Why Do Students Struggle with Rational Numbers?

Several reasons have been suggested for the difficulty students experience when learning rational number concepts and skills:

1. In terms of instructional approaches, lessons are too often focused on procedures and memorizing rules rather than on developing conceptual foundations, such as the quantity represented by the numerator and denominator, prior to skill building.
2. Specific content difficulties occur when students confuse whole number computational procedures with those for fractions. For example, when adding fractions, many students combine both numerators and denominators rather than making certain there must be a common denominator and that denominators are not added. Also, students assume that multiplying fractions will always yield a product larger than the factors, as is the case with whole numbers. When multiplying 6 × 2, 12 is larger than 6 or 2. However, 6 × 1/2 = 3, a product less than one of the factors, 6. Likewise, division of fractions can result in a quotient larger than the dividend, for example 12/1/3 = 36.
3. Estimating rational number answers can be more challenging than estimation with whole numbers. Students must be able to approximate fractions as more or less than, for example, in order to compute efficiently. Fractions have many names, thus presenting more possibilities forerrors.
4. Fractions are unconnected to everyday objects and are seen as too abstract (Alverado & Herr, 2003).
5. Flexible use of notation can be confusing for students. Fractions can be renamed with larger or smaller numerals in the numerator and denominator, as mixed numbers, as improper fractions, and using decimals. It is difficult to rename fractions with limited understanding of their size and the concept of equivalence (Saxe, Tayler, McIntosh, & Gearhart, 2005).