![\"this](\"https:\/\/cohort21.com\/rutheichholtz\/files\/2016\/06\/patterns.jpg\")
<\/a>this student had strong visual skills, creating a proof without words (or algebra)<\/p><\/div>\n
In the last year as I have moved toward more inquiry-based math learning<\/a> in my high school classroom, I have more insight than ever before into how my students think in the subject. And I have realized that we all see so differently. I have students who are incredibly strong with visual patterns but weak in algebra, and other students who can follow all the algebraic rules but can\u2019t visually identify a 90\u00b0 angle. I have noticed that some students struggle to see the 3D shapes in 2D drawings of solids, and I have wondered what I can do to help all of them.<\/p>\n I have read the research on the importance of block play in early childhood<\/a>, and its effects on performance in secondary mathematics (this is so fascinating!). It\u2019s one reason why the club members of GirlTech<\/a> are engaged as leaders in our kindergarten: they lead block play with our youngest students.<\/p>\n Last month I had our school librarian order a copy of a recent publication: Spatial Reasoning in the Early Years<\/strong><\/span><\/a>. This book has been the best reading I have done as a math educator. What follows are the notes I took while reading: mostly thoughts, quotes, connections, and potential links to my classroom.<\/p>\n (@ddoucet<\/a>, @aianovskaia<\/a>, @timrollwagen<\/a>, @gnichols<\/a>, @lmcbeth<\/a>, @danielleganley<\/a> please read on, there is something for everyone here!)<\/em><\/p>\n Ch 1:<\/strong> Spatial reasoning is learned, it is malleable, and even if your kids didn\u2019t play with blocks, there is hope for them to still be successful in math.<\/p>\n Ch 2:<\/strong> This chapter provided a breakdown of types of spatial reasoning. I found this helpful, as I often can identify a deficit but am not sure how to categorize it. Also, it connected to this article that I came across on twitter<\/a> that weekend. Also, my mind exploded a bit when I realized the connection between spatial reasoning and multilingualism. From this Economist article in 2015<\/a>, I knew that multilingual children perform better on these feats of spatial reasoning. That these skills transcend STEM subjects might be obvious, but this connection made me giddy. Language teachers: we build the same skills.<\/p>\n Ch 3:<\/strong> This chapter focused\u00a0on developing spatial thinking, and I wondered if this is what it means to \u201csee\u201d mathematics. From p.35:<\/p>\n \u201cThe strong link between spatial reasoning and mathematics raises the possibility that improving children\u2019s spatial skills might serve as a way to strengthen mathematics learning.\u201d <\/em><\/span><\/p>\n students building objects in order to observe patterns<\/p><\/div>\n I was reminded of the brilliant work being done by the team at Westfield State University, on Discovering the Art of Mathematics<\/a>. If you are a math nerd and haven\u2019t seen their materials, go there now. I visited last November, and was impressed with the quality of math thinking in their undergraduate classes. The use of manipulatives was constant. Why don\u2019t we use more manipulatives in high school?<\/p>\n Also in this chapter, I discovered more studies on the effects of block play. I loved the results from one study showing that free block play was good, guided block play was better, and narrative-driven block play was most effective. Narrative-driven<\/strong>. Did you hear that, English teachers? We need each other.<\/p>\n Intervention programs would be possible, given the malleability of the skills involved in spatial reasoning. This chapter inspired me to want to start a club\/program for grade 9-10 students focused on spatial reasoning instead of more algebra\/calculation\/rule-following.<\/p>\n Ch 4:<\/strong>\u00a0Here I read the history of math education. I was happy to discover\u00a0that the transition from elementary to secondary mathematics has never been smooth.\u00a0A quote on page 54 described the very real struggle of socializing as a math teacher:<\/p>\n \u201cFor we math educators, this discontinuity between elementary and secondary is often encountered as the cocktail-party confession, \u2018I was good at math until grade 6.\u2019 Such remarks, for us, are not unlike the statement, \u2018I was a confident swimmer until my feet stopped touching the bottom.'\u201d<\/em><\/span><\/p>\n Page 60 argues that math is not equal to calculation. AGREED. I think calculation is to math as spelling is to Literature.<\/p>\n Ch 5:<\/strong> Whoa. This chapter was deep, on Theory of Embodiment. I was grateful for my<\/p>\n teams work on logic challenges as they move around the game board<\/p><\/div>\n liberal arts education with the philosophy requirements. I had to dig deep to keep up with this chapter. It described the body of the individual, the body of the group, and the body of knowledge, and I particularly liked the sections describing how concepts and movement are connected (I was already\u00a0using drama games to warm up students\u2019 spatial awareness!). Dan Meyer<\/a> recently pointed me to this stellar resource on dance and mathematics<\/a>. (PE Teachers \u2013 you know all about spatial awareness already. Let\u2019s work together!) I also recently adapted Think Fun\u2019s CodeMaster<\/a> game as a full-body group game for a coding workshop. It was fun!<\/p>\n A little something for my classroom came from p. 76 \u201c\u2026 in re-cognizing the class as a potential collective body engaged in mathematics, we can ask questions about the class, and how it works as a body in and of itself during the lesson with respect to spatial reasoning.\u201d What that means for me: class discussions are important in learning, but the classroom atmosphere that makes the class a body is equally important.<\/span><\/p>\n Ch 6:<\/strong> This chapter was on early elementary tasks. I was happy to discover that complex 3D geometry tasks are as appropriate for young elementary children as they are for teenagers; we don\u2019t usually associate young minds with this level of sophistication in thinking.<\/p>\n Also, p 96 stated, \u201cResearch shows that people who perform well on tasks of mental rotation also tend to perform well across a range of mathematical tasks.\u201d I don\u2019t want to confuse correlation with causation here, but I do think that it would be worth a try to improve the spatial skills of secondary students as a step in remediation.<\/p>\n Ch 7:<\/strong> DRAWING! This chapter had my mind racing.\u00a0I have so many notes.<\/p>\n Ch 8:<\/strong> 2D to 3D. This is something I see my students struggle with and I have been trying to help them through the use of manipulatives like Zometool<\/a>. This chapter is the first time I have seen acknowledgement that the 2D representation of a 3D object is assumed to be obvious, and the connection is glossed over in math books. It deserves more attention in class. The chapter also stresses that this type of representation is all cultural convention and should be explicitly taught. I would like lesson\/activity ideas around this.<\/p>\n Ch 9:<\/strong> The final chapter is a discussion on revamping curriculum to include more spatial reasoning. There is a call for more research (sign me up!!)<\/strong><\/span>. Seriously, how do I get involved?<\/p>\n Finally, a lovely quote from a 1979 study on p 148,<\/p>\n \u201cSpatial reasoning plays a key role in narrative comprehension and memory across every domain of human engagement.\u201d <\/em><\/span><\/p>\n That\u2019s a strong closing argument.<\/p>\n I give the Spatial Reasoning Study\u00a0Group<\/a> a standing ovation for this impressive book!! I was aware of the connection between math understanding\u00a0and spatial reasoning skills, and\u00a0I find myself reassured by the fact that these skills are malleable: we can help students develop them. Along the way, we tie in English, Foreign Languages, Drama, Art, Music, all the Sciences, and certainly the Humanities. This book was such a joy for me to read, as it provided details of\u00a0fascinating research supporting much of what I believe about math learning. More importantly, it gave a new dimension to the interdisciplinary nature of the subject. Math is often sold in school as being so widely \u201capplicable\u201d, as if students will often calculate the trajectory of a projectile in motion on the baseball field, or solve simultaneous equations at the grocery store. The focus on spatial reasoning makes math interdisciplinary\u00a0on a much deeper level, and these connections are worth pursuing, for our students and for ourselves.<\/p>\n","protected":false},"excerpt":{"rendered":" Are you one of those people who can \u201csee\u201d math? Or are you a person who self-identifies as \u201cnot a math person\u201d? I\u2019m an optimist. I actually believe that everyone Continue Reading →<\/a><\/p>\n","protected":false},"author":57,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"wds_primary_category":0,"footnotes":""},"categories":[6,21,7,20],"tags":[40,46,45],"class_list":["post-181","post","type-post","status-publish","format-standard","hentry","category-action-plan","category-lesson-ideas","category-math","category-professional-development","tag-inquiry-in-math","tag-interdisciplinary","tag-spatial-reasoning"],"_links":{"self":[{"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/posts\/181","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/users\/57"}],"replies":[{"embeddable":true,"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/comments?post=181"}],"version-history":[{"count":0,"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/posts\/181\/revisions"}],"wp:attachment":[{"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/media?parent=181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/categories?post=181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cohort21.com\/rutheichholtz\/wp-json\/wp\/v2\/tags?post=181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/a><\/a>\n