{"id":1798,"date":"2019-10-25T10:48:47","date_gmt":"2019-10-25T15:48:47","guid":{"rendered":"http:\/\/www.on-school.com\/blog\/?p=1798"},"modified":"2019-10-25T10:48:56","modified_gmt":"2019-10-25T15:48:56","slug":"como-ensenar-las-matematicas","status":"publish","type":"post","link":"https:\/\/www.on-school.com\/blog\/como-ensenar-las-matematicas\/","title":{"rendered":"\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas?"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img fetchpriority=\"high\" decoding=\"async\" width=\"750\" height=\"422\" src=\"http:\/\/www.on-school.com\/blog\/wp-content\/uploads\/2019\/10\/istock-4871566561.jpg\" alt=\"\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas?\" class=\"wp-image-1799\" srcset=\"https:\/\/www.on-school.com\/blog\/wp-content\/uploads\/2019\/10\/istock-4871566561.jpg 750w, https:\/\/www.on-school.com\/blog\/wp-content\/uploads\/2019\/10\/istock-4871566561-300x169.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><figcaption>\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas?<\/figcaption><\/figure>\n\n\n\n<p>\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas? Cuando de impartir programas de asignaturas se trata, no es extra\u00f1o encontrar que el primer pensamiento de un profesor pueda dirigirse hacia la enumeraci\u00f3n de contenidos que encajan en su armaz\u00f3n l\u00f3gica y que estos contenidos se refieran s\u00f3lo a los conceptos, definiciones, teoremas, etc.\u00a0 Esta reacci\u00f3n podr\u00eda explicarse por una tradici\u00f3n, donde generalmente han primado los conocimientos, sistema conceptual y estos no se han visto en su relaci\u00f3n indisoluble con los modos de actuaci\u00f3n,\u00a0 con las habilidades. <\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; En\ncuanto al trabajo con los conocimientos, no se trata s\u00f3lo de que el profesor\ndefina conceptos, haga las conexiones matem\u00e1ticas o induzca a una organizaci\u00f3n\ndel conocimiento, entre otras acciones; se trata de&nbsp;:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Asociarle formas de proceder con ellas, prever la realizaci\u00f3n de tareas que las contengan en conjunci\u00f3n con las habilidades a desarrollar, por supuesto en funci\u00f3n de los objetivos previstos.<\/li><li>Lograr que el estudiante reproduzca, exteriorice su pensamiento para que bien sea el profesor o a\u00fan mejor, otros estudiantes, influyan a los efectos de correcci\u00f3n ante fallas o insuficiencias, o que por el contrario se estimule a niveles superiores de ejecuci\u00f3n.<\/li><\/ul>\n\n\n\n<p>Se trata adem\u00e1s de mantener un <a href=\"http:\/\/www.on-school.com\/blog\/problematica-del-aprendizaje-de-las-matematicas\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"di\u00e1logo permanente del profesor con los estudiantes y entre los estudiantes (opens in a new tab)\">di\u00e1logo permanente del profesor con los estudiantes y entre los estudiantes<\/a>. Este di\u00e1logo, puede basarse en preguntas como las siguientes:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u00bfC\u00f3mo se expresa la definici\u00f3n del concepto?<\/li><li>\u00bfQu\u00e9 otras formas equivalentes hay para esa definici\u00f3n?<\/li><li>\u00bfQu\u00e9 puede hacer fallar o debilitar el concepto?<\/li><li>\u00bfQu\u00e9 te evoca el concepto?<\/li><li>\u00bfBajo qu\u00e9 condiciones es posible su aplicaci\u00f3n?<\/li><li>\u00bfCon qu\u00e9 otros conceptos es posible asociar o conectar?<\/li><\/ul>\n\n\n\n<p>Si el estudiante adquiere el h\u00e1bito de responder a estas\ninterrogantes o de hacerlas a sus propios compa\u00f1eros de aula comenzar\u00e1n a ver\nel aprendizaje de manera diferente y de hecho se van entrenando para encontrar\nlas ideas esenciales, las regularidades y las conexiones matem\u00e1ticas, que le\npermitir\u00e1n un abordaje mucho m\u00e1s efectivo de los problemas a resolver.&nbsp; Asimismo, dispondr\u00e1n de un recurso eficiente\npara aprender y no solo matem\u00e1tica precisamente.<\/p>\n\n\n\n<p>Por otro lado, no puede haber un conocimiento sin una\nhabilidad mediante la cual funcione, ni puede haber una habilidad que no est\u00e9\nasociada a un conocimiento: \u201cno se puede separar el saber, del saber hacer,\nporque siempre saber es saber hacer algo, no puede haber un conocimiento sin\nuna habilidad, sin un saber hacer\u201d (Tal\u00edzina; 1993:92). <\/p>\n\n\n\n<p>Un sistema b\u00e1sico de Habilidades matem\u00e1ticas (Dra. Herminia\nHern\u00e1ndez; 1989: 32) como integrantes de dicho Sistema B\u00e1sico, se encuentran\nlas habilidades &nbsp;definir <em>&nbsp;y <\/em>demostrar,\nque son las que por su propia naturaleza establecen el v\u00ednculo primario con el\nsistema de conocimientos, as\u00ed como identificar, interpretar, graficar,\nalgoritmizar y calcular, mediante las cuales hacemos matem\u00e1tica es decir,\nresolvemos problemas matem\u00e1ticos en su acepci\u00f3n amplia.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; El haber\nrevelado la existencia de estas habilidades fue beneficioso en tanto, ellas\ndeben estar en el centro de la atenci\u00f3n de la formaci\u00f3n matem\u00e1tica de los\nprofesionales que la requieran, pues ellas mismas podr\u00edan estar en la\nestructura de las habilidades profesionales; adem\u00e1s, deben ser tomadas en\ncuenta en la formaci\u00f3n de docentes de matem\u00e1tica, puesto que ellas son\nconsustanciales al pensamiento que deben poseer primero&nbsp; y ser capaces de formar despu\u00e9s en sus\neducandos.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; De gran\nvalor resulta determinar si los estudiantes de ingenier\u00eda deben profundizar,\npor ejemplo, en las mismas habilidades que las requeridas por un estudiante de\nLicenciatura en matem\u00e1tica.<\/p>\n\n\n\n<p>&nbsp;En efecto, para un\ningeniero es muy importante:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Trabajo con gr\u00e1ficos. Los ingenieros usan los gr\u00e1ficos para representar el comportamiento de muchas magnitudes y fen\u00f3menos.<\/li><li>La interpretaci\u00f3n del concepto de derivada como \u201craz\u00f3n de cambio\u201d. Magnitudes de trabajo sistem\u00e1tico como velocidad, calor espec\u00edfico, etc. as\u00ed lo patentizan.<\/li><li>La interpretaci\u00f3n del concepto de \u201cintegral\u201d como suma para poder usarla en el c\u00e1lculo de diversas magnitudes f\u00edsicas, como momentos, etc.<\/li><li>La habilidad de expresar en lenguaje matem\u00e1tico (modelar matem\u00e1ticamente) fen\u00f3menos y procesos de la realidad. <\/li><li>La habilidad de interpretar los resultados obtenidos, identificando las limitaciones que corresponda.<\/li><li>La habilidad en el empleo de tablas.<\/li><li>Saber interpretar las ecuaciones diferenciales, representadas en un sistema\u00a0 en el dominio del tiempo y la transformada de laplace en el dominio de la frecuencia.<\/li><\/ol>\n\n\n\n<p>\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas? Cuando de impartir programas de asignaturas se trata, no es extra\u00f1o encontrar que el primer pensamiento de un profesor pueda dirigirse hacia la enumeraci\u00f3n de contenidos que encajan en su armaz\u00f3n l\u00f3gica y que estos contenidos se refieran s\u00f3lo a los conceptos, definiciones, teoremas, etc.\u00a0 Esta reacci\u00f3n podr\u00eda explicarse por una [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1799,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[163],"tags":[1345,1452,1453,164,1451],"class_list":["post-1798","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematicas","tag-concepto","tag-herminia-hernandez","tag-laplace","tag-matematicas-2","tag-talizina"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas? - Matem\u00e1ticas - On-School<\/title>\n<meta name=\"description\" content=\"\u00bfC\u00f3mo ense\u00f1ar las matem\u00e1ticas? 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