Networking Units Coordination and Spatial Structuring to Build Models of Student Reasoning about Spatial Measurement: The Case of Jake

Spatial measurement entails both spatial reasoning and the application of numerical concepts and strategies. Although researchers have acknowledged interplay between students’ numerical and spatial reasoning in measurement, few studies have investigated these relationships explicitly. In this study, three preservice elementary school teachers (PSTs) participated in task-based interviews, with the goal of gaining an understanding of how they reason about spatial measurement. We analyzed their responses to length, area, and volume measurement tasks using two theoretical lenses: units coordination and spatial structuring (as well as an elaborated version, spatial-temporal-enactive or S* structuring). Focusing on the reasoning of one PST, Jake, this study contributes deep explanatory accounts of Jake's reasoning by drawing on constructs from both theoretical perspectives. In particular, we explain the mentals operations that Jake used to construct, coordinate, transform, and enumerate spatial and numerical units across length, area, and volume contexts. 

Bio
Joseph Antonides is a Postdoctoral Associate in the Department of Mathematics at Virginia Tech. He received his Ph.D. in mathematics education from The Ohio State University, where he was advised by Michael Battista. Antonides’ scholarship is concerned with applying constructs from radical constructivism and cognitive psychology to build scientific models of students’ mathematical reasoning. Focusing on combinatorics and geometry in particular, a central concern of Antonides’ research is understanding the diversity of students’ ways of reasoning about particular mathematical ideas and explaining students’ ways of reasoning by making inferences about their available mental operations and cognitive structures. He is especially interested in the unit structures that students construct, operate on, and coordinate as they reason within quantitative combinatorial and geometric contexts. In all of his work, Antonides prioritizes decentering to build asset-based models that can psychologically explain students’ mathematical reasoning and learning.