Brief Overview

     Research on the teaching and learning of probability has shown that students of all ages have difficulty understanding chance happenings.  However, research has also shown that students possess many informal and intuitive ideas about probability concepts before instruction, and that these ideas can often lead to inappropriate probabilistic reasoning.  In addition, the use of computer microworlds to enhance mathematics teaching and learning at the elementary level has shown promising uses to enhance children’s conceptions in a variety of domains; however, to date, research has not been done in the domain of probability.  Hence, I developed a computer microworld intended for elementary students to explore probability concepts.  By tapping into children’s informal understandings and intuitive notions of chance and randomness, I conjecture that this microworld can help children develop more normative understandings of probability concepts.  My dissertation research served two purposes: (1) to further understand children’s conceptions of probability, and (2) to further develop the software based on children’s use and their development of probabilistic reasoning.

    The design of the computer microworld and my instructional approach are based on a constructivist theory of learning.  The tools available in the computer environment, the instructional activities, and the social interaction between students and between students and teacher, all operate interactively as potential meaning-making agents for students’ construction of probabilistic concepts.  The interactions between these agents is part of a complex process of each child constructing their own knowledge about probabilistic situations.  The social and digital interactions in a computer environment can provide children with many opportunities to explore probabilistic situations and make sense of experimental results.  These interactions can help students develop more taken-as-shared interpretations of probability concepts such as sample space and theoretical probability in a way that brings them closer to more normative probabilistic conceptions and allows them to communicate socially about their understandings.

 

    The overall goal in designing Probability Explorer was to create a relatively open-ended environment that could easily be used by children to simulate random phenomena and explore interesting chance situations.  The chance situations could be in the context of a game (e.g., dice games) or real world uncertainties (e.g., weather).  The tools and actions available in the computer environment have been purposefully designed to invoke perturbations in a child’s current schema of probability concepts, encourage active reflection and abstraction to refine those conceptions, and facilitate the development of appropriate probabilistic reasoning.

Take a Brief Tour of Probability Explorer

    Download a manuscript on the Theory of Design of the Probability Explorer (Microsoft Word document). This is a work in progress. Please do not cite this paper.  Any comments and suggestions would be greatly appreciated.

 

    I conducted an intensive 6-week constructivist teaching experiment, including pre and post task-based interviews, with three fourth grade students.  The students, myself, my advisor, and a non-participant observer met for about 12 hours over the course of the 6 weeks. Video recording devices were used to capture social interactions and computer actions on video and audio tape. The teaching episodes were not scripted.  Instead, each session began with a major probability task (e.g., determining if a coin is fair) that allowed me to interact with the students and base my future prompts and questions on the children’s mathematical thinking and their use of the tools in the microworld.
     In order to interpret the interactions which are part of the children’s meaning-making processes, my research draws upon an interpretivist approach to inquiry.  Thus, in order to understand children’s probabilistic reasoning while using the Probability Explorer computer microworld, I used qualitative research methods to observe and critically analyze the children’s meaning-making processes and social and computer interactions.

Brief Summary of Research Findings

    The individual case studies detail the children’s probabilistic reasoning during the pre-interview, teaching sessions, and post-interview. After extensive coding, several themes were identified and discussed in each case study (see dissertation document below if interested in reading the case studies). Some of the major themes included: understanding and interpretation of theoretical probability in equiprobable and unequiproable situations; theories-in-action about the law of large numbers; and development of part-whole reasoning as it relates to probability comparisons, a priori predictions, and analysis of relative frequencies.

    The children’s development of probabilistic reasoning and their interactions with the computer tools varied during the study. The children employed different strategies and utilized different combinations of representations (e.g., numerical, graphical, iconic) to make sense of the random data to enact their own theories-in-action. The results from this study imply that the various microworld tools have the potential to both enable and constrain children’s development of intuitive­based probability conceptions. Overall, this study has shown that dynamically-linked multiple representations and flexibility in designing experiments can facilitate an exploratory approach to probability instruction and enhance children’s meaning-making activity and development of probabilistic reasoning.

View a copy of the entire dissertation (affectionately known as "the beast") in PDF format using Adobe Acrobat Reader 3.0 [Warning: This file is about 6.5 MB!!]