{"id":1523,"date":"2016-08-19T21:35:37","date_gmt":"2016-08-19T21:35:37","guid":{"rendered":"http:\/\/www.revista-educacion-matematica.org.mx\/revista\/?p=1523"},"modified":"2016-08-19T22:14:54","modified_gmt":"2016-08-19T22:14:54","slug":"esp1-9-en","status":"publish","type":"post","link":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/08\/19\/esp1-9-en\/","title":{"rendered":"Intuiting and formalizing: coextensive processes"},"content":{"rendered":"<p>Luis Moreno Armella<\/p>\n<p><strong>Abstract<\/strong>: There is a force that goes through the teaching of Calculus: The tension between<br \/>\nthe intuitive and the formal. Calculus continues to be taught as if it were natural<br \/>\nto introduce the study of change and accumulation by means of formalized concepts<br \/>\nknown as the mathematics of e and d. It is frequently considered as a failure that<br \/>\n\u201cstudents still seem to conceptualize limits via the imagination of motion.\u201d This kind of<br \/>\nassertions shows the tension created by traditional teaching between students\u2019 intuitions<br \/>\nand a misdirected formalization. The internal connections of the intuition of change and<br \/>\naccumulation are not correctly translated into that arithmetical approach of e and d.<\/p>\n<p><strong>Keywords<\/strong>: intuition, formalization, infinitesimal, analog cognition, symbol, metaphor,<br \/>\nembodied knowledge, digital medium, mediation.<\/p>\n<p><a href=\"http:\/\/www.revista-educacion-matematica.org.mx\/descargas\/Esp-1-9.pdf\"><img loading=\"lazy\" class=\"alignleft size-full wp-image-279\" src=\"http:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-content\/uploads\/2016\/05\/download.png\" alt=\"download\" width=\"200\" height=\"71\" srcset=\"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-content\/uploads\/2016\/05\/download.png 200w, https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-content\/uploads\/2016\/05\/download-150x53.png 150w\" sizes=\"(max-width: 200px) 100vw, 200px\" \/><\/a><\/p>\n<p><span style=\"border-radius: 2px; text-indent: 20px; width: auto; padding: 0px 4px 0px 0px; text-align: center; font: bold 11px\/20px 'Helvetica Neue',Helvetica,sans-serif; color: #ffffff; background: #bd081c  no-repeat scroll 3px 50% \/ 14px 14px; position: absolute; opacity: 1; z-index: 8675309; display: none; cursor: pointer;\">Guardar<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Luis Moreno Armella Abstract: There is a force that goes through the teaching of Calculus: The tension between the intuitive and the formal. Calculus continues to be taught as if it were natural to introduce the study of change and accumulation by means of formalized concepts known as the mathematics\u2026 <a class=\"continue-reading-link\" href=\"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/08\/19\/esp1-9-en\/\">Continue reading<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[220],"tags":[],"_links":{"self":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1523"}],"collection":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/comments?post=1523"}],"version-history":[{"count":2,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1523\/revisions"}],"predecessor-version":[{"id":1546,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1523\/revisions\/1546"}],"wp:attachment":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/media?parent=1523"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/categories?post=1523"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/tags?post=1523"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}