Experto de la Universidad de Columbia recomienda tres claves para mejorar las clases de matemáticas

Nick Wasserman, académico de Teachers College de la Universidad de Columbia, presentó su proyecto que busca mejorar la formación docente con cursos de matemáticas avanzadas. Conectar con la enseñanza, conexiones matemáticas invertidas y prácticas matemáticas pedagógicas son parte de las recomendaciones.

¿Cómo mejorar la enseñanza de las clases de matemáticas desde la formación docente? Es la pregunta que respondió Nick Wasserman, Doctor en Educación Matemática y profesor del Teachers College de la Universidad de Columbia, en su charla híbrida “Mejorando la preparación de las y los profesores a través de sus cursos de matemáticas avanzado". La instancia se desarrolló en el Edificio de Pedagogías Interfacultades de la Facultad de Educación UC y contó con 25 asistentes presenciales y cerca de 65 personas conectadas por Zoom.

La visita del profesor Nick Wasserman en enmarca en una estancia financiada por el programa Fulbright Specialist y por el Fondo de Apoyo a la Organización de Reuniones Científicas y Seminarios Interdisciplinarios 2022 de la Vicerrectoría de Investigación (VRI), titulado “Conocimiento matemático avanzado para la formación de profesores de matemáticas” que lideran los académicos de la Facultad de Educación UC, y Pilar Herreros de la Facultad de Matemáticas. Durante la exposición, dirigida a académicos/as, investigadores/as y profesores/as de matemáticas, el experto internacional explicó cómo se puede mejorar la enseñanza a las y los estudiantes de educación media mediante la preparación de cursos universitarios.

Según Wasserman, las y los profesores de matemáticas de dicho nivel necesitan de un conocimiento profundo y sólido del contenido de la materia, así como también deben tener las suficientes herramientas pedagógicas para aplicarlas en el aula. Eso lo resume en su proyecto colaborativo “Actualización del aprendizaje para profesores en análisis real” , ULTRA (Upgrading Learning for Teachers in Real Analysis en inglés), desarrollado en conjunto con las universidades Temple y Rutgers, cuyo enfoque instructivo comparte tres modelos de preparación docente a través de cursos de matemáticas avanzadas.

En su charla, Nick Wasserman dio a conocer 3 claves, basadas en los resultados del proyecto ULTRA, para potenciar las habilidades matemáticas en las y los adolescentes:

Conectar con la enseñanza

“Hay un desafío único en cursos de matemáticas avanzados: las ideas matemáticas no se discuten explícitamente con los estudiantes de secundaria”, señaló el profesor Wasserman, agregando que se debe cambiar el “cómo entender las matemáticas y cómo se enseñan”. Por ello recomienda un modelo alternativo en que las y los docentes puedan “aprender habilidades pedagógicas con el uso de situaciones de enseñanza”, y donde “ciertas ideas pedagógicas se pueden aprender a través de las matemáticas avanzadas”.

Conexiones matemáticas invertidas

El académico señaló, también, que es favorable aplicar conexiones matemáticas invertidas; este tipo de clases buscan reorganizar los tiempos y espacios de aprendizaje. En una clase invertida el docente entrega el material de estudio a los estudiantes antes de ingresar al aula y durante la clase se realizan actividades disciplinarias y participativas. Nick Wasserman declaró que dos prácticas disciplinarias como definir y probar “permiten considerar a las matemáticas avanzadas como una instancia de práctica que forma parte de la matemática escolar”, a diferencia del modelo de “conexión matemática típica” que se enfoca en el contenido y deja la enseñanza y comprensión de las matemáticas avanzadas como algo más general y abstracto.

Según el estudio Designing advanced mathematics courses to influence secondary teaching: fostering mathematics teachers’ “attention to scope” realizado por el experto en 2019, la aplicación de prácticas disciplinarias matemáticas invertidas, como atención al rango y el análisis real con el modelo invertido, fueron eficientes en la sala declases para las y los profesores. Asimismo, según el análisis, el 40% de los estudiantes de secundaria participaron de estas prácticas y la mayoría de ellos valoró la técnica de enseñanza.

Prácticas matemáticas pedagógicas

Otro punto importante para el académico es conectar las prácticas matemáticas, definidas como las actividades que realizan las y los matemáticos, con las prácticas pedagógicas, utilizadas por docentes, en prácticas matemáticas pedagógicas (PMP). Estas contienen puntos comunes entre las anteriores, como “los tipos de acciones, hábitos, líneas de razonamiento, etc., en los que las/os matemáticos y las/os profesores participan regularmente”. En ese sentido, algunas PMP son:

● Reconocer y revisar las suposiciones y limitaciones matemáticas (atención al rango).

● Usar casos especiales para ilustrar ideas matemáticas.

● Exponer la lógica como la forma de interpretación matemática.

● Usar objetos más simples para estudiar objetos más complejos.

● Evitar dar reglas sin una explicación matemática que las acompañe.

● Buscar múltiples explicaciones.

Las PMP, explicó, permiten crear un puente “entre conocimientos de las matemáticas avanzadas y las acciones de los docentes”. Por ello recomendó a las y los profesores/as especializarse en estos modelos para potenciar el aprendizaje de las matemáticas en estudiantes de enseñanza media.

Puedes descargar el material expositivo aquí y revivir la charla:

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1 × SELECT u.* FROM educacion_users u
1 × SELECT `id` FROM `educacion_usergroups
1 × SELECT folder AS type, element AS name, params FROM educacion_extensions
1 × SELECT `path` FROM educacion_rsfirewall_ignored
1 × SELECT id, rules FROM `educacion_viewlevels
1 × SELECT b.id FROM educacion_usergroups AS a LEFT JOIN educacion_usergroups AS b ON b.lft <= a.lft AND b.rgt >= a.rgt
1 × SELECT `session_id` FROM `educacion_session`
1 × SELECT `file` FROM educacion_rsfirewall_hashes
1 × SELECT * FROM educacion_rsfirewall_configuratio
1 × SELECT alias, catid FROM educacion_content
1 × SELECT `params` FROM educacion_extensions
1 × SELECT m.id, m.menutype, m.title, m.alias, m.note, m.path AS route, m.link, m.type, m.level, m.language,m.browserNav, m.access, m.params, m.home, m.img, m.template_style_id, m.component_id, m.parent_id,e.element as component FROM educacion_menu AS m LEFT JOIN educacion_extensions AS e ON m.component_id = e.extension_id
1 × SELECT * FROM educacion_languages
1 × SELECT `data` FROM `educacion_session`

OTRAS Tablas:

1 × UPDATE `educacion_session` SET `data` = '__default|a:8:{s:15:\"session.counter\";i:1;s:19:\"session.timer.start\";i:1732294310;s:18:\"session.timer.last\";i:1732294310;s:17:\"session.timer.now\";i:1732294310;s:24:\"session.client.forwarded\";s:12:\"18.117.70.64\";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` = '1732294311'
1 × UPDATE educacion_content SET hits = hits + 1
1 × SHOW FULL COLUMNS FROM `educacion_rsfirewall_logs
1 × INSERT INTO `educacion_session` (`session_id`, `client_id`, `time`) VALUES ('6fa0c3fe2208211ba3b5dc638628e00b', 0, '1732294310'

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Información de Perfil

Uso de Memoria

Registro Database

44 Registro Consultas

34 Tipos de consultas del registro, Ordenado por acontecimientos.

SELECCIONAR Tablas:

OTRAS Tablas: