2013 Conference Proceedings - University of Nevada, Las Vegas

Table 2A Student’s Series of Reasoning between Different RepresentationsExplorations withgeometric representationsPattern observed aftergeometric explorationsExplorations with t-chartPattern observed afterexplorations with t-chartGeometricrepresentation used toexplain pattern observedfrom t-chartConnecting mathematical ideas from different student strategiesAs reported earlier, whole class and small group discussions created opportunities forstudents to connect their reasoning to other students’ reasoning. Teachers discussed howstudents’ ideas were related to one another after using a variety of colors to write differentstudent ideas on a whiteboard (see Figure 4). For example, in one class while working on therelationship between time and distance of a function machine task, one student referred to figure15 and explained her strategy as “the number you have in minutes is going to be the samenumber in feet with a five at the end.” To connect this strategy to the one whereby studentsmultiplied minutes by 10 and then added 5 to get number of feet, the teacher asked, “Why is thisgeneralization of writing a 5 in front working? Why is it giving the same number as multiplyingby 10 and adding 5?” These questions led to a discussion about place value that by writing a 5 infront of the number, the value for minutes gets promoted to a tens place, therefore, the strategiesare mathematically the same.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 185