{"id":1771,"date":"2017-03-31T04:18:20","date_gmt":"2017-03-31T04:18:20","guid":{"rendered":"http:\/\/www.revista-educacion-matematica.org.mx\/revista\/?p=1771"},"modified":"2017-04-06T18:27:34","modified_gmt":"2017-04-06T18:27:34","slug":"bustamante-en","status":"publish","type":"post","link":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2017\/03\/31\/bustamante-en\/","title":{"rendered":"Andrea\u2019s Reflections: A Microgenetic Analysis of the Understanding of Division in the Context of a Problem"},"content":{"rendered":"<p><a href=\"mailto:javierbtte@ hotmail.com\">Alfonso J. Bustamante-Santos<\/a><br \/>\n<a href=\"mailto:rcfm@unam.mx\">Rosa del Carmen Flores-Mac\u00edas<\/a><\/p>\n<p><strong>Abstract:<\/strong> This study describes changes in the meanings of the written representation<br \/>\nof the division algorithm within a partition word problem in Andrea, a<br \/>\nstudent from sixth grade in a public school. Through a clinical interview, she<br \/>\nsolves various word problems. Based on the theory of conceptual fields, we<br \/>\ndiscuss the changes in different theorems-in-act and concepts-in-act that she<br \/>\nuses. She reflects on the relationships between the components of the division,<br \/>\nand reformulates her ideas on how these relationships must be expressed. The<br \/>\nmost significant change observed in Andrea during the interview is related to<br \/>\nher understanding of the division algorithm; she initially writes it based on ideas<br \/>\nlike \u201cthe bigger number must be inside\u201d but, at the end of the interview, she<br \/>\nshowed understanding of the relationship between the word problem and the<br \/>\nwritten algorithm. Likewise, are observed changes in the way she conceives<br \/>\nthe measured-magnitude relationship. Discussion analyzes the relevance of<br \/>\ntaken into consideration student\u2019s concepts and theorems-in-act to strengthen<br \/>\nthe mathematic learning.<\/p>\n<p><strong>Keywords:<\/strong> problem solving, simple proportionality, division, conceptualization,<br \/>\ngraphic representation.<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"http:\/\/www.revista-educacion-matematica.org.mx\/descargas\/Vol29\/1\/Bustamante.pdf\"><img loading=\"lazy\" class=\"size-full wp-image-81 alignright\" src=\"http:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-content\/uploads\/2016\/05\/download.png\" alt=\"\" width=\"200\" height=\"72\" \/><\/a><span class=\"\" lang=\"ES-TRAD\">DOI: 10.24844\/EM2901.04<\/span><\/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<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>Alfonso J. Bustamante-Santos Rosa del Carmen Flores-Mac\u00edas Abstract: This study describes changes in the meanings of the written representation of the division algorithm within a partition word problem in Andrea, a student from sixth grade in a public school. Through a clinical interview, she solves various word problems. Based on\u2026 <a class=\"continue-reading-link\" href=\"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2017\/03\/31\/bustamante-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":[569],"tags":[419,550,575,576,574],"_links":{"self":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1771"}],"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=1771"}],"version-history":[{"count":2,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1771\/revisions"}],"predecessor-version":[{"id":1793,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1771\/revisions\/1793"}],"wp:attachment":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/media?parent=1771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/categories?post=1771"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/tags?post=1771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}