Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

Spatial thinking is important for success in engineering. However, little is known about "how" students learn and apply spatial skills, particularly in kindergarten to Grade 12 engineering learning. The present study investigated the role of spatial thinking in engineering learning at a middle school summer camp. Participants were 26…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…