Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…

One obstacle to understanding abstract concepts such as the "control of variables" strategy (CVS) is the tendency for learners to focus on surface rather than deep features in instructional materials. However, in tasks such as learning CVS, these same surface features may also support understanding, provided learners realize the…