From one half to 12th: acquisition of fraction writing in adult education program students and children

Abstract

Learning fractions is essential for academic and daily life success. A critical first step in acquiring fractions is learning to transcode them (e.g., writing ½ when hearing “one half”). However, little is known about how students master fraction transcoding. We addressed this gap by assessing fraction writing in two groups of Brazilian students with limited education: adults in the first year of an adult education program (AEP-1) and 2nd graders. Both groups made frequent transcoding errors. Errors were classified into three categories, Syntactic: correct numerator/denominator values with an incorrect notation (12th for “one half”); Lexical: incorrect numerals with the correct notation (⅓ for “one half”); Combined: incorrect numerals and notation (15th for “one-half”). AEP-1 students’ performance was strongly bimodal: those with weak fraction writing skills made predominantly syntactic errors, whereas those with strong fraction writing skills made mostly lexical errors. Second graders did not transcode any fractions correctly making exclusively syntactic or combined errors. Approximately half the AEP-1 students with the lowest levels of schooling (< 3 years) succeeded in writing fractions, suggesting an important role of informal experiences. In the early stages of learning fractions transcoding, students know how to write whole numbers, but do not yet know fractions syntax, leading to the preponderance of syntactic errors. As students learn fractions syntax, they make infrequent, predominantly lexical, errors. We conclude by proposing a model of fraction writing development that incorporates formal and informal learning experiences, executive functions, and phonemic awareness to explain the mastery of this important skill.