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We examine classroom situations which allow the learning of rules of mathematical reasoning. Drawing on an epistemological analysis and G. Brousseau's theory of situations, we define a priori theoretical characteristics which such situations must possess. We then use this analysis, and hypotheses about the cognitive functioning of pupils of this age, to establish learning situations for the rule of the excluded middle, and for the use of the figure in geometry. We report the results of experimentation with two of thses situations and show that, through the study of a mathematical problem, debate about these rules can be generated amongst students aged twelve to thirteen. We explain why, in our opinion, for epistemological reasons linked to the two particular rules concerned, it is necessary for the teacher to conclude the debate, and we examine our cognitive hypotheses against the actual results of experimentation. 相似文献
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Seema Bhargava Meghaa Shanta Bhargava Eishaan Kamta Bhargava LM Srivastava 《Indian journal of clinical biochemistry : IJCB》2016,31(2):148-151
Hyperhomocysteinemia (HHCY) has been demonstrated to affect cochlear microvasculature as well as cochlear epithelial cells directly, with a resultant alteration of the expression of matrix metalloproteinases (MMPs) and their inhibitors, tissue inhibitors of metalloproteinases (TIMPs). Hence, ascertaining the optimum concentration of MMPs and TIMPs in the cochlea could help to inhibit hearing loss due to HHCY by the administration of appropriate MMP inhibitors, Since infections/inflammations as well as ototoxic antibiotics have a similar mechanism of otic pathology, the cochlear damage they cause could also be similarly prevented. 相似文献
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R.J. Yquel L.M. Arsac E. Thiaudiere P. Canioni G. Manier 《Journal of sports sciences》2013,31(5):427-437
In this study, we examined the effect of creatine ingestion on muscle power output, muscle phosphocreatine resynthesis, inorganic phosphate and pH during repeated brief bouts of maximal exercise. Nine healthy males performed maximal plantar flexion before and after creatine ingestion (20 g ·day -1 for 6 days). The experimental protocol consisted of five 8 s bouts (bouts 1-5) interspersed with 30 s recovery, followed by bouts 6 (8 s) and 7 (16 s) separated by 1 and 2 min, respectively. Muscle phosphocreatine, inorganic phosphate and pH were estimated every 16 s by 31 P magnetic resonance spectroscopy. After creatine ingestion, muscle power output increased by ~5% ( P ? 0.05) from bouts 3 to 7 and muscle phosphocreatine resynthesis increased ( P ? 0.05) during 10 min recovery. The higher phosphocreatine concentration observed after only 30 s of recovery was accompanied by lower inorganic phosphate accumulation and higher pH. Strong correlations were found between exercise power restoration and the corresponding pre-exercise phosphocreatine and inorganic phosphate concentrations and muscle pH after creatine ingestion. The better maintenance of muscle power output observed after creatine ingestion was attributed to a higher rate of phosphocreatine resynthesis, lower accumulation of inorganic phosphate and higher pH. 相似文献
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In this study, we examined the effect of creatine ingestion on muscle power output, muscle phosphocreatine resynthesis, inorganic phosphate and pH during repeated brief bouts of maximal exercise. Nine healthy males performed maximal plantar flexion before and after creatine ingestion (20 g x day(-1) for 6 days). The experimental protocol consisted of five 8 s bouts (bouts 1-5) interspersed with 30 s recovery, followed by bouts 6 (8 s) and 7 (16 s) separated by 1 and 2 min, respectively. Muscle phosphocreatine, inorganic phosphate and pH were estimated every 16 s by 31P magnetic resonance spectroscopy. After creatine ingestion, muscle power output increased by approximately 5% (P< 0.05) from bouts 3 to 7 and muscle phosphocreatine resynthesis increased (P< 0.05) during 10 min recovery. The higher phosphocreatine concentration observed after only 30 s of recovery was accompanied by lower inorganic phosphate accumulation and higher pH. Strong correlations were found between exercise power restoration and the corresponding pre-exercise phosphocreatine and inorganic phosphate concentrations and muscle pH after creatine ingestion. The better maintenance of muscle power output observed after creatine ingestion was attributed to a higher rate of phosphocreatine resynthesis, lower accumulation of inorganic phosphate and higher pH. 相似文献
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Brooke Klingberg J. J. A. A. M. Hoeboer Natasha Schranz LM Barnett Sanne I. De Vries 《Journal of sports sciences》2019,37(13):1534-1542
Failure to master age-appropriate fundamental movement skills (FMS) at a young age can limit motor skill competence affecting health. Assessments often have issues with feasibility and implementation in a field setting. As such, the purpose of this study was to investigate the validity and feasibility of the Athletic Skills Track (AST), in a pre-school setting. For the validation study sixty-five 3–6 year old children (25 boys and 40 girls) from five pre-schools across Adelaide, Australia participated. Correlations and linear regression analysis (adjusted for age and gender) were used to investigate the association between the time to complete the AST and the raw score of the Test of Gross Motor Development 2 (TGMD-2). For the feasibility study pre-school staff completed a semi-structured interview regarding the feasibility of the AST. The AST took less than a minute per child and the TGMD-2 around 20 minutes for two children. There was a strong negative correlation (r = ?0.63, p < 0.01) between the AST scores and the TGMD-2 scores. All five staff reported strengths of the AST to be its short administration time, setup and appropriateness. These results suggest that the AST could be a feasible and valid method of FMS assessment in Australian pre-schools. 相似文献
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Is it possible to specify teaching situations and to control their effects on students' learning? This general question is essential regarding the scientific character of research on mathematics education. It especially concerns the teacher's role in the class: can she ensure sufficient fidelity to a predefined scenario? This question is of special importance in the case of an experimental scenario the design of which is the result of a collaboration between a researcher and a teacher. This is considered here in the context of two case-studies. These case-studies exhibit two types of factors which tend to hamper fidelity in reproducing a given scenario: - first, constraints on the teacher resulting from the didactical system: time constraints, success of the teaching process; - second, teachers' conceptions about mathematics and learning. These results are considered with reference to prior research on didactical transposition and teacher's beliefs. 相似文献
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Viviane?Durand-GuerrierEmail author Gilbert?Arsac 《Educational Studies in Mathematics》2005,60(2):149-172
Abstract It is widely attested that university students face considerable difficulties with reasoning in analysis, especially when
dealing with statements involving two different quantifiers. We focus in this paper on a specific mistake which appears in
proofs where one applies twice or more a statement of the kind “for all X, there exists Y such that R(X, Y)”, and forgets that in that case, a priori, “Y depends on X”. We analyse this mistake from both a logical and mathematical point of view, and study it through two inquiries, an historical
one and a didactic one. We show that mathematics teachers emphasise the importance of the dependence rule in order to avoid
this kind of mistake, while natural deduction in predicate calculus provides a logical framework to analyse and control the
use of quantifiers. We show that the relevance of this dependence rule depends heavily on the context: nearly without interest
in geometry, but fundamental in analysis or linear algebra. As a consequence, mathematical knowledge is a key to correct reasoning,
so that there is a large distance between beginners' and experts' abilities regarding control of validity, that, to be shortened,
probably requires more than a syntactic rule or informal advice.
Résumé Les difficultés de manipulation, par les étudiants, des énoncés contenant deux quantificateurs différents, rencontrés dans
de nombreux raisonnements en analyse, sont bien attestées. Nous nous intéressons plus spécialement dans cet article à une
erreur qui appara?t dans certaines preuves lorsque l'on applique deux fois ou plus un énoncé de la forme “pour tout X, il existe Y tel que R(X,Y)” et que l'on oublie que dans un tel cas, a priori, “Y dépend de X”. Nous analysons cette erreur d'un point de vue logique et d'un point de vue mathématique, puis nous l'étudions à travers
deux enquêtes, l'une historique et l'autre didactique. Nous montrons que les professeurs de mathématiques soulignent l'importance
de la règle de dépendance pour éviter ce type d'erreur, tandis que la déduction naturelle dans le calcul des prédicats fournit
un cadre de référence logique pour analyser et contr?ler l'usage des quantificateurs. Nous montrons que la pertinence de la
règle de dépendance dépend fortement du contexte: pratiquement sans intérêt en géométrie, elle est tout à fait fondamentale
en analyse et en algèbre linéaire. De ce fait, les connaissances mathématiques sont la clé d'un raisonnement correct, si bien
qu'il y a une grande distance entre le débutant et l'expert concernant le contr?le de la validité, que quelques règles syntaxiques
ou quelques conseils informels ne permettent vraisemblablement pas de réduire. 相似文献
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