Literature Index

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.

This paper presents the results of an instrument designed to probe children's intuitive notions of probability. The test consists of 16 questions, a few of which are analyzed in depth either qualitatively or quantitatively. A good selection of pupils' responses are included to illuminate children's intuitions. It is suggested that a mixture of teaching approaches should be used to help children develop probabilistic concepts coherently.

This paper discusses the premise that young children do not perceive accurate relationships between the behavior of different, but related random generators. Data for this preliminary study has been collected from suburban primary school students aged from 7 - 12 years, who were questioned about their perceptions of the behavior of dice, coins, raffle tickets and a range of different and unusual random generators in identical situations. The findings indicate that children predict different result depending for example, on whether tickets rather than dice are used in a game. Their predictions appears to be based on the observation of the physical differences between dice and raffle tickets. Owing to the size of the preliminary study no tests of significance have been carried out and results are given in simple percentages.

Two studies investigated upper elementary school students' informal understanding of sampling issues in the context of interpreting and evaluating survey results. The specific focus was on the children's evaluation of sampling methods and means of drawing conclusions from multiple surveys. In Study 1, 17 children were individually interviewed to categorize children's conceptions. In Study 2, 110 children completed paper-and-pencil tasks to confirm the response categories identified in Study 1 and to determine the prevalence of the response categories in a larger sample. Children evaluated sampling methods focusing on potential for bias, fairness, practical issues, or results. All children used multiple types of evaluation rationales, and the focus of their evaluations varied somewhat by context and type of sampling method (restricted, self-selected, or random). Children used affective (fairness) rationales more often in school contexts and rationales focused on results more often in out-of-school contexts. Children had more difficulty detecting bias with self-selected sampling methods than with restricted sampling methods because self-selection was initially the most fair (i.e., everyone had a chance to participate). Children preferred stratified random sampling to simple random sampling because they wanted to ensure that all types of individuals were included. When drawing conclusions from multiple surveys, children: (1) considered survey quality; (2) aggregated all surveys regardless of quality; (3) used their own opinions and ignored all survey data; or (4) refused to draw conclusions. Even when children were able to identify potential bias, they often ignored survey quality when drawing conclusions from multiple surveys.