Students' addition of decimal fractions: the effects of context

Queensland and national curriculum documents of recent years suggest that addition and subtraction of decimal fractions can occur in a money context earlier than they do without a context. However, there does not appear to be enough research to support the legitimacy of this approach and the lack of fine detail in the curriculum documents has resulted in a variety of interpretations taken by textbook writers and presumably teachers. Some research has shown that the use of contexts to make mathematics more relevant to students can have unintended results. Among these is the negative impact that using money problems as exemplars can have on the conceptualisation of decimal fractions. Given this finding, together with the limited guidance in the relevant curriculum documents and the variety of presentations by textbook publishers, this study sought data on the following questions: 1. How does accuracy with addition differ when decimal fractions to hundredths are written with dollar signs compared to when they are not? 2. How do addition methods differ when decimal fraction problems using hundredths are contextualised with dollar signs compared to when they are not? A cross-sectional study was undertaken to provide a snapshot of school students' ability to undertake decimal computation addition problems in contextualised and non-context situations. Students in Years 4 and 5 in Queensland state schools completed one of two test papers. One paper presented addition problems involving decimal fractions without any context (e.g., 1.30 + 1.20). The other paper had identical questions but with a dollar sign included for each decimal fraction ($1.30 + $1.20). Altogether 161 students participated. The results showed that there was a difference in accuracy in favour of the group working with non-contextualised decimal fractions. It was also revealed that the group working with the money context reported answers for particular questions in ways that may indicate underlying conceptual errors about money or about the relationship between money and decimal fractions. It was found that the students working without a money context preferred showing their thinking using a standard written method in greater numbers than did the students working with the contextualised problems. The latter group, in contrast, had a greater incidence of writing answers but without recording a method. Although no difference in accuracy was observed between males and females, some difference in method choice was recorded.