Investigador entrega claves para argumentación matemática efectiva

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Invitado por el equipo de Didáctica de la Matemática y el CEPPE a dar una charla en la UC, el académico e investigador de la UDP Sebastián Howard recordó que un buen profesor nunca establece juicios sobre las respuestas de sus alumnos, y que al contrario, siempre los está desafiando para que piensen y argumenten sobre los contenidos expuestos.

Nunca decir de inmediato quién tiene la razón en la respuesta, sino al contrario, devolver permanentemente la responsabilidad de encontrar el razonamiento matemático correcto a todo el grupo curso, fue parte de la recomendación que realizó el académico Sebastián Howard a más de 120 profesores de aula que asistieron a un nuevo Conversatorio sobre Argumentación Matemática en la UC el pasado martes 27 de septiembre.

La actividad fue organizada por los profesores Horacio Solar y Francisco Rojas, del equipo de Didáctica de la Matemática de la Facultad de Educación, con el apoyo de CEPPE-UC.

Howard, quien es Secretario Académico del Doctorado en Educación de la Facultad de Educación de la UDP, centró su presentación en Un análisis de los intercambios en procesos de argumentación en el aula de matemáticas.

El investigador y doctorado en Educación en la UC partió recordando que las Bases curriculares vigentes incluyen como objetivo la Habilidad de Argumentar y Comunicar (Mineduc, 2012), y que de acuerdo a la investigación internacional, “La participación en discusiones aporta al aprendizaje de las matemáticas”.

Sin embargo, admitió que “sabemos poco respecto de cómo son las interacciones que promueven espacios para que los estudiantes desarrollen sus habilidades de argumentar en el aula de matemáticas”.

Precisó que la investigación chilena ha mostrado que existe cierta diferencia al avanzar los niveles de quinto al octavo básico, las interacciones suelen estar focalizadas en la presentación mecánica de la información y en la resolución mecánica de problemas. “Muy escasamente se encuentran procesos de razonamiento matemático”, lamentó.

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-Los estudiantes no tienen oportunidad de indagar, realizar generalizaciones, planear estrategias para resolver problemas, evaluar críticamente o levantar hipótesis. El tipo de pregunta cerrada que suelen dirigir los docentes tiene como consecuencia que ellos mantengan el control del conocimiento, en lugar de promover el pensamiento autónomo- advirtió.

Refutar y Argumentar

De acuerdo a Howard, en la clase de Matemática argumentar no es lo mismo que explicar. Precisó que existen refutaciones, argumentaciones, negociaciones y reformulaciones de manera constante, y que cada una de ellas cumple una tarea específica en el razonamiento matemático grupal.

-Un buen profesor de la disciplina todo el rato está devolviendo la pelota a los alumnos, no establece juicios valóricos ni entrega la respuesta correcta de inmediato. Tampoco escucha al mejor de la clase, que ya sabe la respuesta, porque uno de 40 es un porcentaje muy bajo de aprendizaje. (…) El buen profesor trabaja para la mayoría a la que le cuesta entender, son ellos quienes tienen que aprehender la materia y el razonamiento que hay detrás.El buen profesor reinicia la argumentación de manera permanente, cuestionando y haciendo que la clase cuestione lo que cree o prejuzga –resumió.

A la hora de las conclusiones, el investigador señaló que la interacción que favorece la presencia de procesos de argumentación está conformada por un tipo de interacción que se construye colectivamente. “El buen profesor no negocia ni corrige las intervenciones de los alumnos, sino que negocia meta-discursivamente sus intervenciones buscando la aparición de opiniones contrapuestas”, finalizó.

Ver aquí la presentación de Howard:

https://1drv.ms/p/s!AjlXTF3I7Qygh3zc9EBoKbcKA2We

Texto: Francisco Zabaleta

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1 × UPDATE `educacion_session` SET `data` = '__default|a:8:{s:15:\"session.counter\";i:2;s:19:\"session.timer.start\";i:1743833215;s:18:\"session.timer.last\";i:1743833215;s:17:\"session.timer.now\";i:1743833220;s:24:\"session.client.forwarded\";s:14:\"18.191.165.252\";s:8:\"registry\";O:9:\"JRegistry\":1:{s:7:\"\0*\0data\";O:8:\"stdClass\":0:{}}s:4:\"user\";O:5:\"JUser\":25:{s:9:\"\0*\0isRoot\";b:0;s:2:\"id\";i:0;s:4:\"name\";N;s:8:\"username\";N;s:5:\"email\";N;s:8:\"password\";N;s:14:\"password_clear\";s:0:\"\";s:8:\"usertype\";N;s:5:\"block\";N;s:9:\"sendEmail\";i:0;s:12:\"registerDate\";N;s:13:\"lastvisitDate\";N;s:10:\"activation\";N;s:6:\"params\";N;s:6:\"groups\";a:0:{}s:5:\"guest\";i:1;s:13:\"lastResetTime\";N;s:10:\"resetCount\";N;s:10:\"\0*\0_params\";O:9:\"JRegistry\":1:{s:7:\"\0*\0data\";O:8:\"stdClass\":0:{}}s:14:\"\0*\0_authGroups\";a:1:{i:0;i:1;}s:14:\"\0*\0_authLevels\";a:2:{i:0;i:1;i:1;i:1;}s:15:\"\0*\0_authActions\";N;s:12:\"\0*\0_errorMsg\";N;s:10:\"\0*\0_errors\";a:0:{}s:3:\"aid\";i:0;}s:20:\"com_rsfirewall.geoip\";s:2:\"US\";}' , `time` = '1743833221'
1 × UPDATE educacion_content SET hits = hits + 1
1 × SHOW FULL COLUMNS FROM `educacion_rsfirewall_logs

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