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La Yupana, Material Manipulativo Para La Educación Matemática

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La Yupana, Material Manipulativo Para La Educación Matemática TESIS DOCTORAL Doctorado en Educación LA YUPANA, MATERIAL MANIPULATIVO PARA LA EDUCACIÓN MATEMÁTICA. Justicia social y el cambio educativo en niños de las comunidades quechuas alto andinos del Perú Herbert Jhon Apaza Luque Director: Dr. Santiago Atrio Cerezo Departamento de Didácticas Específicas FACULTAD DE FORMACIÓN DE PROFESORADO Y EDUCACIÓN UNIVERSIDAD AUTÓNOMA DE MADRID 2017 Herbert Jhon Apaza Luque 2 La Yupana, material manipulativo para la educación matemática A los alumnos del Centro Escolar N° 56392 de Kayno, Livitaca- Cusco. Matriculados los años 2006-2008. A los alumnos y profesores de los centros de: Surimana, Tungasuca, Pampamarca, Pabellones, Yanaoca (N° 56107), Pongoña, Huinchiri, Chirupampa, Pataqueña, participantes del Proyecto “Yupana para la educación matemática cultural andina” – 2015. 3 Herbert Jhon Apaza Luque 4 La Yupana, material manipulativo para la educación matemática ÍNDICE GENERAL AGRADECIMIENTOS ........................................................................................................... 13 Capítulo 1. INTRODUCCIÓN .......................................................................................... 17 Capítulo 2. BASES TEÓRICAS DE JUSTICIA SOCIAL ........................................... 31 2.1. El reconocimiento y el multiculturalismo en Charles Taylor ....... 33 2.1.1. Taylor en la historia de la filosofía ............................................................ 33 2.1.2. Ideas epistemológicas de Charles Taylor: metodología .................... 38 2.1.3. Ideas antropológicas de Taylor: psicología, sociología y ontología ......................................................................................................................... 40 2.1.4. Ideas morales de Taylor: autenticidad..................................................... 44 2.1.5. Ideas jurídicas de Taylor: derecho Justicia y política ......................... 45 2.1.6. Multiculturalismo y reconocimiento político .................................... 48 2.2. La lucha por el reconocimineto de Alex Honneth ............................. 49 2.2.1. El reconocimiento en Honneth ................................................................... 49 2.2.2. Críticas de Honneth a Habermas ................................................................ 51 2.2.3. Concepto de reconocimiento en la Filosofía Moral ............................. 52 2.2.4. Tres niveles de reconocimiento intersubjetivo .................................... 54 2.2.5. Justicia social desde el la lucha por el reconocimiento ..................... 58 2.3. Concepción de Justicia social en el pensamiento de John Rawls . 61 2.3.1. Introducción ....................................................................................................... 61 2.3.2. Ideas fundamentales sobre Justicia como equidad ............................. 62 2.3.3. Principios de la Justicia .................................................................................. 65 2.3.4. Los menos aventajados .................................................................................. 69 2.3.5. Posición original ............................................................................................... 71 2.4. Justicia como Redistribución, Reconocimiento y Representación ..................................................................................................................................... 73 2.4.1. Primera aproximación de la Justicia: redistribución y reconocimiento ............................................................................................................. 73 5 Herbert Jhon Apaza Luque 2.4.2. Segunda aproximación de la Justicia: redistribución, reconocimiento y participación .............................................................................. 76 2.5. Lucha por el reconocimiento de la Justicia cultural en Perú ......... 79 2.5.1. Corrientes ideológicas peruanas: Gonzales Prada ............................... 79 2.5.2. Movimientos por la lucha del reconocimiento de la Justicia cultural: Asociación Pro-Indígena.......................................................................... 80 2.5.3. Justicia cultural y Justicia Social en José Carlos Mariátegui ............. 81 2.6. La filosofía y la racionalidad andina ...................................................... 88 2.6.1. Racionalidades: occidental y andina ......................................................... 90 2.6.2. Configuración geográfica de los Andes .................................................... 91 2.6.3. Los procedimientos y actitudes de las racionalidades: Occidental y Andina ............................................................................................................................... 92 2.6.4. Presupuestos de la filosofía andina ........................................................... 93 2.6.5. Relacionalidad del todo: la lógica andina ................................................ 97 2.6.6. Principios fundamentales de la racionalidad andina .......................101 2.6.7. Aproximación de la concepción de Justicia social desde el paradigma de la racionalidad andina .................................................................102 Capítulo 3. CAMBIO EDUCATIVO Y JUSTICIA SOCIAL ......................................105 3.1. Cambio educativo y educación para la Justicia social ................... 107 3.1.1. El concepto de Justicia social en educación..........................................107 3.1.2. Educación para la Justicia Social ..............................................................110 3.1.3. Escuelas justas para la Justicia social .....................................................114 3.2. Una aproximación al análisis de la crisis educativa ...................... 116 3.2.1. La influencia del poder en educación .....................................................116 3.2.2. Los profesores como intelectuales transformativos ........................118 3.2.3. Currículo ............................................................................................................122 3.2.4. La Escuela ..........................................................................................................124 3.3. Una mirada de la educación peruana desde el pensamiento pedagógico de José Antonio Encinas ........................................................... 129 6 La Yupana, material manipulativo para la educación matemática 3.3.1. La escuela social en José Antonio Encinas ........................................ 130 3.3.2. La escuela rural ........................................................................................... 130 3.3.3. Evaluación ......................................................................................................... 132 Capítulo 4. EDUCACIÓN MATEMÁTICA Y ETNOMATEMÁTICA PARA LA JUSTICIA SOCIAL ................................................................................................................ 135 4.1. Educación matemática para la Justicia social .................................. 137 4.2. Educación matemática equitativa/pedagogía matemática equitativa .............................................................................................................. 138 4.2.1. La equidad en educación matemática .................................................... 138 4.2.2. La alfabetización matemática .................................................................... 141 4.3. Educación matemática liberadora/ educación matemática cultural .................................................................................................................. 142 4.3.1. Etnomatemática .............................................................................................. 142 4.4. Educación matemática democrática/pedagogía participativa . 147 4.4.1. Relación de la educación matemática y la democracia .................... 147 4.4.2. Complejidad de la sociedad de información ........................................ 148 4.4.3. Participación de todos para el beneficio de todos ............................. 149 4.4.4. ¿Cómo se concretan los procesos de participación en una pedagogía democrática?. ......................................................................................... 150 4.5. Metodología constructivista de la educación matemática cultural. Enculturación matemática ............................................................ 151 4.5.1. La cultura ........................................................................................................... 151 4.5.2. La Educación Matemática ........................................................................... 153 4.5.3. Uso de la lengua originaria y segunda lengua ..................................... 156 4.5.4. Algunos modelos explicativos sobre la cosmovisión andina ........ 160 4.5.5. Las actividades matemáticas ..................................................................... 163 4.5.6. Valores de la cultura matemática............................................................. 167 4.5.7. Niveles para la construcción de conocimientos y saberes ............. 170 4.5.8. Uso de materiales concretos: La Yupana .............................................. 172 7 Herbert Jhon Apaza Luque 4.5.9. Alternativa metodológica para el tratamiento de las actividades matemáticas .................................................................................................................173 4.5.10. El currículo en la educación matemática ............................................180 4.5.11. Procesos
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