Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

Reducing the oral quinine-quinidine-cinchonin (Quinimax) treatment of uncomplicated malaria to three days does not increase the recurrence of attacks among children living in a highly endemic area of Senegal

A 3 d shortened course of the quinine-quinidine-cinchonin association Quinimax (trademark) was compared to the usual 7 d regimen for routinely treating 462 acute uncomplicated #Plasmodium falciparum$malaria attacks in 72 children under the age of 10 years in Dielmo, a holoendemic village in Senegal. 25 mg/kg Quinimax (trademark) salt daily, given in 3 equal doses, improved clinical status in 99.6$ and the partial acquired immunity of the children were probably responsible for the absence of any difference between the courses. Oral Quinimax (trademark) for 3 d is a possible alternative regimen to chloroquine and sulfadoxine-pyrimethamine for treating uncomplicated malaria in highly endemic areas of Africa where clinical resistance to these drugs exists. (Résumé d'auteur

Diagnosing students' difficulties in learning mathematics

This study considers the results of a diagnostic test of student difficulty and contrasts the difference in performance between the lower attaining quartile and the higher quartile. It illustrates a difference in qualitative thinking between those who succeed and those who fail in mathematics, illustrating a theory that those who fail are performing a more difficult type of mathematics (coordinating procedures) than those who succeed (manipulating concepts). Students who have to coordinate or reverse processes in time will encounter far greater difficulty than those who can manipulate symbols in a flexible way. The consequences of such a dichotomy and implications for remediation are then considered

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

Complications des otites moyennes chroniques

Objectif de l’étude : Rapporter la fréquence des complications des otites moyennes chroniques et présenter notre expérience dans leur prise en charge.Matériel et méthodes : Etude rétrospective concernant la période allant du 1er janvier 2000 au 31 décembre 2009. Les complications ont été réparties en 2 grands groupes : extracrâniennes et intracrâ-niennes.Résultats : 57 patients sur 350 reçus pour OMC ont présenté une complication, soit une fréquence de 18,38 %. Le cholestéatome était le plus grand pourvoyeur de ces complications (84,2%). Dix-neuf patients présentaient plus d’une complication, soit au total 76 cas. Les complications extracrâniennes ont été les plus fréquentes, 63 cas (83%), dominées par la mastoïdite extériorisée profuse (68,3%). Les complications intracrâniennes au nombre de 13 (17%) étaient dominées par la méningite purulente otogène (46,2%). La mastoïdectomie associée à une antibiothérapie à large spectre, occupait une place im-portante dans la prise en charge de ces complications. Elle a été réalisée chez 45 patients (79%). La mortalité a été estimée à 3,5% (2 cas de décès). Un drainage neurochirurgical a été effectué dans 4 cas (8,6 %).Conclusion : Cette étude se caractérise par un taux de complications d’OMC plus élevé que ceux rappor-tés dans la littérature, ainsi que par la prédominance des formes étendues et des associa-tions de complications chez un même patient.Mots clés : Otite moyenne chronique, Complications, Cholestéatome.The objective of this study : was to report the frequency and our experience of management of complications of chronic otitsmedia.Methods : We conducted a retrospective study covering 10 years period (from 1st January 2000 to 31 December 2009). Complications were divided into 2 groups: extracranial and intracranial.Results : Among 350 patients received for chronic otitis media, 57 presented complications, such as a rate of 18.38%. Cholesteatoma was the largest provider of these complications in order of 84.2%. Nineteen (19) patients had more than one complication. So, a total of 76 cases of complications were listed. Subperiostal mastoiditis was the most common findings, 68.3% of the extracranial complications. The intracranial complications, (17%), were domi-nated by otogenic purulent meningitis (46.2%). Radical mastoïdectomy with broad spectrum antibiotics occupied an important place in the management of these complications, performed in 45 patients (79%). Neurosurgical drainage was performed in 4 cases (8.6%). Mortality was estimated at 3.5% (2 deaths).Conclusion : COCM are characterized, in this study, by an elevated rate compared to that reported in the literature, the prevalence of extended forms and associations of complications in the same patient.Keys words : Chronic otitis media, Complications, Cholesteatoma

Myringoplastie par la technique des boutonnières

Introduction : La réparation des lésions tympaniques et ossiculaires au cours de l’otite chronique fait appel à plusieurs procédés bien codifiés par leurs utilisateurs.Le but de ce travail est de rapporter nos résultatsde myringoplastie par la technique des boutonnières, chez des patients porteurs de séquelles d’otite moyenne chronique non cholestéatomateuse.Patients et méthode : Etude rétrospective concernant 49 patients opérés consécutivement de tympanoplastie pour otite moyenne chronique non cholestéatomateuse, entre janvier 2003 et décembre 2009, sélectionnés parmi 140 autres opérés de tympanoplasties selon d’autres procédés. Le temps de réparation de la membrane tympanique (Myringoplastie) a été effectué par la technique d’amarrage antérieur du greffon, technique dite des boutonnières. Les critères d’évaluationétaient l’état du tympan à la dernière consultation, le rinne moyen post opératoire ou rinne résiduel et le gain moyen auditif. Le gain auditif était représenté par la différence entre le rinne pré-opératoire et le rinne post opératoire et tous les paramètres fonctionnels appréciés sur les fréquences 500, 1000 et 2000 hertz.Résultats : L’âge moyen était de 29 ans avec des extrêmes de 8 et 64 ans. La perforation tympanique était importante, centrale ou subtotale dans 32 cas (65,30%), avec une ancienneté remontant à l’enfance dans 19 cas (38,77%). L’oreille controlatérale était porteuse d’une pathologie dans 23 cas (47%). Le rinne moyen pré-opératoire était de 37,04 dB. Avec un recul moyen de 26 mois, la restauration anatomique du tympan en position normale était notée dans 35 cas (71,42 %). Le taux de reperforation a été estimé à 20,4% (10 cas), tandisque la médialisation a été observée dans 2 cas (4,08%), la latéralisation dans 1 cas (2,04%), le blunting ou comblement de l’angle antérieur tympano-méatal dans 1 cas (2,04%). Nous avons noté un rinne moyen post opératoire de 20,38 dB avec un gain moyen post opératoire de 14dB.Conclusion : Les résultats obtenus dans cette première série de myringoplastiepar la technique des boutonnières ont été modestes, mais améliorés dans le temps avec la maitrise de la technique opératoire et des facteurs de risque d’échec représentés ici par l’ancienneté, l’importance et l’évolutivité des lésions.Mots clés : Otite chronique, Myringoplastie, Technique des boutonnières.Objective : Several methods well codified by their users had been described for the repairing of tympanic and ossicular damage during chronic otitis media. The aim of this study was to report our results of myringoplasties by the technic of buttonholes procedure, in patients with sequelae of non chlesteatoma chronic otitis media.Patients and methods : A retrospective study on 49 patients, with sequalea of non cholesteatoma chronic otitis media, operated consecutively of myringoplasty by the technic of buttonholes, between january 2003 and december 2009, was caried out. The patients had been selected among 140 others operated throught others procedures. The criteria of evaluation were the ear drum’s aspect at the last clinical examination, the average air bone gap and the average hearing gain established as the difference between pre opérative and post operative air bone gap. The parameters for the post operative functional outcome had been assessed on the frequencies 500, 1000 and 2000 kHz.Results: The average age was 29 years and ranged from 8 to 64. The tympanic membrane’s perforation was important, central or subtotal in 32 cases (65,30%), with a long term évolution dating back to childhood in 19 cases (38,77%). Pathological disease was noticed in the controlateral ear in 23 cases (47%). The average pre operative air bone gap was 37.04 dB. After a mean follow up of 26 month, the succeful rate of closure of the tymapanic membrane, in the normal position, was 71,42%. The recidive of perforation (reperforation) was estimated at 20,4% (10 cases), whereverthe medialization was observed in 2 cases (4,08), lateralization and the blunting or filling the anterior tympano-méatal angle in respectively 1 case (2,04%). We noted an average post oprative air bone gap of 20,38 dB with an average hearing gain of 14 dB.Conclusion: The results obtained in this first round of myringoplasty with buttonhole procedure were modest, but improved over time withthe mastery of the surgery technic and risks factors of failure represented here by the age, size and scalabillity of the lesions.Keyswords : Chronic otitis media, Myringoplasty, Technic of buttonhole

Osteolipoma: An unusual tumor of the parotid region

SummaryPurpose of studyOncology of the parotid region is rich and varied, like its components. During his career, the ENT surgeon may come across such an exceptional tumor as osteolipoma. The aim of this study was to describe the rarity and the etiopathogeny of osteolipoma with parapharyngeal location.Patients and methodWe had the opportunity to find this uncommon tumor in a 21-year-old female patient. The mass located in the parotid region was hard, barely mobile and at first looked like a parotid tumor. Total parotidectomy with facial nerve preservation was performed. It revealed a stony and dented tumor inside the internal lobe of the parotid located in the parapharyngeal space between the vertical portion of the mandible anteriorly and the styloid apophyse posteriorly. Macroscopic examination of the piece evidenced a lipomatous mass with hard as bone nodes in its middle. Histology revealed an osteolipoma.ConclusionA review of the literature shows the uncommon occurrence of this type of tumor. A few rare cases were reported among which two involving the parapharyngeal space

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420