This study was conducted to investigate the effects of learning trajectories-based coding (LTs) and LTs-based program on preschoolers' length, area, volume, and angle measurement skills. A quasi-experimental research design was utilized with a quantitative approach. The study's participants were 47 children between the ages of 55-71 months who…

In this study, we explore the use of analogies with classical physics in introductory quantum physics (QP) teaching. This work is part of a larger project in which a learning sequence covering three introductory QP topics was designed, tested, and evaluated in collaboration with high school teachers and physics education researchers. Based on the…

"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…