College Students' Achievement and Understanding of Experimental and Theoretical Probability: The Role of Tasks.

COLLEGE STUDENTS’ ACHIEVEMENT AND UNDERSTANDING OF EXPERIMENTAL AND THEORETICAL PROBABILITY: THE ROLE OF TASKS By Irini Papaieronymou This study examined the role of particular tasks implemented through two instructional methods on college students’ achievement and understanding of probability. A mixed methods design that utilized a pre-test and post-test was used. This included treatment and control groups, each comprised of students in three sections of an introductory statistics course taught by the researcher at a college in Cyprus. During the study, students in the treatment group worked in small groups on four in-class activities about experimental and theoretical probability (Instructional Method B), and students in the control group worked in small groups on solutions to four sets of probability problems from the course textbook (Instructional Method A). An initial analysis of pre-test scores indicated that the students in the control group had comparable initial probability knowledge to the students in the treatment group. Quantitative as well as qualitative analysis were then carried out to address the research questions. With regards to students’ achievement on the multiple-choice items on probability, the results of the Wilcoxon Signed-Ranks test which was carried out to analyze gain scores indicated that the multiplechoice scores of students in the control group were significantly lower on the post-test compared to the pre-test. In the case of the treatment group, student scores on the multiple-choice items did not increase significantly from the pre-test to the post-test. Possible explanations to this phenomenon are provided in the last chapter of this dissertation. In addition, an analysis of normalized gain scores was carried out. Positive as well as negative normalized gains existed in both groups. The Mann-Whitney test resulted in a p-value of 0.001 (< 0.05) indicating that the normalized gain scores of the treatment group were significantly different from the normalized gain scores of the control group. Relative to students’ achievement on the open-ended items included on the post-test, the Mann-Whitney test resulted in a p-value of 0.001 indicating that the scores of the treatment group on these items were significantly higher than the scores of the control group. Therefore, Instructional Method B was successful in producing significantly better achievement scores than Instructional Method A. In this dissertation, students’ understanding of probability was measured through a distractor analysis and a qualitative analysis of audio-taped student conversations. Specific to the distractor analysis relative to probabilistic heuristics defined in the literature, the mean percentage of students who applied these mostly increased in the case of the control group whereas it mostly decreased in the case of the treatment group. These results are in line with past research that indicated that the use of activity-based instruction may help students with respect to probabilistic misconceptions (e.g. Shaughnessy, 1977, 1981). For the purposes of qualitative analysis, the framework by Jones, Thornton, Langrall and Tarr (1999) was used. Based on the results of the qualitative analysis of students’ levels of reasoning relative to the constructs presented on the framework i) Instructional Method B (treatment) produced better results than Instructional Method A (control) relative to experimental probability and the concept of sample space and ii) it was difficult to identify which instructional method had a better effect on students’ understanding of theoretical probability, conditional probability and independence, discrete probability distributions and the binomial distribution. Copyright by IRINI PAPAIERONYMOU 2012