{"id":1669,"date":"2016-11-29T01:38:33","date_gmt":"2016-11-29T01:38:33","guid":{"rendered":"http:\/\/www.revista-educacion-matematica.org.mx\/revista\/?p=1669"},"modified":"2016-11-29T01:38:33","modified_gmt":"2016-11-29T01:38:33","slug":"vol28-3-6en","status":"publish","type":"post","link":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/11\/29\/vol28-3-6en\/","title":{"rendered":"How Abundant are the Sets of Numbers? Students Comparing Infinite Sets of Numbers"},"content":{"rendered":"<p><strong>Authors:<\/strong> Virginia Montoro, Nora Scheuer, Ma. del Puy P\u00e9rez Echeverr\u00eda<\/p>\n<p><strong>Abstract:<\/strong> We studied how students with different mathematical background<br \/>\nconceive infinite cardinality of number sets. We analyzed a task in which high<br \/>\nschool and college students were requested to compare infinite number sets.<br \/>\nStudents were classified according to their ideas on infinity. Using this classification<br \/>\ntogether with the students\u2019 level of math education, we performed a<br \/>\ncorrespondence factorial analysis. A gradient was found in the depth of students\u2019<br \/>\nideas. At one end we found what we called horror infiniti, based students<br \/>\npropensity avoid infinity and instead construe it as something undefined. These<br \/>\nviews were associated with students with less mathematical education. In an<br \/>\nintermediate zone, the finitist conception was placed. It was the most frequent<br \/>\nway of thinking among the participants of the study, with three versions: tacitly<br \/>\ninfinitist, explicitly finitist, or taking the integers as model of inclusion. At the<br \/>\nother end, the infinitist conception was placed. It was present among students<br \/>\nwith college mathematical education, according to two types: thinking of the<br \/>\ncardinality of number sets as a unique infinite quantity; or conceiving different<br \/>\ninfinite cardinals. The latter was found only in advanced mathematics students.<\/p>\n<p><strong>Keywords:<\/strong> comparison, number sets, cardinal infinity, mathematics education.<\/p>\n<p><a href=\"http:\/\/www.revista-educacion-matematica.org.mx\/descargas\/Vol28\/3\/6.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>&nbsp;<\/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>Authors: Virginia Montoro, Nora Scheuer, Ma. del Puy P\u00e9rez Echeverr\u00eda Abstract: We studied how students with different mathematical background conceive infinite cardinality of number sets. We analyzed a task in which high school and college students were requested to compare infinite number sets. Students were classified according to their ideas\u2026 <a class=\"continue-reading-link\" href=\"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/11\/29\/vol28-3-6en\/\">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":[],"_links":{"self":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1669"}],"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=1669"}],"version-history":[{"count":1,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1669\/revisions"}],"predecessor-version":[{"id":1670,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1669\/revisions\/1670"}],"wp:attachment":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/media?parent=1669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/categories?post=1669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/tags?post=1669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}