ABSTRACT
Lamon considered that "the ultimate goal of instruction is to help students to understand fractions as numbers in their own right, and, as such, as objects that can be manipulated with arithmetic". Mok, Cai and Fung describe an instructional situation in which a teacher overlooks strategies for comparing fractions presented by a student and insists on finding a common denominator. Even though Farey addition only makes sense on fractions and not on rational numbers, it shows up in a variety of mathematical situations. As such, exploring various ways to combine fractions additively raises one's awareness of the potential variety, as well as of potential pitfalls. Fractions and rational numbers are renowned as one of the challenging topics in elementary mathematics. Students encounter them year after year and yet often show no significant improvement in their performance on exercises.
