{"id":281,"date":"2017-11-06T09:20:40","date_gmt":"2017-11-06T17:20:40","guid":{"rendered":"http:\/\/theothermath.com\/?p=281"},"modified":"2017-11-06T09:53:00","modified_gmt":"2017-11-06T17:53:00","slug":"virtual-manipulatives-in-cpa","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2017\/11\/06\/virtual-manipulatives-in-cpa\/","title":{"rendered":"Virtual Manipulatives in CPA"},"content":{"rendered":"<p><img loading=\"lazy\" class=\"alignright wp-image-282 size-medium\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2017\/11\/virtual-manipulatives-300x225.png\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/theothermath.com\/wp-content\/uploads\/2017\/11\/virtual-manipulatives-300x225.png 300w, https:\/\/theothermath.com\/wp-content\/uploads\/2017\/11\/virtual-manipulatives.png 400w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>While nothing can adequately replace the REAL thing, virtual manipulatives play an essential role in a student&#8217;s journey towards developing a profound understanding of mathematics. That&#8217;s a bold claim! Let&#8217;s go a little deeper&#8230;<\/p>\n<p>You&#8217;ve heard of CPA? Concrete &#8211; Pictorial &#8211; Abstract. Sometimes it is referred to as CRA. (Concrete &#8211; Representational &#8211; Abstract)<\/p>\n<p>These are the three ways a math concept can be represented.<\/p>\n<ul>\n<li>Concrete &#8211; using actual physical objects represent the math concept<\/li>\n<li>Pictorial &#8211; using pictures\/drawings to represent the math concept<\/li>\n<li>Abstract &#8211; using numbers, strategies, and\/or algorithms to represent the math concept<\/li>\n<\/ul>\n<p>So in which representation do virtual manipulatives belong? It is not entirely clear, but virtual manipulatives seem to occupy the space in\u00a0between\u00a0the representations. They serve as a transition from the concrete world to the pictorial&#8230;not quite concrete, but far more flexible than pictorial. The nature of the virtual manipulatives also allows the algorithm and the pictures to be placed side-by-side, making it easier for the students to shift towards abstract understanding.<\/p>\n<p>Here is a small <a href=\"https:\/\/embarc.online\/course\/view.php?id=45#section-6\" target=\"_blank\" rel=\"noopener\">collection<\/a>\u00a0of virtual manipulatives to get you started.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>While nothing can adequately replace the REAL thing, virtual manipulatives play an essential role in a student&#8217;s journey towards developing a profound understanding of mathematics. That&#8217;s a bold claim! Let&#8217;s go a little deeper&#8230; You&#8217;ve heard of CPA? Concrete &#8211; Pictorial &#8211; Abstract. Sometimes it is referred to as CRA. (Concrete &#8211; Representational &#8211; Abstract) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":286,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[36,37,35,38],"_links":{"self":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/281"}],"collection":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/comments?post=281"}],"version-history":[{"count":2,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/281\/revisions"}],"predecessor-version":[{"id":284,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/281\/revisions\/284"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media\/286"}],"wp:attachment":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media?parent=281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/categories?post=281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/tags?post=281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}