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Series Y Largometrajes Como Recurso Didáctico En Matemáticas En TESISDOCTORAL 2 0 1 5 SERIESYLARGOMETRAJESCOMORECURSODIDÁCTICOEN MATEMÁTICASENEDUCACIÓNSECUNDARIA pablo beltrán pellicer Ingeniero de Telecomunicación por la Universidad de Zaragoza Máster en Tecnologías de la Información y Comunicaciones en Redes Móviles e Inalámbricas por la Universidad de Zaragoza Máster en Innovación e Investigación en Educación por la UNED. departamento de didáctica, organización escolar y didácticas especiales Facultad de Educación Dirección de la tesis: dr. antonio medina rivilla Codirección: dra. mercedes quero gervilla departamento de didáctica, organización escolar y didácticas especiales Facultad de Educación SERIESYLARGOMETRAJESCOMORECURSODIDÁCTICOEN MATEMÁTICASENEDUCACIÓNSECUNDARIA pablo beltrán pellicer Ingeniero de Telecomunicación por la Universidad de Zaragoza Máster en Tecnologías de la Información y Comunicaciones en Redes Móviles e Inalámbricas por la Universidad de Zaragoza Máster en Innovación e Investigación en Educación por la UNED. Dirección de la tesis: dr. antonio medina rivilla Codirección: dra. mercedes quero gervilla A Sara, Arturo y Alonso, mi luna y estrellas. Gracias por quererme a pesar del tiempo robado. AGRADECIMIENTOS El germen de esta tesis hay que buscarlo en mi trabajo fin de máster, que realicé bajo la tutela de Isabel Escudero. Ella me animó a continuar y comenzó a dirigirme. Poco después, y debido a avatares de la vida, Isabel tuvo que apartarse de este proyecto. No sé si el resultado final es el que ella imaginaba, pero lo justo es agradecerle aquí la confianza que depositó en mí. En aquellos titubeantes primeros pasos, Mercedes Quero asumió la codirección con Isabel. El agradecimiento para ella es doble. Por un lado, sus consejos y orientaciones a la hora de estructurar la investigación y el documento final han sido siempre certe- ros y necesarios. Sus palabras fueron en todo momento palabras de aliento. Por otra parte, Mercedes actuó como un auténtico nexo de unión, allanando el camino para que Antonio Medina dirigiera la tesis hasta el final. Para Antonio, siempre atento y disponible, solamente tengo elogios. Este humilde trabajo no habría sido lo mismo de no haber contado con su dilatada experiencia y espectacular bagaje académico. Todo ello, unido a que Antonio es un torrente de ideas, me ha permitido aprender lo inimaginable, creciendo como profesor y como investigador. Por ello, desde estas líneas le digo gracias. Pero sobre todo, por el valor que demostró al tomar el timón de un barco que ya había zarpado. Mientras desarrollaba el trabajo fin de máster, tuve la ocasión de entrevistar a José Mª Sorando, uno de los pioneros en utilizar fragmentos de cine y series en clase de Matemáticas, y cuyas referencias salpican el texto de la tesis. La inspiración que me produjo aquella charla todavía persiste a día de hoy. Después de leer los primeros textos sobre la teoría de las situaciones didácticas, me asaltaron una serie de inquietudes que me hicieron ponerme en contacto con investi- iv gadores expertos en la materia. Aunque el marco teórico que he terminado utilizando ha variado bastante desde aquellos compases iniciales, nunca olvidaré los correos de Nicholas Balacheff ni la charla telefónica con Pilar Orús. Espero que sus consejos se noten en la filosofía seguida en el diseño de las secuencias didácticas. El proyecto eTwinning nunca habría sido lo mismo de no haber conocido a Anna Asti. Su implicación e ilusión fueron un acicate para mi investigación. Agradezco sinceramente las opiniones de Antonio F. Costa, Ángel Requena y Al- fonso J. Población, así como a los expertos que participaron en la evaluación del cues- tionario piloto de las fase avanzada, Miguel Ángel García, Lamberto López y Jaime Martínez. Carlos y María jugaron un papel fundamental en el desarrollo de la investigación, prestándose a poner en práctica las secuencias didácticas y recoger los datos de los mapas de humor, así como de los cuestionarios de los alumnos. Hacen falta más pro- fesores como ellos. En la elección de los mapas auto-organizados como herramienta de análisis, ha tenido mucho que ver el que ya la hubiera empleado en mi proyecto fin de carrera. Agradezco desde estas líneas al que fuera mi director entonces, David Buldain, que me hizo ver todo el potencial que tenían. Cada vez que he hablado con Ana Gascón sobre la tesis, al día siguiente me encon- traba con un correo lleno de sugerencias. Gracias Ana. Por último, debo añadir que cualquier investigador sabrá que no es fácil compaginar el trabajo que conlleva una tesis con la vida familiar y laboral. En mi caso, no tengo duda de que ha requerido de altas dosis de comprensión y de ayuda por parte de mi entorno cercano. No tengo palabras para ellos. En definitiva, a todos que han hecho posible que llegara hasta aquí. Ha sido mucho tiempo dedicado a ella y seguramente me olvide de nombrar a alguien. Espero que sepan perdonarme. v ÍNDICEGENERAL Acrónimos xi Índice de figuras xii Índice de tablas xviii i introducción 1 1 introducción 3 1.1 Justificación y oportunidad 3 1.2 Objeto de estudio 6 1.3 Preguntas de investigación y objetivos 8 1.3.1 Preguntas de investigación 8 1.3.2 Objetivos 9 1.4 Metodología 10 1.5 Estructura de la tesis 12 ii marco teórico 15 2 estudios previos sobre matemáticas en el cine y su utilización didáctica 17 2.1 Una reflexión inicial 17 2.2 Estudios sobre aplicaciones didácticas del cine en Matemáticas 19 2.3 Estudios sobre referencias matemáticas en el cine y las series 24 2.3.1 Páginas web 24 2.3.2 Artículos y libros 33 2.4 Estudios sobre el papel del contexto en Matemáticas 36 2.4.1 Educación matemática realista 36 2.4.2 El cine como contexto 43 3 marco conceptual 49 3.1 Enfoque ontosemiótico 50 vi índice general vii 3.1.1 Valoración de la idoneidad didáctica de un proceso de enseñanza- aprendizaje 51 3.2 Ingeniería didáctica: fases de un estudio EOS 55 3.2.1 Análisis preliminares 57 3.2.2 Análisis a priori y diseño de las secuencias de clase 58 3.2.3 Experimentación 58 3.2.4 Análisis a posteriori y validación 59 3.3 Recogida de información emocional: mapas de humor 59 3.4 Análisis de datos: mapas auto-organizados 66 3.4.1 Fundamentos de los mapas auto-organizados 71 3.4.2 Visualizaciones de los mapas y Java SOMToolbox 75 4 implicaciones didácticas 79 4.1 Clasificaciones de fragmentos de películas o series 81 4.2 Diversidad de contextos 87 iii diseño de secuencias didácticas 89 5 modelo de diseño y análisis de las secuencias didácticas 91 5.1 Modelo de diseño 91 5.2 Modelo de análisis 94 5.2.1 Estudio de la idoneidad didáctica 94 5.2.2 Idoneidad epistémica 96 5.2.3 Idoneidad cognitiva 96 5.2.4 Idoneidad interaccional 97 5.2.5 Idoneidad mediacional 98 5.2.6 Idoneidad afectiva 99 5.2.7 Idoneidad ecológica 101 6 secuencias didácticas y sus análisis a priori 103 6.1 Bloque de números 104 6.1.1 Contact: números primos 104 6.1.2 Blackjack: porcentajes (descuentos) 115 6.1.3 Granujas de medio pelo: fracciones 126 6.1.4 Los Simpson: fracciones (total sabiendo una parte) 133 viii índice general 6.1.5 Futurama: fracciones (intereses) 140 6.2 Bloque de álgebra 148 6.2.1 Cielo de octubre: ecuaciones de 2º grado 148 6.2.2 Jungla de Cristal III: ecuaciones, resolución de problemas 161 6.2.3 The Big Bang Theory: valor numérico 172 6.2.4 Los Simpson: ecuaciones de segundo grado 183 6.2.5 La vida es bella y Los caballeros de la mesa cuadrada: enuncia- dos engañosos 191 6.3 Bloque de funciones y gráficas 203 6.3.1 Los Simpson Inteligencia vs Felicidad 203 6.3.2 Pandorum - Crecimiento de la población 211 6.4 Bloque de geometría 218 6.4.1 Annapolis: ángulos 218 6.4.2 Numb3rs: volumen 225 6.4.3 El mago de Oz, teorema de Pitágoras 234 6.4.4 Apollo XIII, ángulos 241 6.5 Bloque de probabilidad y estadística 248 6.5.1 Moneyball: estadística 248 6.5.2 Numb3rs, episodio piloto: experimentos aleatorios 259 6.6 Conclusiones de los análisis a priori 266 iv trabajo de campo 275 7 planteamiento del trabajo de campo 277 8 fase inicial 283 8.1 Descripción general del trabajo en la fase inicial 283 8.1.1 Enfoque de investigación 283 8.1.2 Muestra 284 8.1.3 Instrumentos 285 8.2 Objetivos y estructura del proyecto 285 8.3 Desarrollo del proyecto 288 8.3.1 Trabajo con escenas: Jungla de cristal III 288 8.3.2 Trabajo con escenas: Granujas de medio pelo 291 índice general ix 8.4 Evaluación final y resultados 293 8.4.1 Cuestionario final para los alumnos 295 8.5 Conclusiones de la fase inicial 298 9 fase avanzada 301 9.1 Descripción general del trabajo 301 9.1.1 Enfoque de la investigación en la fase avanzada 301 9.1.2 Muestra del estudio 302 9.1.3 Instrumentos de investigación 303 9.2 Cuestionario inicial 306 9.2.1 Descripción 306 9.2.2 Muestra para el cuestionario 307 9.2.3 Elaboración del cuestionario 307 9.2.4 Análisis estadístico descriptivo global 312 9.2.5 Conclusiones del cuestionario inicial 332 9.3 Recogida y análisis de la información 334 9.3.1 Mapas de humor 334 9.3.2 Análisis de la idoneidad emocional con mapas auto-organizados 336 9.4 Análisis de los grupos 343 9.4.1 Grupo 1 343 9.4.2 Grupo 2 371 9.4.3 Conclusiones de los análisis con SOM 396 v conclusión 399 10 conclusiones de la tesis 401 11 líneas futuras de investigación 409 11.1 Diseño de procesos de enseñanza-aprendizaje 409 11.2 Desarrollo de herramientas online 410 11.3 Mapas auto-organizados condicionados 410 Referencias 413 Referencias a películas y series de ficción 421 x índice general vi apéndices 423 a cuestionario de la fase avanzada 425 b currículo oficial de 2º de eso 469 b.1 Contenidos comunes 469 b.2 Bloque de números 471 b.3 Bloque de álgebra 474 b.4 Bloque de geometría 475
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