{"id":1903,"date":"2023-09-19T11:10:43","date_gmt":"2023-09-19T18:10:43","guid":{"rendered":"https:\/\/theothermath.com\/?p=1903"},"modified":"2024-05-03T07:25:34","modified_gmt":"2024-05-03T14:25:34","slug":"mathing-vs-studenting","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2023\/09\/19\/mathing-vs-studenting\/","title":{"rendered":"Mathing vs Studenting"},"content":{"rendered":"<p class=\"c0\"><span class=\"c1\">TL;DR<\/span><\/p>\n<ul>\n<li class=\"c0\"><span class=\"c1\">Mathing is the process of students understanding math concepts.<\/span><\/li>\n<li class=\"c0\"><span class=\"c1\">Studenting is the process of students applying that understanding to a worksheet.<\/span><\/li>\n<li class=\"c0\"><span class=\"c1\">Both need to happen.<\/span><\/li>\n<li class=\"c0\"><span class=\"c1\">Mathing is more important than studenting.<\/span><\/li>\n<\/ul>\n<p class=\"c0\"><span class=\"c1\">&#8212;<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">Let me briefly share a recent 1st grade lesson I taught to explain what are mathing and studenting and why we need BOTH!<\/span><\/p>\n<p class=\"c0\">I was recently invited into a 1st grade classroom to demonstrate what a Bansho lesson might look like. (For more on Bansho, check out <span class=\"c5\"><a class=\"c3\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2023\/09\/05\/a-formula-for-inquiry-and-direct-instruction\/&amp;sa=D&amp;source=editors&amp;ust=1695149418807063&amp;usg=AOvVaw2IMaVVGbQBwJEOrppJG8wj\">this blog post<\/a><\/span>\u00a0and <span class=\"c5\"><a class=\"c3\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2023\/09\/12\/planning-a-bansho-lesson\/&amp;sa=D&amp;source=editors&amp;ust=1695149418807209&amp;usg=AOvVaw1aKzYmvA0K55xYgP-vKUpQ\">this one too<\/a><\/span>.) Since it was early in the school year, I started with a word problem that is technically a Kindergarten <span class=\"c5\"><a class=\"c3\" href=\"https:\/\/www.google.com\/url?q=https:\/\/docs.google.com\/document\/d\/1FkPEpbml-i21CJpJGHh_oItBiz2qTbAqDG7DjnWkXss\/edit?usp%3Dsharing&amp;sa=D&amp;source=editors&amp;ust=1695149418807336&amp;usg=AOvVaw3AfMpB0Vp880riu-Vh5as8\">problem type<\/a><\/span><span class=\"c1\">.<\/span><\/p>\n<p class=\"c0\"><img id=\"ed.s7c6ys2z95kc\" title=\"\" src=\"https:\/\/docs.google.com\/drawings\/d\/sbCuW9RNjIwnAE-njwUCCsg\/image?parent=e\/2PACX-1vSK23LQPLT2h4wClHOP_qe_2MtOy1PxCWlMYw75Hq5byZdUQrWexv5lS4xjPMbUQ1ZnstwplwJMY_w4&amp;rev=142&amp;drawingRevisionAccessToken=DjaFnbFiEWVYbw&amp;h=144&amp;w=262&amp;ac=1\" alt=\"\" \/><\/p>\n<p class=\"c0\"><span class=\"c1\">After I introduced the problem with a quick Three-Read protocol, students began working at their desks to model this story. Some students used cubes, while others began by drawing frogs on their whiteboards. Occasionally, I would announce to the class something along the lines of &#8220;Hey everybody. Look at what Alonzo is doing. He drew circles to represent the frogs. Can you all draw circles too? Give it a try.&#8221; Or &#8220;Hey everybody. Look at the number bond Camilla created to represent the story. Try using a number bond to represent the cubes you are using\u2026or the circles you are drawing.&#8221;<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">As students were working individually or in pairs at their desks, I supported individual students informally, providing them with the &#8220;just in time&#8221; instruction they needed at the time. \u00a0I call this &#8220;teaching between the seats&#8221;.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">Eventually students had had enough time working on this problem and we were ready to share student thinking. I had selected and sequenced three students to share out. Each student had used one or more of the representations: concrete, pictorial representation, abstract.<\/span><\/p>\n<p class=\"c0\"><a href=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/000.png\"><img loading=\"lazy\" class=\"alignnone wp-image-1904 size-medium\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/000-300x171.png\" alt=\"\" width=\"300\" height=\"171\" srcset=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/000-300x171.png 300w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/000.png 568w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><a href=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/001.png\"><img loading=\"lazy\" class=\"alignnone wp-image-1905 size-medium\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/001-300x171.png\" alt=\"\" width=\"300\" height=\"171\" srcset=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/001-300x171.png 300w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/001.png 569w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><a href=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/002.png\"><img loading=\"lazy\" class=\"alignnone wp-image-1906 size-medium\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/002-300x172.png\" alt=\"\" width=\"300\" height=\"172\" srcset=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/002-300x172.png 300w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/002.png 567w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p class=\"c0\"><span class=\"c1\">One student used cubes, so I drew cubes on the board. Another student used circles to represent the frogs. A third student share the number bond she drew.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">Underneath each student&#8217;s idea, I wrote the number sentence 5 + 3 = 8.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">I told students for their next problem I wanted them to attach a number sentence to however they modeled the problem. I then posted the second story problem for students to work on.<\/span><\/p>\n<p class=\"c0\"><img id=\"ed.jr5dkk4xm564\" title=\"\" src=\"https:\/\/docs.google.com\/drawings\/d\/sjrDCsKUbzZZ2c6nKfh0V4Q\/image?parent=e\/2PACX-1vSK23LQPLT2h4wClHOP_qe_2MtOy1PxCWlMYw75Hq5byZdUQrWexv5lS4xjPMbUQ1ZnstwplwJMY_w4&amp;rev=100&amp;drawingRevisionAccessToken=YnkrZmsWdtfCoQ&amp;h=143&amp;w=262&amp;ac=1\" alt=\"\" \/><\/p>\n<p class=\"c0\"><span class=\"c1\">It did not take long for all students to model the problem in at least one way AND write the corresponding number sentence 4 + 5 = 9.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">Now it was time for independent practice, so the teacher handed out a worksheet that was nearly identical in math content. <\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">The worksheet was pretty typical for this type of math content.<\/span><\/p>\n<p class=\"c0 c2\"><a href=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/003.png\"><img loading=\"lazy\" class=\"alignnone size-large wp-image-1907\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/003-711x1024.png\" alt=\"\" width=\"355\" height=\"512\" srcset=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/003-711x1024.png 711w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/003-208x300.png 208w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/003-768x1106.png 768w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/003-1067x1536.png 1067w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/003.png 1111w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/a><a href=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/004.png\"><img loading=\"lazy\" class=\"alignnone size-large wp-image-1908\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/004-699x1024.png\" alt=\"\" width=\"350\" height=\"512\" srcset=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/004-699x1024.png 699w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/004-205x300.png 205w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/004-768x1125.png 768w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/004-1048x1536.png 1048w, https:\/\/theothermath.com\/wp-content\/uploads\/2023\/09\/004.png 1092w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/a><\/p>\n<p class=\"c0\"><span class=\"c1\">Almost immediately confused students were raising their hands asking what to do. There were boxes and blank spaces that students didn&#8217;t know what they were expected to do with them. This is when I recognized the difference between mathing and studenting.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">My lesson got students mathing. <em><strong>Mathing<\/strong><\/em> is the process of students developing a deep and profound understanding of mathematical concepts and procedures. Mathing is the work students do when they are behaving like mathematicians: using manipulatives, drawing pictures, using numbers and symbols to represent the math story.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">The worksheet is studenting. <em><strong>Studenting<\/strong><\/em> is the act of students learning to conform their mathematical understanding (their mathing) to expected norms of math textbooks. For example, blank boxes and blank spaces are the cultural shorthand way of saying &#8220;Put a number here.&#8221;<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">Studenting, like all other cultural norms, must be explicitly taught much like teaching our children to say &#8220;Bless you&#8221; when someone sneezes. <\/span><\/p>\n<p class=\"c0\"><strong><span class=\"c1\">Mathing is math. Studenting is NOT math!<\/span><\/strong><\/p>\n<p class=\"c0\"><span class=\"c1\">A common lesson structure I&#8217;ve seen observed is teachers guiding students problem-by-problem (blank space by blank space) through a worksheet. Sometime this studenting is necessary! Students NEED to learn the cultural norms of blank spaces and other unspoken rules of textbooks and worksheets. But this is NOT mathing! We are doing our students a disservice when we conflate studenting with mathing.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">Studenting probably does not need to happen daily. Mathing does!<\/span><\/p>\n<p class=\"c0\"><strong><span class=\"c1\">Students need both.<\/span><\/strong><\/p>\n<p class=\"c0\"><span class=\"c1\">Let&#8217;s start with mathing\u2026to learn the math. Then occasionally throw in some studenting to help our students learn the cultural norms.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">Using the FIABs and IABs from the CAASPP website is another great source for studenting. How often have I heard teachers notice the disconnect between the mathing occurring in the classroom and how the same math concepts are presented on the FIAB. This is a great time to use problems from a FIAB to explicitly teach students the norms of how psychometricians design test questions.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">As you teach in your classroom\u2026notice when you are mathing and when you are studenting. Mathing is most important\u2026studenting less so.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">.<\/span><\/p>\n<p class=\"c0\"><span class=\"c1\">.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>TL;DR Mathing is the process of students understanding math concepts. Studenting is the process of students applying that understanding to a worksheet. Both need to happen. Mathing is more important than studenting. &#8212; Let me briefly share a recent 1st grade lesson I taught to explain what are mathing and studenting and why we need [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1909,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[87,88,89,46],"_links":{"self":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/1903"}],"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=1903"}],"version-history":[{"count":1,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/1903\/revisions"}],"predecessor-version":[{"id":1910,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/1903\/revisions\/1910"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media\/1909"}],"wp:attachment":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media?parent=1903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/categories?post=1903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/tags?post=1903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}