Cognition and Instruction: Reasoning about Bias in Sampling

Although sampling has been mentioned as part of the chance and data component of the mathematics curriculum since about 1990, little research attention has been aimed specifically at school students¡¯ understanding of this descriptive area. This study considers the initial understanding of bias in sampling by 639 students in grades 3, 5, 7, and 9. Three hundred and forty-one of these students then undertook a series of lessons on chance and data with an emphasis on chance, data handling, sampling, and variation. A post-test was administered to 285 of these students and two years later all available students from the original group (328) were again tested. This study considers the initial level of understanding of students, the nature of the lessons undertaken at each grade level, the post-instruction performance of those who undertook lessons, and the longitudinal performance after two years of all available students. Overall instruction was associated with improved performance, which was retained over two years but there was little difference between those who had or had not experienced instruction. Results for specific grades, some of which went against the overall trend are discussed, as well as educational implications for the teaching of sampling across the years of schooling based on the classroom observations and the changes observed.