Date of Award

12-20-2005

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Middle-Secondary Education and Instructional Technology

First Advisor

Karen A. Schultz - Chair

Second Advisor

Christine Thomas

Third Advisor

Draga Vidakovic

Fourth Advisor

William L. Curlette

Abstract

The emphasis given to probability and statistics in the K-12 mathematics curriculum has brought attention to the various approaches to probability and statistics concepts, as well as how to teach these concepts. Teachers from fourth, fifth, and sixth grades from a small suburban Catholic school engaged their students (n=87) in a study to compare learning traditional probability concepts to learning traditional and subjective probability concepts. The control group (n=44) received instruction in traditional probability, while the experimental group (n=43) received instruction in traditional and subjective probability. A Multivariate Analysis of Variance and a Bayesian t-test were used to analyze pretest and posttest scores from the Making Decisions about Chance Questionnaire (MDCQ). Researcher observational notes, teacher journal entries, student activity worksheet explanations, pre- and post-test answers, and student interviews were coded for themes. All groups showed significant improvement on the post-MDCQ (p < .01). There was a disordinal interaction between the combined fifth- and sixth-grade experimental group (n=28) and the control group (n=28), however the mean difference in performance on the pre-MDCQ and post-MDCQ was not significant (p=.096). A Bayesian t-test indicated that there is reasonable evidence to believe that the mean of the experimental group exceeded the mean of the control group. Qualitative data showed that while students have beliefs about probabilistic situations based on their past experiences and prior knowledge, and often use this information to make probability judgments, they find traditional probability problems easier than subjective probability. Further research with different grade levels, larger sample sizes or different activities would develop learning theory in this area and may provide insight about probability judgments previously labeled as misconceptions by researchers.

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