Year of Award


Document Type


Degree Type

Doctor of Philosophy (PhD)

Degree Name

Mathematics (Mathematics Education Option)

Department or School/College

Department of Mathematical Sciences

Committee Chair

Ke Wu

Committee Co-chair

Bharath Sriraman

Commitee Members

James Hirstein, David Patterson, David Erickson


distributions, reasoning, statistics, variability, variation


University of Montana


Current curricular documents including the Common Core State Standards (2010) and the Guidelines for Assessment and Instruction in Statistics Education (2005) have increased the need for students' understanding and reasoning about statistics at both the K-12 and college levels. In addition, an increasing number of students are taking the Advanced Placement Statistics Exam (College Board, 2011) or a college-level introductory statistics course (Scheaffer & Stasny, 2000). One of the main components for statistical thinking is consideration of variation (Wild & Pfannkuch, 1999). Previous studies have shown that students have misconceptions about variation (e.g. Reading, 2004; Torok & Watson, 1999) and students often lack the ability to give sophisticated answers (Shaughnessy, 2007). The goal of this study was to better understand how students' reasoning about variation in a distributional context changes as they progress through an introductory college-level statistics course. In order to better understand the longitudinal nature of this process during a semester-long introductory statistics course, both quantitative and qualitative data were collected at three different times (beginning, middle, and end of the course) in surveys and interviews. The Structure of Observed Learning Outcomes (SOLO) Taxonomy (Biggs & Collis, 1982) was used to understand and assess the quality of their reasoning. Qualitative data came from two sources: three interviews from each of the ten interviewees and three survey questions on each of three surveys from all participants. The interviews were transcribed and responses were sorted into appropriate locations in the SOLO Taxonomy. After coding responses to each question in each interview, themes of progress were then identified. These themes showed that students progressed through four different paths of reasoning including: improved, maintained, decreased, and inconsistent. Quantitative data showed that while students were good at reasoning about situations involving bar graphs and dot plots with regards to comparing variability in distributions, they struggled with reasoning about histograms. Overall, this study found that there was no statistically significant improvement in reasoning about variability when comparing distributions as students progressed through a college-level introductory statistics course. This lack of improvement suggested that perhaps college students needed to have direct intervention or cognitive conflict in order to make more progress in reasoning about variability when comparing distributions.



© Copyright 2015 Rachel Marie Chaphalkar