Why you have to probe to discover what year 8 students really think about fractions. Mathematics Education for the Third Millennium: Towards

Many researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. This paper examines the persistence of whole number schemes among 14 year-old students who appear to have successfully mastered routine algorithms for working with fractions. Uncovering whole number thinking among such students is therefore difficult, and is illustrated through the use of several probing interview tasks, revealing quite different forms of whole number thinking. These forms of thinking can give correct answers also making it difficult for teachers to identify incorrect thinking about fractions. Representations of fractions using number lines can assist in identifying and correcting such thinking. Hunting (1986), Streefland (1984), Bezuk (1988) and Kieren (1980a; 1980b) have suggested that difficulties experienced by children solving rational number tasks arise because rational number ideas are sophisticated and different from natural number ideas and that children have to develop the appropriate images, actions and language to precede the formal work with fractions, decimals and rational algebraic forms. The research reported above has focused quite properly on difficulties experienced by young children when they first encounter rational numbers. Relatively, little research has taken place with older students. Like Hannula (2003), this paper focuses on difficulties with fractions experienced by older students. Many of these students appear still to use whole number thinking which Behr, Wachsmuth, Post and Lesh (1984) defined as “making separate comparisons of numerators and denominators using the ordering of whole numbers ” (p. 332). Hart (1981) also notes that “a fraction of course involves two whole numbers which have to be dealt with as if they were irrevocably linked ” (p.69). The ratio between numerator and denominator is, according to Hart (1981), the “irrevocable ” link