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HOMOTECIA Nº 10-13 Octubre 2015

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HOMOTECIA Nº 10-13 Octubre 2015 HOMOTECIA Nº 10 – Año 13 Jueves, 1° de Octubre de 2015 1 En la editorial del número anterior afirmamos que “las dificultades de aprendizaje de la matemática tienen un trasfondo de debilidad cultural. No sólo del estudiante sino también del docente: por poner un ejemplo, a pesar de hacerse del conocimiento matemático, ni uno ni el otro intenta en lo cotidiano utilizar este conocimiento para resolver los problemas que se le presentan a diario…. esta situación es más grave en el docente que en el alumno… Pero como algo sumamente importante, el docente de matemática no sólo debe ser culto en la propia asignatura (conocimientos, historia, epistemología) sino que su discurso debe ser culto más allá de la matemática. Es decir, así como debe ser culto en el mundo matemático, lo debe ser en lo general, en lo que puede llamarse cultura social, la que debería en teoría compartir con el resto de los seres humanos…”. Puede afirmarse que se entiende que la aspiración es lograr un conocimiento matemático socializado, teniendo como propósito crear una condición para la integración del conocimiento matemático (la actividad docente), el conocimiento social general (cultura general compartida) y la condición natural o vivencial del ser humano (docente y estudiante comprometidos en la misión de enseñar y aprender) propiciándose realizaciones especiales en la vida de cada quien, como también etapas dinámicas, heurísticas, de colectivos, pueblos o entidades, abriéndose trascendentalmente a nuevas opciones del conocimiento (Barrera, 2006). Se vislumbra entonces, que al docente se le hace necesario apropiarse lo más que pueda de un conocimiento general y significativo del mundo, no parcializado, evitando la hiper-especialización y en consecuencia, conocer y sensibilizarse lo más que pueda del proceso de crecimiento cualitativo de la humanidad, su dinámica y sus logros, tener claridad en el qué somos y así al enseñar, ser lo más fidedigno en la transmisión de los valores de la herencia humana, buscando el beneficio de la sociedad. Pero ¿cuál es ese conocimiento general y significativo apropiable por parte del docente? ¿Cuál es el que debe transmitir? El recordado Rigoberto Lanz estableció dos categorías, conocimiento globalizado y conocimiento mundializado (2006, Noviembre 25). Para él, el globalizado se refiere al conocimiento que las naciones centros del poder mundial quieren certificarle al resto de las naciones. Pero esta certificación por parte de instituciones destinadas para ello, conduce a establecer jerarquías tanto entre las naciones como entre las personas, por lo que se puede considerar que es parcializado o hiper-especializado. En cambio opinó que el mundializado tiene que ver más con las cualidades de los pueblos, con lo mejor de su cultura, con lo mejor culturalmente intercambiable entre las naciones, tanto referido al folclore como a la producción intelectual aplicado en lo social. Lanz, según esta categorización, incluye en el mundializado al globalizado. Es decir, oferta como conocimiento a aprehender al mundializado. Sin que contradiga lo anterior, con fundamento en la idea generalizada entre muchos estudiosos en cuanto a que todo aspecto de la experiencia humana, ha de ser, por necesidad, multifacético, viéndose que así como la mente humana no existe sin cerebro, tampoco puede hacerlo sin tradiciones familiares, sociales, genéricas, étnicas, raciales, que sólo hay mentes encarnadas en cuerpos y culturas, y que el mundo físico es el mundo entendido por seres biológicos y culturales (Pakman, 1994), surge de la mente del notable Edgar Morin (2005), la idea del pensamiento complejo aspirando al logro del pensamiento multidimensional, que no se refiere ni al pensamiento completo ni al pensamiento simplista o simplificador, “porque el pensamiento complejo está animado por una tensión permanente entre la aspiración a un saber no parcelado, no dividido, no reduccionista, y el reconocimiento de lo inacabado e incompleto de todo conocimiento”. Señala también Morin (2000) que: Reducir el conocimiento de lo complejo al de uno de sus elementos, considerado como el más significativo, tiene consecuencias peores en ética que en estudios de física. Ahora bien, es también el modo de pensar dominante, reductor y simplificador aliado a los mecanismos de incomprensión el que determina la reducción de una personalidad múltiple por naturaleza a una sola de sus rasgos. Si el rasgo es favorable, habrá desconocimiento de los aspectos negativos de esta personalidad. Si es desfavorable, habrá desconocimiento de sus rasgos positivos”. ¿Cómo pueden entenderse estas ideas de Morin en el proceso de enseñanza de la matemática cuando el docente, débil culturalmente, se presenta ante el grupo de estudiantes con una actitud reduccionista y simplificadora? Posiblemente, tanto docente como alumno consideren que enseñar y aprender matemática se limite a conocer y aplicar un determinado algoritmo para resolver un ejercicio específico o aprenderse memorísticamente un concepto o una definición de un objeto matemático. Pero si queremos entender la propuesta del pensamiento complejo de Morin, también debería ser preocupación de ambos interrogantes como las siguientes: ¿Qué razón histórica llevó al logro de este conocimiento? ¿Qué necesidades de la ciencia matemática hizo que en la mente de un ser humano se hiciera presente este conocimiento? ¿Qué utilidad puede tener para mí y para mi comunidad el conocimiento matemático que he aprendido? ¿Cómo lo utilizo para resolver los problemas que afectan a mi comunidad diariamente?, y así por estilo, sin asumir la cómoda posición de quienes afirman que el conocimiento matemático florece silvestremente entre los matemáticos hasta que un científico de la física, la química o de cualquier otra ciencia le dé un adecuado uso práctico. Un intento de explicación de lo grave de la situación la podemos conseguir en un ejemplo dado por Camargo y Guzmán (2005): “Desafortunadamente, los estudiantes de los primeros semestres universitarios, manifiestan gran confusión y diferentes interpretaciones erróneas en torno al concepto de pendiente de una recta y la pendiente de la recta tangente a una curva como medida de la rapidez del cambio de una magnitud que depende de otra. Como consecuencia de esto, se obstaculiza la comprensión de conceptos posteriores del cálculo”. Podríamos decir que esta falla se produce por el trabajo del docente, y aunque sea cierto… ¿el docente no se sigue por un programa?; entonces la confusión también proviene desde lo curricular. Es decir, la debilidad cultural a la que nos referimos al principio tiene también su carácter institucional. Indudablemente cabe aquí una reflexión sobre este particular tema. Reflexiones “Considero más valiente al que conquista sus deseos que al que conquista a sus enemigos, ya que la batalla más dura es la victoria sobre uno mismo”. ARISTÓTELES HOMOTECIA Nº 10 – Año 13 Jueves, 1° de Octubre de 2015 2 GORO SHIMURA Nació el 23 de febrero de 1930 en Hamamatsu, Japón. El padre de Goro Shimura trabajó para un banco y lo cambiaban con frecuencia de una sucursal a otra, lo que obligaba a la familia a cambiar de ciudad. Incluso después del nacimiento de Goro, la familia se trasladó de una casa a otra en la propia Hamamatsu, ciudad situada a unos 240 km al oeste de Tokio. Era el más joven de los cinco hijos de sus padres; Goro tiene tres hermanas y un hermano. En marzo de 1933 la familia se trasladó a Tokio y, tres años después, en abril de 1936, fue cuando Goro comenzó su escolaridad. En 1938, la familia se mudó a una casa más grande en Tokio pero Goro continuó asistiendo a la misma escuela primaria hasta que completó el cuarto grado. Después asistió a una escuela primaria que quedaba cerca de su casa en el distrito de Nishi-Ohkubu, allí completó los quinto y sexto grados. Shimura inició sus estudios en la Escuela Media Prefectural Cuarta de Tokio en 1942, pero en esta había poco que le entusiasmara en cuanto a la enseñanza en matemáticas [1]: Las clases de matemáticas no eran muy interesantes. Nuevamente estudiamos operaciones aritméticas de fracciones y decimales, lo que estaba bien. Pero nos solicitaron resolver problemas aritméticos artificiales sin utilizar el álgebra. ... Nunca encontré interesante este tipo de problemas. Eran tiempos difíciles debido a la II Guerra Mundial - significaba que se vivía en una atmósfera tensa con entrenamiento militar como parte del currículum escolar. En noviembre de 1944 la escuela fue cerrada y los chicos fueron enviados a trabajar en fábricas ubicadas en los campo. Goro Shimura escribe en la referencia [1]: Mientras la escuela secundaria estaba cerrada, durante el último periodo de la guerra nos vimos obligados a trabajar en una fábrica que hacía partes para aviones de combate, y en ese momento supe el significado de trabajar en un lugar como ese. Su casa fue destruida en un bombardeo, pero la familia sobrevivió. Cuando terminó la guerra, la escuela abrió de nuevo y Goro continuó su educación. En este tiempo, el hogar familiar estaba en Mitaka, al oeste de Shinjuku, y viajaba en tren a la escuela. Hubo escasez de alimentos durante la guerra pero, después de que esta terminó, la escasez empeoró y Shimura estaba constantemente hambriento. En 1946 Shimura entró a la First High School. Era un internado y tenía asignado un dormitorio pero la escasez de alimentos significó que después de un par de semanas todo el mundo fue enviado a su casa a pasar unas vacaciones. En la escuela secundaria estudió matemáticas, inglés, alemán y francés pero encontró los cursos de matemáticas bastante decepcionantes. Sintió que el curso que tomó en geometría analítica fue enseñado por un maestro que no entendía completamente el tema. Shimura comenzó sus estudios en la Universidad de Tokio en 1949. Nuevamente criticó el contenido que le fue enseñado, sin embargo [1]: Mi deseo de capacitarme aprendiendo un montón de buenas matemáticas en la Universidad pronto fue traicionado por la realidad. Por un lado, mientras que en la escuela secundaria había adquirido una decente cantidad de conocimiento matemático, no había mucho de nuevo en lo que se enseñaba en el primer año en la Universidad.
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