0@Loc: Curtis/quilt/quilt4.cha1@PID: 11312/t-00001872-12@Begin3@Languages: eng4@Participants: TEA Carmen_Curtis Teacher, STU Student, INV Investigator5@ID: eng|Curtis|TEA|||||Teacher|||6@ID: eng|Curtis|STU|||||Student|||7@ID: eng|Curtis|INV|||||Investigator|||8@Media: quilt4, video9*TEA: could we do that? ▶10*STU: no. ▶11@Comment: Carmen Curtis a second grade teacher at Country View grades12school in Veronia Wisconsin has been working with the13quilting unit for five years. She has adapted software14developed by IBM and the education development center to15suit her own classroom practice.16*TEA: xxx copy core copy core with that design would the green squares17end up in the middle? ▶18*STU: no. ▶19*TEA: no. ▶20*TEA: if we did copy core copy core copy core would it be symmetrical? ▶21*STU: no. ▶22*STU: yeah. ▶23*STU: it would. ▶24*TEA: right. ▶25@Comment: For several weeks we followed Carmen and her students with26video cameras to document their discovery of geometry27through quilt design.28*INV: I wondered if you can cast back a few years and talk about the way29you used to teach mathematics, especially mathematics of space and30the way you teach mathematics now. ▶31*INV: what's different? ▶32*TEA: okay well everything different (.) about the way I teach math. ▶33*TEA: but in particular what this unit brings [//] you know so brings34home to me is how differently I teach geometry to second graders. ▶35*TEA: because the typical way to teach geometry to second graders was a36two or three week unit. ▶37*TEA: um I personally put it at the beginning of the year because the38emphasis used to be so much on learning number facts with second39graders. ▶40*TEA: and so many of my beginning second graders struggled even to know41facts to ten. ▶42*TEA: this is different. ▶43*TEA: this is wonderful. ▶44*TEA: they accomplished more in the first three days of quilting than I45used to in my entire geometry unit. ▶46@Comment: Quilting introduces children to shapes, their properties47and ways to manipulate them to make new shapes and patterns.48When thinking about design the children have the opportunity49to develop an understanding of mathematical concepts like50motion in the plane and symmetry. Moreover the process of51design has the advantage of introducing children to a52problem solving approach that resembles the thinking of53mathematicians and scientists.54*STU: xxx and these and these and if these squares they have the &ex [//]55the same exact color in each triangle it's just once you flip it56it's going to look different. ▶57*TEA: but I know you said xxx. ▶58@Comment: Traditional math assignments assume there is a59predetermined answer to a given question and the goal for60the students is to find it. Design is different. In61designing students sketch out ideas ask open ended questions62experiment with solutions and constantly evaluate their63results. The process of designing quilts requires the64execution of a series of practical steps. Carmen uses each65step as an opportunity to encourage both hands on and66individual engagement and group discussion about67mathematical concepts. The first step in quilts is the68constructions of a single core square69@Situation: Making a core square70*TEA: what we are going to try to figure out today [//] try to find out71by working together and thinking together is if we only had blue72squares and green squares how many core squares do you thiink we73could possibly design using only blue squares and green squares. ▶74*TEA: we want to find all of them that we can. ▶75@Comment: Carmen always puts constraints on specific tasks as a way76of introducing new issues. As the case of the core square77exercise where she limits the students to the use of only78two colors, blue and green. The constraints help the79children to focus on the mathematical aspects of their80design decisions. After time spent physically manipulating81the shapes within a core square the children come together82and translate what they've learned into more formal83language.84*TEA: xxx core square and I'm going to flip to the right as Justin said.85▶86*TEA: and we'll see when we're [//] I'm finished it looks like Kelly's87idea. ▶88*TEA: now does it look like what Kelly said? ▶89@Comment: Together the class develops their collective ideas through90group conversation. By the end of the conversation they are91beginning to understand the key concepts of geometric92transformation and are even able to do theoretical93manipulations like a team of mathematicians.94*TEA: like that? ▶95*STU: yeah (.) and then turn it [/] turn it up. ▶96*STU: um (.) one move forth hmm um to the [/] to the left. ▶97*TEA: did he make Danny's four square? ▶98*STU: yes. ▶99*TEA: yeah:. ▶100*TEA: so I think [//] wait [/] wait let's add [//] I lost track. ▶101*TEA: did we find four or five ways to make Amanda's look like Danny's? ▶102@Comment: Flipping and turning are important tools for the children103to learn. In the next step of the process the students use104these moves to build two by two designs from there core105square106@Situation: Building 2x2 designs107@Date: 29-NOV-2006108@Bg: symmetry - flip109*TEA: this is the core they started with. ▶110*TEA: and they want it to look like that. ▶111*TEA: I'm going to first flip it up. ▶112*TEA: watch what happens. ▶113*TEA: okay. ▶114*TEA: now I'm going to got back to where we started. ▶115*TEA: and now I'm going to flip it down. ▶116*TEA: hmm: (.) what happens each time? ▶117@Eg: symmetry - flip118*STU: it's the same. ▶119*STU: it's the [//] it goes to the same thing. ▶120*TEA: flipping it up. ▶121*TEA: do you think we have to test it on their core square? ▶122*STU: yeah. ▶123*TEA: alright. ▶124*TEA: okay now are they the same? ▶125*STU: yes. ▶126@Bg: symmetry - flip127*TEA: I'm going to flip this one up (.) maybe. ▶128*TEA: there I'm going to flip that one up. ▶129*TEA: and I'm going to flip this one down. ▶130*STU: same. ▶131*STU: same. ▶132*TEA: okay. ▶133*TEA: hold on I want to make sure their designs get back together. ▶134@Comment: In this exercise Carmen helps the children realize the135manipulations that are different can lead to the same136results.137*TEA: alright I'm going to flip this up. ▶138*TEA: I'm going to flip this one down. ▶139*STU: it's the same. ▶140*TEA: what did we find out? ▶141*STU: they're the same. ▶142*TEA: an up down flip yeah. ▶143*TEA: so from now on if someones going to [//] if you want me to flip it144up or down what we call that is an up down flip. ▶145*TEA: we don't call it an up flip. ▶146*TEA: we don't call it a down flip. ▶147*TEA: we call it an up down flip. ▶148*TEA: because that shows people we're talking to that we know it doesn't149matter if you flip it up or you flip it down. ▶150@Eg: symmetry - flip151*TEA: you get the same results. ▶152@Comment: It's not enough for Carmen that the children to be able to153manipulate the core squares they must also be able to154recognize the need for common usage or consensus in155mathematical language.156*STU: flip it right once. ▶157*TEA: could I flip it left? ▶158*STU: yeah. ▶159*STU: you could flip it either. ▶160*STU: do a sldeways flip. ▶161*STU: sideways flip. ▶162@Comment: Carmen often stress their are many equally valid ways of163achieving a goal but that as mathematicians they must be164able to justify the steps they took along the way in order165to prove the legitimacy of their thinking.166*TEA: it needs to end up like this. ▶167*TEA: Nasforatu ? ▶168*STU: turn it [/] turn it to the left two fourths. ▶169*TEA: turn it to the left two fourths. ▶170*TEA: one two. ▶171*TEA: yeah. ▶172*TEA: okay we'll have to write that one down. ▶173@Comment: The time spent building a common vocabulary and a means of174coming to a consensus in the classroom quickly pays off. By175the third week of the unit the children are invested in the176project as a group.177*TEA: this group usually leaves me with a very [/] a very good sense of178themselves as a math class not as just math individuals. ▶179*TEA: but I think they take pride in the way that their class on the180whole thinks and works together and the projects they tacial. ▶181*TEA: and by later in the year they know the things they're doing are182different from some other second graders might be doing. ▶183*TEA: or maybe some thrid or fourth graders are doing. ▶184*TEA: and I think they start to relize that it's because of [//] that185they are willing to think and they are willing to work hard like186that. ▶187@Comment: In this week Carmen asks the children to continue the work188with two by two designs while writing down the steps they189took to build them. The steps have to be accurate enough to190guide another person in recreating the same two by two.191@Situation: Quilt Families192@Date: 01-DEC-1994193@G: symmetry - flip up194*TEA: xxx sideways flips. ▶195*STU: uhhuh. ▶196*TEA: okay. ▶197*TEA: and then do an up down flip. ▶198@Bg: symmetry - combination199*TEA: oh so you had a combination of two flips. ▶200*TEA: alright. ▶201*TEA: and slide it into place. ▶202*TEA: and then this one you don't have done yet. ▶203*TEA: but that's okay you're thinking about it. ▶204*STU: I thought I did but I did it wrong. ▶205*TEA: okay and now I'm going to open up [//] I'm going to see if these206three core squares are in the position you had planned. ▶207*TEA: yep. ▶208*TEA: yep. ▶209*TEA: yep. ▶210*TEA: that means you are writing excellent directions. ▶211@Eg: symmetry - combination212*TEA: all year these kids have gotten the message that I care about what213you think. ▶214*TEA: what they are thinking. ▶215*TEA: and how their thinking is changing. ▶216*TEA: and how they decribe to someone else what it is they are thinking.217▶218*TEA: and defend their ideas. ▶219*TEA: or how they challenge someone elses ideas to help them sort through220their own thinking. ▶221*TEA: that's what we do. ▶222*TEA: all day. ▶223*TEA: everyday. ▶224@End