FORMACIÓN DEL DOCENTE Y SU ADAPTACIÓN AL MODELO TPACK

La carrera de Físico Matemático (FIMA) de la Facultad de Filosofía, Ciencias y Letras de la Educación de la Universidad de Guayaquil (FFUG), forma docentes para el ciclo de bachillerato en el área de la Física y las Matemáticas. El docente universitario que imparte clases en la Carrera de FIMA, debe tener diferentes tipos de competencias para dar a sus estudiantes alternativas de aprendizaje, contextualizado al mundo actual. La presente investigación tiene como objetivo, diagnosticar el tipo de educación que están recibiendo los estudiantes de la Carrera y si es posible la adaptación del modelo Technological, Pedagogical and Content Knowledge / Conocimiento Tecnológico, Pedagógico del Contenido (TPACK). Para lograr determinar si posible adaptar el modelo TPACK, se aplicó un modelo de cuestionario validado por docentes universitarios. Estos cuestionarios han sido aplicados a los estudiantes y docentes de la Carrera FIMA. Los resultados fueron tabulados y a continuación se aplicó el coeficiente de fiabilidad Alfa de Cronbach, aproximándose al valor máximo de uno, indicando la fiabilidad de los resultados. Además, se realizó varias entrevistas para contrastar estos resultados. De esta manera se da a conocer la presente investigación, poniendo a su consideración el proceso de la misma y sus conclusiones. Palabras Claves: Formación Docente, Físico Matemático, Adaptación, TPACK. ABSTRACTThe Physics Mathematical career/ Físico Matemático (FIMA) in the Faculty of Philosophy, Letters and Science Education at the University of Guayaquil/Facultad de Filosofía, Letras y Ciencias de la Educación de la Universidad de Guayaquil (FFUG), form teachers for High School cycle in the area of Physics and the Mathematics. The university teacher that teaches at the FIMA Career, should have different types of skills to give the students the learning alternative, contextualized the current world. The present investigation has as purpose; diagnose the type of education that FIMA students are receiving and if it is possible the adaptation of the model Technological, Pedagogical and Content Knowledge (TPACK). To achieve determine whether it is possible to adapt the model TPACK, applied model questionnaires validated by university teachers. These questionnaires have been applied to the students and teachers of the FIMA career. The results were tabulated and then the reliability coefficient alpha of Cronbach was applied, approaching the maximum value of one, indicating the reliability of the results. In addition, several interviews were conducted to compare these results. Thus it is disclosed this investigation, putting the process and the conclusions at your consideration.Key Words: Teacher Training, Physics Mathematical, Adaptation, TPACK

The Development of Arabic Digit Knowledge in 4- to 7-Year-Old Children

Recent studies indicate that Arabic digit knowledge rather than non-symbolic number knowledge is a key foundation for arithmetic proficiency at the start of a child’s mathematical career. We document the developmental trajectory of 4- to 7-year-olds’ proficiency in accessing magnitude information from Arabic digits in five tasks differing in magnitude manipulation requirements. Results showed that children from 5 years onwards accessed magnitude information implicitly and explicitly, but that 5-year-olds failed to access magnitude information explicitly when numerical magnitude was contrasted with physical magnitude. Performance across tasks revealed a clear developmental trajectory: children traverse from first knowing the cardinal values of number words to recognizing Arabic digits to knowing their cardinal values and, concurrently, their ordinal position. Correlational analyses showed a strong within-child consistency, demonstrating that this pattern is not only reflected in group differences but also in individual performance.

The Mathematical Work of S.C.Kleene

§1. The origins of recursion theory. In dedicating a book to Steve Kleene, I referred to him as the person who made recursion theory into a theory. Recursion theory was begun by Kleene's teacher at Princeton, Alonzo Church, who first defined the class of recursive functions; first maintained that this class was the class of computable functions (a claim which has come to be known as Church's Thesis); and first used this fact to solve negatively some classical problems on the existence of algorithms. However, it was Kleene who, in his thesis and in his subsequent attempts to convince himself of Church's Thesis, developed a general theory of the behavior of the recursive functions. He continued to develop this theory and extend it to new situations throughout his mathematical career. Indeed, all of the research which he did had a close relationship to recursive functions.Church's Thesis arose in an accidental way. In his investigations of a system of logic which he had invented, Church became interested in a class of functions which he called the λ-definable functions. Initially, Church knew that the successor function and the addition function were λ-definable, but not much else. During 1932, Kleene gradually showed1 that this class of functions was quite extensive; and these results became an important part of his thesis 1935a (completed in June of 1933).