A Study on the Method of Introducing Improper Fractions and Mixed Numbers Using Additions - Hyewon Chang (Korea Society of Educational Studies in Mathematics, 2020)
Whereas proper fractions are natural for young learners from the perspectives of histo-genetics or learning psychology, improper fractions or mixed numbers imply some learning difficulty due to their property of second concepts as they are extended from proper fractions. This study aims to propose an alternative method for teaching improper fractions and mixed numbers meaningfully. Henceforth, critical review was implemented about the teaching period, their definition, and relation to the addition of proper fractions through longitudinal and latitudinal analyses of elementary mathematics textbooks in Korea and some other countries. The results showed that the context of introducing fractions equal to or larger than 1 is especially unsatisfactory. Based on the results, an alternative method for introducing or defining improper fractions and mixed numbers using the addition of proper fractions or the addition of a natural number and a proper fraction has been proposed. To secure the validity of the method, several didactical discussions about the teaching period, method of definition, integration of fractions and their additions, and effective instructional representations have been included in the study.