{"id":336,"date":"2016-05-18T16:48:43","date_gmt":"2016-05-18T16:48:43","guid":{"rendered":"http:\/\/www.hillbrook.us\/voices\/?p=336"},"modified":"2016-05-18T22:14:27","modified_gmt":"2016-05-18T22:14:27","slug":"the-power-and-joy-of-collaborative-learning-in-lower-school-math","status":"publish","type":"post","link":"http:\/\/www.hillbrook.us\/voices\/2016\/05\/the-power-and-joy-of-collaborative-learning-in-lower-school-math\/","title":{"rendered":"The Power – and Joy – of Collaborative Learning in Lower School Math"},"content":{"rendered":"

As we look back on another fun- and sunshine-filled Walkathon, our annual trek through our 14-acre campus in support of professional development for teachers, Learning Specialist Autumn Vavoso\u00a0shares how teacher learning is evolving and enhancing student engagement and hands-on academic experiences in lower school math.<\/em><\/p>\n

By Autumn Vavoso, Learning Coach In-Residence at Hillbrook School<\/p>\n

\"File_002\"<\/a>\u00a0 \u00a0 \u00a0\u00a0\u00a0\"IMG_5364\"<\/a><\/p>\n

Counting Collections in Kindergarten:<\/strong><\/p>\n

We have been working hard as collaborative math teams to test some new ideas. The\u00a0kindergarten team began by researching\u00a0this article on Counting Collections<\/a>. One team member was also able to attend the National Council of Teachers of\u00a0Mathematics<\/a>\u00a0(NCTM) conference in San Francisco earlier this spring where a session on counting collections was offered by a\u00a0team of researchers from UCLA. As a collaborative teaching team, the resources and experiences garnered at the conference were then brought back to the group at Hillbrook. Together, we collaborated and used the ideas from the article as well as the conference conference to plan a\u00a0series of math workshops around investigating how to count collections.<\/p>\n

We wanted the children to explore different types of materials as well as\u00a0varied quantities, and so we\u00a0created an experience where kindergarten students\u00a0engaged in counting collections of eyeballs, pink and purple shiny lips, fruit, spheres,\u00a0and fuzzy pom poms. With these colorful and engaging articles in hand, the the children were off to count!<\/p>\n

As they worked their way through their task, our young learners soon quickly discovered that making piles by equal numbers (2\u2019s or 10\u2019s) can help make the\u00a0counting more efficient. Meanwhile, making groups by color really did not help us get to the total number\u00a0in the collection efficiently. After a few days of exploration the children were then asked to\u00a0represent their thinking around how they counted their collection.<\/p>\n

\"picture1\"<\/a>Ryan made groups of letters. His first and second piles had 10, his\u00a0third pile had 15 and his fourth pile had nine. We interviewed Ryan to see how he was planning\u00a0on finding out how many in his collection. He counted:<\/p>\n

\u201cTen and ten is twenty and 15 more\u00a0would make – pause – thirty and five oh, 35! And then nine more would be like ten more but one\u00a0less. It is 45 but one less and that would make 44.\u201d<\/p><\/blockquote>\n

The students and teachers were amazed\u00a0with the way Ryan could think with flexibility\u00a0about numbers. We believe that the continued practice of\u00a0counting collections with meaningful grouping will build the ability to think flexibly about numbers\u00a0in all students.<\/p>\n

\"IMG_5018\"<\/a><\/p>\n

Number Talks in Fourth Grade:<\/strong><\/p>\n

\"IMG_5364\"<\/a>The fourth grade team and learning coach collaborated on introducing Number Talks, a mental\u00a0math problem solving strategy, and designing inquiry lessons around area and perimeter. Mrs.\u00a0Butler and Mrs. Vavoso also attended the NCTM conference where they\u00a0learned a great deal from\u00a0Sherry\u00a0Parrish<\/a>, the author of Number Talks<\/em>,\u00a0about the importance of using\u00a0this collaborative\u00a0strategy to help students build flexibility in mentally solving\u00a0computation problems – together. We jumped right in with the students and had them mentally solve a\u00a0string of related problems while we recorded their mathematical process for other students to\u00a0see. The children were then encouraged to solve the string of problems in a different way. As\u00a0students listened to each other they learned efficient strategies other students are using that\u00a0may also be able to help them.<\/p>\n

As a\u00a0team, we then all worked together to design a series of inquiry math workshops\u00a0around area and perimeter. The students were given graph paper and three sentences to\u00a0consider: What do you know about area and perimeter? What are you wondering?<\/p>\n

And after the exploration:\u00a0What do you now understand about area and perimeter?<\/p>\n

\"File_003<\/a><\/p>\n

Students were then challenged to draw shapes and find the area and perimeter of each. They were then\u00a0asked to come up with a few theories to test in their “I Wonder” section.<\/p>\n

\"File_005<\/a>Chris amazed us when\u00a0he found out that any rectangle that has one side with a perimeter of two will always have a\u00a0perimeter of the area plus four. Wow! As we move to exploring the area and perimeter of\u00a0composite shapes our fourth graders will continue to investigate and test their mathematical\u00a0theories.<\/p><\/blockquote>\n

Once we feel these theories can hold true after being tested, we added them to our\u00a0classroom chart of “Understandings.”<\/p>\n

 <\/p>\n

Taking the time to investigate and logically think through\u00a0the ideas around area and perimeter help solidify\u00a0children\u2019s understanding of these core concepts. Before teaching them formulas, we wanted\u00a0the students to be anchored in their understanding of area and perimeter for a deeper, sustainable learning experience.\u00a0Sometimes, formulas without conceptual understanding promote a \u201cgoing through\u00a0the motions\u201d approach to math, where the “why” is never clearly investigated by the learners themselves. We want more for our students!<\/p>\n

\"IMG_5369<\/a><\/p>\n

The synergy of a collaborative faculty team that believes in sharing work along with the opportunity to partake in\u00a0professional development opportunities that promote leading-edge educational practices are helping to transform classrooms everyday. These moments, that combine faculty collaboration with resources made possible through a leading-edge commitment to professional development, continue to offer our students new resources that promote subject mastery through deep-dive understanding as well as the joy and profound enrichment of collaborative learning.<\/p>\n","protected":false},"excerpt":{"rendered":"

As we look back on another fun- and sunshine-filled Walkathon, our annual trek through our 14-acre campus in support of professional development for teachers, Learning …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","content-type":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[58,57,112,62,76,20,152],"tags":[154,157,156,24,155],"class_list":["post-336","post","type-post","status-publish","format-standard","hentry","category-co-teaching","category-extraordinary-educational-experience","category-flexible-learning-spaces","category-hands-on-learning","category-inspiring-education","category-lower-school","category-professional-development","tag-collaboration","tag-fourth-grade","tag-kindergarten","tag-lower-school","tag-math"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/posts\/336","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/comments?post=336"}],"version-history":[{"count":4,"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/posts\/336\/revisions"}],"predecessor-version":[{"id":348,"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/posts\/336\/revisions\/348"}],"wp:attachment":[{"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/media?parent=336"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/categories?post=336"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.hillbrook.us\/voices\/wp-json\/wp\/v2\/tags?post=336"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}