Skill acquisition theorists conceptualize second language (L2) learning as the acquisition of a set of perceptual, cognitive, and motor skills. The dominant view in skill acquisition theory is to regard L2 skill acquisition as a three-stage process "from initial representation of knowledge through initial changes in behavior to eventual…

Proficiency with fractions serves as a foundation for later mathematics and is critical for learning algebra, which plays a role in college success and lifetime earnings. Yet children often struggle to learn fractions. Educators have argued that a conceptual understanding of fractions involves learning that a fraction represents a magnitude…