Why is learning fraction and decimal arithmetic so difficult?

Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in sciences and 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. I will discuss a series of experiments examining a potential source of difficulty in fraction arithmetic: shallow understanding of fraction multiplication and division. These experiments were conducted with 12- and 14-year-old students, as well as pre-service teachers. I will also discuss the implications of these findings for education.