Year of Publication

2019

Degree Name

Doctor of Education (EdD)

Document Type

Doctoral Dissertation

College

Education

Department

Curriculum and Instruction

First Advisor

Dr. Xin Ma

Abstract

The ultimate goal of statistics education is to create a statistically literate society in which people can appropriately use statistical thinking. Although the need to improve the teaching of introductory statistics courses is not a new one, with increased demand on these courses, there has been constant effort to seek out better ways of teaching these courses. The University of Kentucky (UK) began a reform of its general education program in November 2005. Thinking and reasoning are the central themes of this well-designed general education curriculum.

The main goal of this dissertation is to fill in some gaps in the research literature on the teaching and learning of statistics. This dissertation includes two independent studies (experiments). The first study will examine the instructional effects of physical versus virtual manipulatives (see definitions later) on learning outcomes in introductory statistics, whereas the second study will investigate the impact of different styles in teaching statistics (inverted classroom versus traditional classroom) on learning outcomes in introductory statistics. In general, this dissertation strives to join many other reform efforts to explore instructional ways that engage students in reasoning and thinking statistically. To combat the abstract nature of probability and statistics, the use of manipulatives may represent one of the most effective strategies in the statistics classroom. There are fundamental reasons to inherently value the inverted classroom’s emphasis on activity-based learning and increased responsibility of the students to become active participants in their own learning.

The results of the first study revealed that there were no significant differences between the business as usual group who received traditional concrete manipulatives and the experimental group who received online virtual manipulatives. There -were no statistically significant interaction effects between types of manipulatives and high school ACT mathematics scores, informing the literature that ability levels neither intensify nor weaken the effects of types of manipulatives. The results of the study did not show a significant difference in GPA one year later between the experimental group and the business as usual group.

The results of the second study revealed that there were some significant differences between the business as usual group who received traditional lecture type classroom and the experimental group who received inverted. We compared all seven outcomes for the two groups: projects average, tests average, classwork, midterm attendance average, class final attendance average, midterm grade and class final grade. Students in the traditional classroom did better than students in the inverted classroom in projects average, classwork, midterm attendance average, midterm grade and class final grade. We used tree different blocks with student background variables as predictors. The first one, individual student background, is explained by age, gender and ethnicity. High school background variables is explained by high school GPA and ACT mathematics scores. The third one, university program background, is explained by university cumulative GPA and student major.

After controlling for student background variables, students in the traditional classroom did better than students in the inverted classroom in projects average, overall classwork and midterm grade. The model when controlling for student high school background variables showed that students in the traditional classroom did better than students in the inverted classroom in projects average, overall classwork and midterm grade. Finally, after controlling for student university background variables, students in the traditional classroom performed similarly to students in the inverted classroom in projects average, test average, overall classwork, midterm attendance average, class final attendance, midterm grade and class final grade. When controlling for all (i.e., student background variables, student high school background variables, and university program variables), students in the traditional classroom did better than students in the inverted classroom in midterm grade only.

The results of the study may not be generalized to the population of all undergraduate students. It also gives no indication of how the results would generalize to other content domains. Further studies may explore along these lines of inquiry regarding the effects of virtual manipulatives in comparison with concrete manipulatives and the effects of the traditional classroom in comparison with inverted. Further studies may seek some longer period of using and comparing the two teaching methods.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2020.044

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