This dissertation investigated children's probabilistic reasoning during a twomonth<br>teaching experiment. As part of the research process, the researcher developed a<br>computer microworld environment, Probability Explorer, for children's explorations with<br>probability experiments. The design of the microworld is based on a constructivist theory<br>of learning, design of mathematical computer microworlds, and research on students'<br>understanding of probability and rational number concepts. Two major features in the<br>microworld include a dynamic link between numerical, graphical and iconic<br>representations of data that are updated simultaneously during a simulation, and the<br>ability to design experiments and assign probabilities to the possible outcomes.<br>The teaching experiment was conducted with three nine-year-old children. The<br>children participated in 10 hours of teaching sessions using the microworld. Each child<br>also participated in pre- and post- task-based interviews to assess their reasoning in<br>probabilistic situations. Each teaching session was videotaped, and computer interactions were recorded through internal mechanisms to create a video, including children's audio, of all actions in the microworld. These tapes provided the basis for analysis and interpretation of the children's development of probabilistic reasoning while using the microworld tools.<br>The individual case studies detail the children's probabilistic reasoning during the<br>pre-interview, teaching experiment, and post-interview. After extensive coding, several<br>themes were identified and discussed in each case study. Some of the major themes<br>included: understanding and interpretation of theoretical probability in equiprobable and<br>unequiproable situations; theories-in-action about the law of large numbers; and<br>development of part-whole reasoning as it relates to probability comparisons, a priori<br>predictions, and analysis of relative frequencies.<br>The children's development of probabilistic reasoning and their interactions with<br>the computer tools varied during the study. The children employed different strategies<br>and utilized different combinations of representations (e.g., numerical, graphical, iconic)<br>to make sense of the random data to enact their own theories-in-action. The results from<br>this study imply that open-ended microworld tools have the potential to act as agents for<br>children's development of intuitive-based probability conceptions. Dynamically linked<br>multiple representations and flexibility in designing experiments can facilitate an<br>exploratory approach to probability instruction and enhance children's meaning-making<br>activity and probabilistic reasoning.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education