Prospective elementary teachers’ development of fraction language for defining the whole

This article examines the ways in which prospective elementary teachers’ develop an understanding of language use for defining the whole throughout a 9-day rational number unit. Student work samples and classroom conversations are used to illustrate their difficulties and growth with defining the whole and corresponding language use for describing fractional amounts. The results indicate that three mathematical ideas became taken - as - shared by the class. The first was that fractions depend on a group or whole. The second included defining an of what . The third was developing language in terms of what the denominator represents. Difficulties prospective teachers had conceptualizing language included distinguishing among the phrases of a , of one , of the , and of each. Implications for mathematics education courses and future research studies are also discussed.