A MIXED METHODS STUDY: PROCEDURAL AND CONCEPTUAL KNOWLEDGE IN BASIC STATISTICS FOR UNIVERSITY STUDENTS

Author

Jie Shi Liew, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2025

Degree Name

Doctor of Philosophy

Department

Curriculum and Instruction

First Advisor

Lin, Cheng-Yao

Abstract

The purpose of this explanatory mixed methods dissertation study was to explore how university students understand descriptive statistics by integrating quantitative assessment with qualitative exploration of their verbal and non-verbal procedural fluency, as well as explicit and implicit conceptual reasoning. The quantitative phase used the DSKAT assessment that was developed by the researcher in alignment with the GAISE (2020) guidelines, alongside two supplementary questionnaires that evaluated university students’ basic math computational skills and attitudes toward learning statistics. Regression analyses revealed two unexpected findings: (1) only mixed operations significantly predicted DSKAT performance, while fractions and integers alone did not; and (2) only liking subscale of the Attitude Scale Toward Learning Statistics (ATLS) survey, which indicated university students’ interest for learning statistics, showed a negative relationship with DSKAT performance, while other categories such as existing university experience, attitudes toward statistics, and confidence in learning statistics were not significant predictors. The qualitative phase involved a purposeful selection of six participants to collect qualitative data to help explained the quantitative findings. Qualitative data were collected using semi-structured interview questions, a drawn concept map, and a think-aloud protocol that reflected the DSKAT assessment, which included five statistical tasks related to cereals. These statistical tasks also aligned with the Discovery-based Learning (DBL) lesson plan implemented in this study as an intervention. Four overarching themes from the semi-structured interview questions—Appreciation and Reengagement in Learning, Initial Resistance and Later Curiosity, More Than Just Computation, and Learning Tools that Enabled Conceptual Growth— underscored the affective, cognitive, and instructional factors influencing university students' statistics learning experience. Five overarching themes from think-aloud protocol—Surface Familiarity Struggle with Deep Application, Confidence Gaps Despite Correct Reasoning, Conceptual Transfer Through Real-World Analogy, Misconception Hidden in Assessment but Revealed in Talk, and Mismatch Between Verbal and Non-verbal PK— provided valuable insights into university students’ statistical reasoning processes.The combined findings suggest that basic math computational skills with mixed operations may serve as an indicator of procedural flexibility and contextual transfer in statistics, whereas merely having an increased interest in learning statistics, as indicated by the liking subscale of the ATLS survey, does not guarantee a gain in conceptual statistics understanding, even if it motivates university students to learn more about statistics. This dissertation also highlights the importance of using multimodal, context-rich assessments, such as concept maps and verbal reasoning through think-aloud statistical tasks. The qualitative findings revealed that university students sometimes held misconceptions uncovered through interviews, even when they had selected correct answers on the DSKAT assessment. Conversely, others demonstrated sound reasoning and partial understanding during think-aloud tasks, despite incorrect responses on the DSKAT assessment, thus highlighting possible statistical knowledge that is often overlooked on traditional paper-based tests. Practical implications are discussed for instructional design, assessment practices, and the development of inclusive pedagogies in university-level statistics education.