Abstracted Quantitative Structures: Using Quantitative Reasoning to Define Concept Construction

Over the most recent several decades, researchers have argued the importance of quantitative and covariational reasoning for students’ learning. These same researchers have illustrated the importance of these reasoning processes with respect to local and longitudinal development. In both grain sizes, researchers are detailed in their descriptions of the intended topics or reasoning processes. There is, however, a lack of specificity of generalized criteria for concept construction from a quantitative reasoning perspective. In this chapter, we introduce such criteria through the construct of an abstracted quantitative structure, which has its roots in quantitative reasoning, covariational reasoning, and various Piagetian notions. In introducing the construct, we focus on ideas informing its development and its criteria, and we use it to characterize examples of student actions. We close with comments regarding implications for both teaching and research.