Clear and rigorous quantum reasoning is needed to explain quantum physical phenomena. As pillars of true quantum physical explanations, we suggest specific quantum reasoning derived from quantum physical key ideas. An experiment is suggested to support such a quantum reasoning, in which a quantized radiation field interacts with an optical beam…

The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

Statistical literacy and statistical reasoning are important learning goals that instructors aim to develop in statistics students. However, there is a lack of clarity regarding the relationship among these learning goals and to what extent they overlap. The REasoning and Literacy Instrument (REALI) was designed to concurrently measure statistical…

This study connects descriptions of effective teaching with descriptions of teacher development to advance an initial understanding of how effective teaching may develop. The study's main premise is that descriptions of effective teaching develop cumulatively where more basic teaching strategies and behaviors are required before teachers may…

This study reports the results of the first systematic investigation into Astro 101 students' conceptual and reasoning difficulties with cosmology. We developed four surveys with which we measured students' conceptual knowledge of the Big Bang, the expansion and evolution of the universe, and the evidence for dark matter. Our classical test theory…