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…

This article considers the appeal of cognitive neuroscience research to the general public within the context of the deep puzzles involved in using our minds to understand how our minds work. It offers a few promising examples of findings that illuminate the ways of the mind and reveal these workings to be counter-intuitive with our subjective…