Rethinking How We Teach Fractions and Rational Numbers

If you open almost any middle school mathematics textbook today, you will find a neat little chart that tries to draw a firm line between two fundamental concepts: · Fractions are defined as numbers in the form a/b, where a and b are whole numbers (b ≠ 0). · Rational Numbers are defined as numbers in the form p/q, where p and q are integers (q ≠ 0). On paper, this sounds like a clean, orderly progression. We start young children off with positive whole numbers because they can touch them and visualize slices of pizza. Later, when they grow older, we introduce negative numbers and present Rational Numbers as an advanced concept. However, when we examine this distinction closely, we notice that it introduces an unnecessary conceptual barrier in a student's mathematical understanding.