A key element in developing ideas associated with statistical inference involves developing concepts of sampling. The objective of this research was to understand the characteristics of students' constructions of the concept of sample. Sixty-two students in Grades 3, 6, and 9 were interviewed using open-ended questions related to sampling; written responses to a questionnaire were also analyzed. Responses were characterized in relation to the content, structure, and objectives of statistical literacy. Six categories of construction were identified and described in relation to the sophistication of developing concepts of sampling. These categories illustrate helpful and unhelpful foundations for an appropriate understanding of representativeness and hence will help curriculum developers and teachers plan interventions.
This paper presents an analysis of three questionnaire items which explore students' understanding of chance measurement in relation to the development of ideas of formal probability. The items were administered to 1014 students in Grades 3, 6 and 9 in Tasmanian schools. The analysis, using the NUDIST text analysis software, was based on the multimodal functioning SOLO model. An analysis of the results and a developmental model for understanding chance measurement are presented, along with implications for curriculum and teaching practice.
The objective of this study was to provide baseline data in an area of the mathematics curriculum that is beginning to receive greater attention than previously. Four survey items were completed by 2615 students in grades 5 to 11. Two survey items asked for estimates of probability or frequency for everyday events (A), (B), and their conjunction (A and B). Two survey items asked for estimates of probability or frequency for conditional events, (XjY) and (YjX). Cross-sectional and longitudinal analyses revealed improvement with grade in expressing probability numerically and in distinguishing conditional events, but no change in incidence of conjunction errors. The relationships of responses to conjunction items with those to conditional items, and of both with responses to other items of basic chance measurement were considered. Implications were related to interpretation of the results in terms of previous research and suggestions for educators.
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