{"id":240,"date":"2013-09-09T00:03:02","date_gmt":"2013-09-09T04:03:02","guid":{"rendered":"https:\/\/annie.mathematicalthinking.org\/?p=240"},"modified":"2024-08-26T14:59:35","modified_gmt":"2024-08-26T18:59:35","slug":"noticing-and-wondering-in-elementary-school","status":"publish","type":"post","link":"https:\/\/annie.mathematicalthinking.org\/index.php\/2013\/09\/09\/noticing-and-wondering-in-elementary-school\/","title":{"rendered":"Noticing and Wondering in Elementary School"},"content":{"rendered":"

My colleague Max recently blogged about noticing and wondering in high school,\u00a0 Noticing and Wondering in High School<\/a> and I thought it would be fun to blog about using it at the elementary level.\u00a0\u00a0The essence of our “I Notice, I Wonder” activity is that you give students a mathematical situation or picture or story, without asking any specific questions, and ask them to list everything that they notice<\/em><\/strong> about it, and everything that it makes them wonder<\/em><\/strong> about.<\/p>\n

I’ve written about it in the past, including in one of our Teaching with the Problems of the Week documents, How to Start Problem Solving in Your Classroom<\/a> [PDF].\u00a0\u00a0In that, I tell the story of the first time I explicitly asked students (who were “low-level” eighth graders) to tell me everything they “noticed” about a picture.\u00a0\u00a0The short version is that the students were awesome and their teacher was amazed at how much math they came up with.<\/p>\n

Just as I started composing my post, I got email from my friend Debbie, who teaches at an elementary school school in the district I live in.\u00a0\u00a0She described the first lesson she did with a new class she’s co-teaching, in which she asked the students to notice and wonder.\u00a0\u00a0I asked her if I could use her story as a “guest post” on my blog, since I think it’s as compelling as anything I could have written.\u00a0\u00a0She agreed, so here goes.<\/p>\n

\n

Debbie’s Story<\/strong><\/p>\n

I taught an amazing lesson today.\u00a0\u00a0It was the first day of math class for the year.\u00a0\u00a0Our whole district is starting a new math program.\u00a0\u00a0Our fifth grade is grouping homogenously for math.\u00a0\u00a0Instead of teaching the highest ability students as I usually do as \u201cTeacher of the Gifted,\u201d I\u2019m co-teaching the lowest two classes with two other teachers, a regular education teacher and a special educator.\u00a0\u00a0Together we have 22 struggling math students.<\/p>\n

Predictably, the topic for lesson 1.1 was place value.\u00a0\u00a0But my goals were to engage the students, to create a safe space for learning, to get them thinking and asking questions, and to evaluate their understanding of place value.\u00a0\u00a0Instead of using the lessons from the book, which used place value charts with the places labeled, I started by handing out blank, unlabeled place value charts and asking pairs of students to talk about them.\u00a0\u00a0I suggested that they notice and wonder.\u00a0\u00a0And the three teachers got to wander and listen in.\u00a0\u00a0It was amazing.<\/p>\n

First, they had to decide the orientation of the paper.\u00a0\u00a0Some kids held it vertically and saw it as a thermometer or list.\u00a0\u00a0Most held it horizontally.\u00a0\u00a0Many recognized it as a chart to use with money or decimals or place value.\u00a0\u00a0It was gratifying to see that they recognized the format.\u00a0\u00a0When we reconvened to share ideas as a group, our conversation was directed by their noticings and wonderings.\u00a0\u00a0I was able to review concepts of place value, numbers vs. digits, etc. not by following the book, but by following the comments from the kids.\u00a0\u00a0I praised their questions, asked them to respond to each other\u2019s comments, and kept the discussion flowing.<\/p>\n

At one point the kids parroted the places: ones, tens, hundreds, thousands\u2026 and I wrote them on the board.\u00a0\u00a0They got to millions, ten millions, hundred millions and then got stuck.\u00a0\u00a0Some thought that next comes thousand millions and others thought next comes billions.\u00a0\u00a0It was a perfect teachable moment; all I did was draw the lines between hundreds, thousands, millions and point out that there were three columns in each, and there was a collective \u201cah-ha!\u201d<\/p>\n

Eventually, I asked the kids to put the place labels into their charts.\u00a0\u00a0It was fascinating.\u00a0\u00a0About a third of them labeled left to right.\u00a0\u00a0That certainly told us a lot about their level of understanding of place value!\u00a0\u00a0We have a lot of work to do.\u00a0\u00a0But that meant that about two-thirds of them were able to label the places correctly, which is good.\u00a0\u00a0I used one of the incorrectly labeled charts and we started talking about it.\u00a0\u00a0I asked if putting a 7 in different places changed the number of M&Ms the digit represented.\u00a0\u00a0I covered up parts of the chart and asked them to read the number, then revealed the next column.\u00a0\u00a0Again, we had \u201cah-has.\u201d\u00a0\u00a0I\u2019m not sure who was more excited, the kids or me.<\/p>\n

I had been worried that the other two teachers were going to object to my non-traditional approach, especially on the first day of using a new program.\u00a0\u00a0I was pleasantly surprised; they saw the value.\u00a0\u00a0During the lesson, the regular education teacher kept flipping through the teacher\u2019s manual.\u00a0\u00a0She realized that I had covered material from the first THREE lessons, although I\u2019d not completely finished any of the lessons.\u00a0\u00a0So while my approach was non-traditional, I was covering the curriculum and we weren\u2019t \u201cbehind.\u201d More importantly, both of them recognized and valued the high level of student engagement.\u00a0\u00a0In fact, one pointed out that one boy who struggles with attention had been totally attentive and even participative.\u00a0\u00a0They saw the excitement among the students, they noticed that even reluctant students participated, and they recognized the significance of the multiplicity of \u201cah-ha moments.\u201d<\/p>\n

It took me at least another hour to come off the \u201chigh\u201d from the lesson.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

My colleague Max recently blogged about noticing and wondering in high school,\u00a0 Noticing and Wondering in High School and I thought it would be fun to blog about using it at the elementary level.\u00a0\u00a0The essence of our “I Notice, I Wonder” activity is that you give students a mathematical situation or picture or story, without … <\/p>\n

Continue reading “Noticing and Wondering in Elementary School”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts\/240"}],"collection":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/comments?post=240"}],"version-history":[{"count":4,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts\/240\/revisions"}],"predecessor-version":[{"id":390,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts\/240\/revisions\/390"}],"wp:attachment":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/media?parent=240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/categories?post=240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/tags?post=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}