Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

In this article, we present the results of an eight-week in-class intervention, during which binomial expressions comprised of academic vocabulary (results and conclusions, facts and circumstances) were presented to intermediate-level learners of English. Constraints that govern the preferred order of highly fixed binomials were explained as the…

Adult Japanese speakers often experience difficulty learning English /r/-/l/. Previous research has reported the effectiveness of using perception-based high-variability identification training with natural speech stimuli on improving Japanese speakers' perception and production of /r/-/l/. Recent studies have also shown the effectiveness of using…