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This paper argues for creating learning trajectories of children's mathematics by integrating evidence of shifts in the mathematics of students, theory of goal-directed instructional design, and evidence of instructional supports. We networked two theories in support of this stance: a radical constructivist theory of learning, and Duality, Necessit...
Context in source publication
Context 1
... our aim was to support a WoT that functions can be representations of covariation and can be explored and understood through a covariational lens (Thompson & Carlson, 2017). Consequently, we devised a dynamic representation of proportionally-growing rectangles in which students could investigate situations that, to us, entailed the three continuously covarying quantities, height, length, and area (Figure 1). ...
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The aim of this research is to characterize the understanding of the numerical sequence concept in high school students (14-16 years old). The study draws on the APOS theory, which considers how students use mathematical elements, the relationships established between them, theirs modes of representation and the cognitive structures that are showed...
Citations
... In some of our own work on learning trajectories (Ellis et al., 2016;Fonger, Ellis, & Dogan, 2019;Fonger, Ellis, & Dogan, forthcoming), we frame learning trajectories as a networked relationship between transitions in students' ways of thinking and related instructional supports. In Figure 2a we offer a visual depiction of how students' mathematics (their ways of thinking and ways of understanding, ala Harel, 2014), transitions together with instructional supports (tasks, teacher moves, and norms) as guided by goal-directed activity (arrow). ...
