Understanding decimal numbers: an investigation of student meaning constructions in intermediate and high school

Abstract

This study grew out of informal observations of the poor achievement of 13 year old New Zealand students with decimal numbers. These observations were confirmed by the results of large-scale quantitative tests with 11 to 14 year olds both in New Zealand and overseas. The research design combined quantitative and qualitative approaches. Initially a decimal numbers survey was administered to a sample of 11 to 14 year olds (n = 102). Next a series of stimulus cards was constructed based on the survey results and the researcher’s observations. These cards formed the basis of interview protocols for a longitudinal study of 11 to 14 year olds (n = 28) over two years. Additionally, the individual interviews investigated the students’ views of learning mathematics and mathematics teaching, including their affective responses to decimal numbers and mathematics. The research was influenced by the constructivist view of learning in which the emphasis is on the individual actively constructing his/her own interpretations from incoming stimuli. In particular, use was made of the generative learning model to account for students’ constructions of meaning. Students employed these constructions of meaning, or mini-theories, to describe and explain their ideas when solving problems with decimal numbers. The findings gave further support to a constructivist view of learning mathematics, and pointed to the strong influence of affective variables in mathematics learning. It was considered that the generative learning model, with its strong cognitive emphasis, may be criticized for its inattention to attitudinal factors. As well, (and contrary to generative learning model postulates) the research suggested that learning was often of a fragmented and situation-specific nature and that students held incorrect mini-theories without testing them against a number of existing ideas. The implications of the findings for teaching and learning, the curriculum, assessment procedures, and in-service and pre-service teacher education are discussed in the final chapter.