UC Berkeley

This dissertation investigates the interplay between second and fourth graders’ use of rulers and paper strips to solve number line measurement problems. Drawing upon and extending Vygotsky’s (1978, 1986) approach to mediation in problem solving, and Saxe’s (2012) treatment of microgenesis of representational activity, I analyzed 36 second and 39 fourth graders’ measurement activity as they participated in videotaped semi-structured interviews. At each grade, students were randomly assigned to ruler, short paper strip, or long paper strip conditions, and solved five number line problems first without the tool available and then five similar problems with the tool available. For each problem, two numbers were labeled (e.g., 4 and 6) and students were asked to place a third number appropriately (e.g., 9). Problems and tools were designed to elicit unitizing strategies (splitting, iterating, counting) as students coordinated tool with target to produce a linear measure. I report findings related to the precision of students’ estimates contrasting tool absent and present conditions, and findings related to students’ adaptation of tools to serve measurement functions. Analyses of students’ precision revealed that with or without the support of tools, fourth graders were more precise than second graders, though the utility of tool varied with tool and problem type. The long paper strip was particularly difficult for second graders, and at both grades, many students rejected using the long paper strip. Students generally became precise with tools when a solving a problem type that displayed a linear unit of 1 instead of a larger unit, though this varied with tool type. On other problem types, tools interfered with precision, and on still other problem types, tools interfered with the precision of second, but supported the precision of fourth graders. Analyses of strategies revealed three levels in students’ ability to coordinate a unitization of tool and target as they tried to adapt tools to serve measurement functions. I argue that these findings can productively inform our understanding of the interplay between tool use in students’ developing measurement activity as well as the design of instructional problem environments to support students’ tool using in linear measurement.