{"id":924,"date":"2016-08-03T17:29:00","date_gmt":"2016-08-03T17:29:00","guid":{"rendered":"http:\/\/www.revista-educacion-matematica.org.mx\/revista\/?p=924"},"modified":"2016-08-03T17:29:00","modified_gmt":"2016-08-03T17:29:00","slug":"infinite-iterative-processes-and-transcendent-objects-a-model-of-construction-of-mathematical-infinity-from-the-apos-theory","status":"publish","type":"post","link":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/08\/03\/infinite-iterative-processes-and-transcendent-objects-a-model-of-construction-of-mathematical-infinity-from-the-apos-theory\/","title":{"rendered":"Infinite iterative processes and transcendent objects: A model of construction of mathematical infinity from the APOS Theory"},"content":{"rendered":"<p><strong>Authors:<\/strong> Diana Paola Villabona Mill\u00e1n, Solange Roa Fuentes<\/p>\n<p><strong>Abstract:<\/strong> The present study aims to examine the mental structures that a person<br \/>\ncan develop to construct the mathematical concept of infinity in two particular contexts: \u201cthe paradox of Achilles and the tortoise\u201d and the \u201cSierpin\u00b4 ski triangle\u201d.<br \/>\nBased on the genetic generic decomposition of the infinite, proposed by<br \/>\nRoa-Fuentes and Okta\u00e7 (2014), this investigation focuses on the study of the<br \/>\nparticular characteristics, mechanisms and structures produced by each context.<br \/>\nThe analysis of data from work done by postgraduate students (in Mathematics<br \/>\nand Mathematics Education) shows how from the infinite iterative process<br \/>\n(potential infinity) advances towards to a transcend object (actual infinity).<br \/>\nFurthermore, the results reflect the importance of the coordination mechanism<br \/>\nin the construction of infinite iterative process.<\/p>\n<p><strong>Key words<\/strong>: APOS theory, paradoxes, Sierpin\u00b4 ski triangle, infinite iterative processes,<br \/>\ntranscendent objects.<\/p>\n<p><a href=\"http:\/\/www.revista-educacion-matematica.org.mx\/descargas\/Vol28-2-5.pdf\"><img loading=\"lazy\" class=\"alignright 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","protected":false},"excerpt":{"rendered":"<p>Authors: Diana Paola Villabona Mill\u00e1n, Solange Roa Fuentes Abstract: The present study aims to examine the mental structures that a person can develop to construct the mathematical concept of infinity in two particular contexts: \u201cthe paradox of Achilles and the tortoise\u201d and the \u201cSierpin\u00b4 ski triangle\u201d. Based on the genetic\u2026 <a class=\"continue-reading-link\" href=\"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/08\/03\/infinite-iterative-processes-and-transcendent-objects-a-model-of-construction-of-mathematical-infinity-from-the-apos-theory\/\">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":[2],"tags":[101,328,331,506,507],"_links":{"self":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/924"}],"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=924"}],"version-history":[{"count":1,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/924\/revisions"}],"predecessor-version":[{"id":925,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/924\/revisions\/925"}],"wp:attachment":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/media?parent=924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/categories?post=924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/tags?post=924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}