Middle School Teachers' Conceptions of Empirical and Theoretical Probability: A Study of Pedagogy
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Date
2006-05-08
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Abstract
The purpose of this study is to address the insufficiency of research in teachers' understanding of probability. This present study specifically investigates middle school teachers' conceptions of empirical and theoretical probability using teachers' pedagogical decisions as a lens for their understanding. This study also explores how teachers' utilize models and representations, examples, and approaches of empirical and theoretical probability.
The participants in the study are inservice classroom teachers in North Carolina public schools who are involved in a 5 year NSF funded professional development project. Four participants from the project were chosen as case studies. The design of this qualitative study utilizes Pretest and Posttest assessment instruments, a videotaped lesson of a probability teaching episode involving empirical and theoretical probability, and a written reflection of the videotaped lesson by each participant.
The conceptual framework for the study considers two theoretical perspectives as a basis for understanding middle school teachers' conceptions of empirical and theoretical probability: 1) Lee, Rider, and Tarr's (2005) bi-directional model relating empirical data and theoretical probability, and 2) Even and Kvatinisky's (2002) analytical framework for teacher knowledge and understanding about empirical and theoretical probability.
Findings from the study indicate that participants attempt to make connections between empirical and theoretical probability while teaching probability lessons; however, they do not have a robust understanding of the relationship between empirical and theoretical probability. Although participants rely heavily on a theoretical estimation as the true probability, some have difficulty calculating the likelihood of uncertain events using a theoretical approach. Some participants are unable to move flexibly between empirical data and a theoretical model, ignoring sample size, variation, and independence. Most participants' use of representations and basic repertoire of examples are limited. Participants use approaches of probability both appropriately and inappropriately.
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teachers' understanding of probability, empirical probability, theoretical probability, middle school, probability, teaching and learning of probability
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Degree
MS
Discipline
Math, Science and Technology Education
