Why is learning fraction and decimal arithmetic so difficult?

• We review the literature on the development of fraction and decimal arithmetic.
• We analyze why these capabilities are so difficult to learn.
• We identify and describe several difficulties that are inherent to fraction and decimal arithmetic.
• We describe several sources of difficulties determined by cultural values and characteristics of educational systems.
• We discuss interventions that have helped children master fraction and decimal arithmetic.

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 fraction and decimal arithmetic and to stimulate greater amounts of research in the area, we devoted this review to analyzing why learning fraction and decimal arithmetic is so difficult. We identify and discuss two types of difficulties: (1) inherent difficulties of fraction and decimal arithmetic and (2) culturally contingent difficulties that could be reduced by improved instruction and prior knowledge of learners. We conclude the review by discussing commonalities among three interventions that have helped children overcome the challenges of mastering fraction and decimal arithmetic.