in Aging (CCNA). HLD and JPL hold a Desjardins scholarship from the Fondation du CHU de Québec. HLD hold a bourse d’excellence du Centre Thématique de Recherche en Neurosciences (CTRN) du CHU de Québec. The authors would like to thank all the students and staff who helped with the blood collections in Cambridge, Quebec City and Montreal and importantly, all patients and their families for being so generous with their time in participating to this stud

Portrait of blood-derived extracellular vesicles in patients with Parkinson's disease.

The production of extracellular vesicles (EV) is a ubiquitous feature of eukaryotic cells but pathological events can affect their formation and constituents. We sought to characterize the nature, profile and protein signature of EV in the plasma of Parkinson's disease (PD) patients and how they correlate to clinical measures of the disease. EV were initially collected from cohorts of PD (n = 60; Controls, n = 37) and Huntington's disease (HD) patients (Pre-manifest, n = 11; manifest, n = 52; Controls, n = 55) - for comparative purposes in individuals with another chronic neurodegenerative condition - and exhaustively analyzed using flow cytometry, electron microscopy and proteomics. We then collected 42 samples from an additional independent cohort of PD patients to confirm our initial results. Through a series of iterative steps, we optimized an approach for defining the EV signature in PD. We found that the number of EV derived specifically from erythrocytes segregated with UPDRS scores corresponding to different disease stages. Proteomic analysis further revealed that there is a specific signature of proteins that could reliably differentiate control subjects from mild and moderate PD patients. Taken together, we have developed/identified an EV blood-based assay that has the potential to be used as a biomarker for PD

Réflexions méthodologiques, épistémologiques et éthiques sur les données de recherche recueillies en salle de classe : l’expérience vécue par le chercheur

Cet article se situe en continuité d’un premier et aborde une variété de questions concernant les données de recherche, relativement aux travaux conduits en salle de classe. L’entrée sur le sujet se fait à partir des travaux de recherche en didactique des mathématiques que mon équipe mène sur le calcul mental. Ceux-ci ont été des déclencheurs de réflexions méthodologiques, épistémologiques et éthiques relatives aux notions de collecte, de production et de fiabilité des données. À partir d’une anecdote, ce deuxième article traite de la question de l’expérience vécue par le chercheur en classe relativement à la nature des données de recherche.This article addresses questions concerning research data related to work conducted in classrooms. I use my own work in didactics of mathematics regarding mental mathematics. It acts as an important trigger for epistemological, methodological, and ethical reflections about data collection, production and reliability. Through an anecdote, this second article discusses issues related to the researcher’s experience in the classroom and the developed relation with the research data gathered.Este artículo es la continuación de otro previo y aborda una variedad de preguntas sobre los datos de investigación, en particular en los trabajos realizados en el aula. Se inicia el tema a partir de los trabajos de investigación en didáctica de la matemática que mi equipo desarrolla sobre el cálculo mental. Estos trabajos han desencadenado una serie de reflexiones metodológicas, epistemológicas y éticas sobre las nociones de toma, producción y fiabilidad de los datos. A partir de una anécdota, este segundo artículo trata de la cuestión de la experiencia vivida por el investigador en el aula en relación con la naturaleza de los datos de investigación