Comparing the Didactic-Mathematical Knowledge of Derivative of In-Service and Pre-service Teachers

Background: The knowledge that a mathematics teacher should master has taken an increasing interest in recent years. Very few studies focused on comparing didactic-mathematic knowledge of in-service and pre-service teachers aimed at identifying features of the teachers’ didactic-mathematical knowledge on specific topics that can establish a line between pre-service and in-service teachers’ knowledge for teaching. Objective: The research aims to compare derivative knowledge of pre-service and in-service teachers to identify similarities and differences between teachers’ knowledge. Design: This research is a mixed and interpretative study. Settings and Participants: The participants were 22 pre-service teachers, and 11 in-service teachers enrolled in a pre-service teacher education programme and a master’s programme, respectively. Data collection and participants: Data were collected based on a questionnaire designed purposefully for the study. Results: The results show that pre-service teachers lack both epistemic derivative knowledge, while in-service teachers not only have this knowledge but relates it to its use in teaching. Pre-service teachers may not be making sense of the concept of derivative means, much less related to teaching. Conclusions: The insufficiencies found in pre-service teachers’ knowledge justify the pertinence to design specific formative cycles to develop prospective teachers’ epistemic facet of didactic-mathematical knowledge. It is recommended that both in-service and pre-service teachers discuss activities in which they can identify and reflect on possible mistakes and errors made by students. The development of these formative cycles should consider the complexity of the global meaning of the derivative

Towards a methodology for the characterization of teachers´ Didactic-Mathematical knowledge

ABSTARCT: This research study aims at exploring the useof some dimensions and theoretical-methodological tools suggested by the modelof Didactic-Mathematical Knowledge (DMK) for the analysis,characterization and development of knowledge that teachers should have inorder to efficiently develop within their practice. For this purpose, weanalyzed the activity performed by five high school teachers, in relation to anactivity about patterns suggested in the framework of the Master of MathematicsEducation Program at University of Los Lagos, Chile. As a result of theanalysis, it becomes evident that teachers can indeed solve items related tothe common content knowledge, but have certain difficulties when they faceitems that aim at exploring other dimensions of their knowledge, for example,about extended content knowledge, of resources and means, or of the affectivestate of students

A Proposal to Enhance Preservice Teacher’s Noticing

ABSTARCT: This paper presents a proposal for the development of ‘Teacher noticing’ with the help of dimensions taken from the teacher’s didactic-mathematical knowledge model, that makes up a Guide for Didactical Reflection. The proposal is based on a study conducted during a time span of two years while the preservice teachers were in their teaching practicum. The methodology was qualitative and data were taken in video, audio, observing rubrics, and interviews formats. The results not only indicate that the Guide can help develop teachers’ noticing, in order to identify and to question several specific domains of teacher knowledge involved in mathematics teaching, but also suggest that prospective teachers are moved into action and translate their noticing in didactic action during class. We hypothesize that preservice effective noticing occurs at the intersection of practice and discussion over the practice, with the help of ‘noticing tools’ with respect to the mathematical activities of students

Conocimiento didáctico-matemático de profesores en formación: explorando el conocimiento especializado sobre la derivada

El estudio sobre los conocimientos que debe tener un profesor de matemáticas para que su enseñanza sea efectiva, ha sido motivo de estudio en los últimos 30 años. Sin embargo, las investigaciones orientadas al diseño de instrumentos que permitan explorar aspectos sobre el conocimiento didáctico-matemático de los profesores sobre temas específicos no son numerosas. En el presente trabajo se informa sobre algunos resultados obtenidos a partir de la aplicación de un instrumento que se ha diseñado para explorar aspectos relevantes la faceta epistémica del conocimiento didáctico-matemático sobre la derivada de futuros profesores de bachillerato

Mathematics preservice teachers’ argumentation

ABSTARCT: This research deals with the preservice teachers’ dialogic argumentationswhen presenting geometry tasks to their colleagues, during discussion sessions previous to teaching to children. An argumentation analysis tool is used that complement Toulmin’s analysis proposal and that includes features related to mathematicallogic, rhetoric and dialectic features.We propose both a representation for the dialogic argumentation and a way to identify its structural qualitie

The antiderivative understanding by students in the first university courses

ABSTARCT: In this article, we present the results of a questionnaire designed to evaluate college students’ understanding of the antiderivative. Specifically, by civil engineering students when answering the questionnaire’ tasks, in order to identify and characterize the meanings on the antiderivative that are mobilized by them. In order to analyse the answers given, we used some theoretical and methodological notions provided by the theoretical model known as the Onto-Semiotic Approach (OSA) of mathematics cognition and instruction. The results show knowledge of antiderivative by the Civil Engineering students. Furthermore, the comparison between the mathematical activity of students provides information that allows concluding that the meanings that they mobilized might be shared among their communities

Successful strategies implemented towards the elimination of canine rabies in the Western Hemisphere

Almost all cases of human rabies result from dog bites, making the elimination of canine rabies a global priority. During recent decades, many countries in the Western Hemisphere have carried out large-scale dog vaccination campaigns, controlled their free-ranging dog populations and enforced legislation for responsible pet ownership. This article reviews progress in eliminating canine rabies from the Western Hemisphere. After briefly summarizing the history of control efforts and describing the approaches listed above, we note that programs in some countries have been hindered by societal attitudes and severe economic disparities, which underlines the need to discuss measures that will be required to complete the elimination of canine rabies throughout the region. We also note that there is a constant threat for dog-maintained epizootics to re-occur, so as long as dog-maintained rabies "hot spots" are still present, free-roaming dog populations remain large, herd immunity becomes low and dog-derived rabies lyssavirus (RABLV) variants continue to circulate in close proximity to rabies-naïve dog populations. The elimination of dog-maintained rabies will be only feasible if both dog-maintained and dog-derived RABLV lineages and variants are permanently eliminated. This may be possible by keeping dog herd immunity above 70% at all times, fostering sustained laboratory-based surveillance through reliable rabies diagnosis and RABLV genetic typing in dogs, domestic animals and wildlife, as well as continuing to educate the population on the risk of rabies transmission, prevention and responsible pet ownership. Complete elimination of canine rabies requires permanent funding, with governments and people committed to make it a reality. An accompanying article reviews the history and epidemiology of canine rabies in the Western Hemisphere, beginning with its introduction during the period of European colonization, and discusses how spillovers of viruses between dogs and various wild carnivores will affect future eradication efforts (Velasco-Villa et al., 2017)

Recuperación del epitelio germinal masculino de ratones tratados con dosis única de Busulfán

The DNA replication is disrupted by Busulfan which is a bifunctional alquilant as an ester agent. High dose of this compound are applied before transplants of bone marrow and germ cells. However quantification of the damage to the reproductive system and its recovery have not been established. The aim of this study was to quantify both spermatogenesis and spermiogenesis recovery in mice from damage caused by an injection of Busulfan. We used Balb C mice which were evaluated 30, 54 and 72 days after the intraperitoneal injection of 40 mg/kg body weight. We took the following variables: testicular weight, spermatic concentration in epididimus line and histological cuts to measure the diameter of the seminiferous tubules. Results were analyzed with the test U Mann-Whitney p>0.05. By day 30, testicular weight, spermatic concentration and diameter of the seminiferous tubules were reduced to 77,8%, 97,9% and 34,3% respectively compared to the controls. At day 54, testicular weight and diameter of the seminiferous tubules showed a recovery of 70%. Recovery was complete by day 72. Therefore Busulfan applied in a sigle dose, affects significantly spermatogenesis and the completed recovery takes two spermatic cycles in mice.Busulfán es un agente alquilante bifuncional tipo-éster, que interfiere con la replicación del ADN. Dosis elevadas de este compuesto son aplicadas antes de los transplantes de médula ósea y de células germinales, sin embargo no han sido cuantificados el daño ni la recuperación del sistema reproductor. Para cuantificar la recuperación del efecto en la espermatogénesis, se usaron ratones de la cepa Balb C, a los que se les inyectó Busulfán intraperitonealmente, 40 mg/kg de peso corporal, y se evaluó el peso testicular y la concentración espermática en cola de epidídimo, a los 30, 54 y 72 días y se realizaron cortes histológicos de testículo. Los resultados fueron analizados con la prueba U Mann-Whitney p>0.05. A los 30 días el peso testicular, la concentración espermática y el diámetro de los túbulos seminíferos presentaron una drástica reducción del 77,8%, 97,9% y 34,3% respectivamente, comparados con el grupo control. A los 54 días, el peso testicular y el diámetro testicular muestran una recuperación del 70%. A los 72 días, la recuperación es completa en los parámetros evaluados. Por lo tanto, Busulfán aplicado en una sola dosis afecta significativamente la espermatogénesis en el ratón y se logra la recuperación completa en dos ciclos espermáticos

A mathematical model of the transmission dynamics of tuberculosis with exogenous reinfection in the infection-free state

In the present work, a perturbation of the model presented by Feng, Castillo-Chávez and Capurro (2000) will be carried out, where the dynamics of tuberculosis transmission will be described, where recovery from the disease will be incorporated. The model will include four epidemiological populations: Susceptible (S), Exposed (E), Infected (I) and Infected with treatment (T). This will allow to know how the interaction that exists with the infected can cause the permanence of the individuals with the disease. For which, its qualitative behavior will be analyzed as its evolution in time of the epidemiological populations for the model by the ordinary differential equations (ODE) and its perturbation to the dalay differential equations (DDE). In this way, it will allow us to know how the parameters influence the spread of the disease at the point free of infection and with a computational extension to evaluate an endemic situation.Campus Lima Nort