Fostering the concept of fractions at the boundary of primary and lower secondary school grades

Abstract

This paper focuses on the ways of fostering the concept of fractions. The main concern to be discussed is the controversy between the concept of fractions pupils possess at the end of their primary school years (Grade 4) and the expectation raised by the textbooks in Grade 5. In their primary years, students encounter fractions as either fractions with 1 as numerator or the multiples of such fractions – both with various kinds of manipulative or visual aids. To the contrary, in Grade 5, fractions immediately appear as rational numbers, i.e., the ratio of two whole numbers. In order to appropriately build the concept of fractions in Grade 4, we advise to emphasize the so-called “second interpretation” (C. Neményi) of fractions. This “second interpretation” of the multiples of fractions with 1 as numerator means that multiples of a unit are divided into equal parts according to the denominator. Our message has been approved and supported by means of analyzing textbook passages and results available in the international literature.