Abstract
This research focuses on fourth-grade (9-year-old) students’ informal and intuitive conceptions of probability and distribution revealed as they worked through a sequence of tasks. These tasks were designed to study students’ spontaneous reasoning about distributions in different settings and their understanding of probability of various binomial random events that they explored with a set of physical chance mechanisms. The data were gathered from a pilot study with four students. We analyzed the interplay of reasoning about distribution and understanding of probability. The findings suggest that students’ qualitative descriptions of distributions could be developed into the quantification of probabilities through reasoning about data in chance situations.
Highlights
Stochastic ideas and intuitions are widely used in almost every field of our lives, from sciences to sports and from games to legal cases, as we make decisions under uncertainty
Data and chance are two related topics that deal with uncertainty, and statistics and probability are the mathematical ways of dealing with these two ideas, respectively (Moore, 1990)
When the National Council of Teachers of Mathematics (NCTM) publicly strengthened their emphasis on these topics in the school mathematics curriculum at all grade bands (e.g., NCTM, 1989, 2000), probability and data analysis began to be introduced from Prekindergarten through Grade 12 in the United States
Summary
Stochastic ideas and intuitions are widely used in almost every field of our lives, from sciences to sports and from games to legal cases, as we make decisions under uncertainty. Data and chance are two related topics that deal with uncertainty, and statistics and probability are the mathematical ways of dealing with these two ideas, respectively (Moore, 1990). Knowledge of probability and data analysis becomes of critical importance for ordinary citizens to make judgments in chance situations as well as to make decisions on the basis of numerical information. When the National Council of Teachers of Mathematics (NCTM) publicly strengthened their emphasis on these topics in the school mathematics curriculum at all grade bands (e.g., NCTM, 1989, 2000), probability and data analysis began to be introduced from Prekindergarten through Grade 12 in the United States. There is no conceptual connection in the curriculum between
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