Teachers' ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects…

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…

Effectively leading whole-class mathematics discussions is made more difficult when students' contributions are incomplete, imprecise, or not yet correct, and not easily correctable--what we call "errors." Through purposefully designed opportunities to investigate, enact, and reflect on teaching, teacher candidates (TCs) can develop…