{"id":1527,"date":"2016-08-19T21:42:30","date_gmt":"2016-08-19T21:42:30","guid":{"rendered":"http:\/\/www.revista-educacion-matematica.org.mx\/revista\/?p=1527"},"modified":"2016-08-19T22:17:27","modified_gmt":"2016-08-19T22:17:27","slug":"esp1-11-en","status":"publish","type":"post","link":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/08\/19\/esp1-11-en\/","title":{"rendered":"Division of fractions as a multiplicative comparison based on methods invented by students"},"content":{"rendered":"<p>Alfinio Flores Pe\u00f1afiel<\/p>\n<p><strong>Abstract<\/strong>: We present several methods invented by students in grades 5th through 8th<br \/>\nto solve division of fractions problems. For each method we discuss how the teacher<br \/>\ncan help students develop their understanding of multiplicative comparison of fractions,<br \/>\nby emphasizing fundamental mathematical principles that allow students generalize,<br \/>\nextend, and relate their methods with other methods. The methods presented are repeated<br \/>\nsubtraction and interpretation of the remainder; use of the multiplicative identity and<br \/>\ninverses; division as missing factor; inverse and direct proportional thinking; division of<br \/>\nfractions as composition of operations; and division of fractions as a ratio between two<br \/>\nquantities.<\/p>\n<p><strong>Keywords<\/strong>: fractions, division, multiplicative comparison, proportional reasoning, students<br \/>\nmethods.<\/p>\n<p><a href=\"http:\/\/www.revista-educacion-matematica.org.mx\/descargas\/Esp-1-11.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>Alfinio Flores Pe\u00f1afiel Abstract: We present several methods invented by students in grades 5th through 8th to solve division of fractions problems. For each method we discuss how the teacher can help students develop their understanding of multiplicative comparison of fractions, by emphasizing fundamental mathematical principles that allow students generalize,\u2026 <a class=\"continue-reading-link\" href=\"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/2016\/08\/19\/esp1-11-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":[550,390,551,552,553],"_links":{"self":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1527"}],"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=1527"}],"version-history":[{"count":2,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1527\/revisions"}],"predecessor-version":[{"id":1547,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/posts\/1527\/revisions\/1547"}],"wp:attachment":[{"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/media?parent=1527"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/categories?post=1527"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.revista-educacion-matematica.org.mx\/revista\/wp-json\/wp\/v2\/tags?post=1527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}