Abstract
Variation and variability are key concepts in K-16 statistics education. Prior research has investigated students’ reasoning about variability in different contexts. However, there is a lack of research on students’ development of understanding of variability when comparing distributions in bar graphs, dot plots, and histograms as they took an introductory college-level statistics course. This exploratory case study conducted three interviews with each of the ten participants through a four-month period, at the beginning, middle, and end of the course. The Structure of Observed Learning Outcomes (SOLO) taxonomy was used to analyze participants’ responses. Results indicated that overall the group of participants demonstrated a stable understanding of variability over the semester (i.e. lack of improvement). However, when examining each student’s reasoning, four types of reasoning development paths were found: improvement, lack of change, decline, and inconsistent. This study provides implications in teaching college introductory statistics course and recommendations for future research.
Highlights
Variation and variability are important concepts in K-12 and postsecondary statistics education (Guidelines for Assessment and Instruction in Statistics Education (GAISE) Pre-K-12 Report, 2007; GAISE College Report ASA Revision Committee, 2016; Common Core State Standards for Mathematics, 2010)
Students’ conceptual knowledge and reasoning about variability in the context of different graphical representations of data has been examined in histograms (Cooper & Shore, 2008; delMas, Garfield, Ooms, & Chance, 2007; Kaplan, Gabrosek, Curtiss, & Malone, 2014), bar graphs (Cooper & Shore, 2010; Whitaker & Jaccobe, 2017), dot plots (Friel & Bright, 1995; Watson & Moritz, 1999), as well as changes over time (BenZvi, 2004; Leavy & Middleton, 2011; Watson, 2001). Though these representations all graph a single variable, they are different in many aspects such as: (1) a histogram summarizes data whereas a dot plot demonstrates
The Introductory to Statistics course was offered from the Department of Mathematical Sciences
Summary
Variation and variability are important concepts in K-12 and postsecondary statistics education (Guidelines for Assessment and Instruction in Statistics Education (GAISE) Pre-K-12 Report, 2007; GAISE College Report ASA Revision Committee, 2016; Common Core State Standards for Mathematics, 2010). Students’ conceptual knowledge and reasoning about variability in the context of different graphical representations of data has been examined in histograms (Cooper & Shore, 2008; delMas, Garfield, Ooms, & Chance, 2007; Kaplan, Gabrosek, Curtiss, & Malone, 2014), bar graphs (Cooper & Shore, 2010; Whitaker & Jaccobe, 2017), dot plots (Friel & Bright, 1995; Watson & Moritz, 1999), as well as changes over time (BenZvi, 2004; Leavy & Middleton, 2011; Watson, 2001). Students’ grades were mostly based on exams (69%), with homework, participation, and worksheets making up the rest of the grade (31%)
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