2013 Conference Proceedings - University of Nevada, Las Vegas

In Figure 2, both students worked with the largest scrip piece (4), but one used two 3s whilethe other used three 2s. This aspect later proved interesting as when asked to count to verifytotals, some students used a skip counting process rather than counting by 1s. In Figure 3, astudent used three 3s and a 1 to make 10. Several students used a similar configuration, but in adifferent order. This provided an opportunity for the teacher to compare and contrast howFigure 3 Figure 4arrangements were similar or different. Figure 4 shows a student had completed twocombinations of 10 and was working on a third.After allowing time for each child to make a collection of 10, the teacher called the class tosit on the carpet at the front of the room with their work. Individual students were asked to showtheir collection and tell the numbers involved. For example, the student who showed thecollection in Figure 3 would say, “3, 3, 1, 3.” As was planned in the lesson, the teacher at thispoint, while holding two different collections, engaged students in exploring, “Is 3, 1, 3, 3 thesame or different from 3, 3, 1, 3?” Teachers were excited by the appropriate students’ responses.On a day following the research lesson, one teacherworked with a group of students to further talk aboutsimilarities and differences. She had students share anexample they had made or could make and recorded theirsuggestions on poster paper as shown in Figure 5. She madethe effort to both draw the arrangement and to use thenumerical values in the discussion and had students describe acollection, such as Jaycha’s, by saying, “One scrip and twoscrip and two scrip and two scrip and three scrip make aFigure 5collection with 10 scrip.”Teacher reflection on the Lesson Study ProcessAfter all five teachers had taught the lesson, they responded to the following prompt, “Howsuccessful do you think the problem your team selected for the lesson study addressed yourProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 105