Investigating College-Level Introductory Statistics Students’ Prior Knowledge of Graphing

In the age of big data, we are constantly inventing new data visualizations to consolidate massive amounts of numerical information into smaller and more digestible visual formats. These data visualizations use various visual features to convey quantitative information, such as spatial position in scatter plots, color saturation in heat maps, and area in dot maps. These data visualizations are typically composed of ensembles, or groups of related objects, that together convey information about a data set. Ensemble perception, or one's ability to perceive summary statistics from an ensemble, such as the mean, has been used as a foundation for understanding and explaining the effectiveness of certain data visualizations. However, research in data visualization has revealed some perceptual biases and conceptual difficulties people face when trying to utilize the information in these graphs. In this tutorial review, we will provide a broad overview of research conducted in ensemble perception, discuss how principles of ensemble encoding have been applied to the research in data visualization, and showcase the barriers graphs can pose to learning statistical concepts, using histograms as a specific example. The goal of this tutorial review is to highlight possible connections between three areas of research-ensemble perception, data visualization, and statistics education-and to encourage research in the practical applications of ensemble perception in solving real-world problems in statistics education.

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“…(1) Histograms are (like) bar graphs (Biehler, 1997;Cooper & Shore, 2010;Meletiou-Mavrotheris & Lee, 2010).…”

Section: An Example Of Using Graphs: Histogramsmentioning

confidence: 99%

Synergy between research on ensemble perception, data visualization, and statistics education: A tutorial review

Cui

Liu

2021

Atten Percept Psychophys

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“…Histograms are adept at revealing the distribution of data values, especially the shape of the distribution and any outlier values. Previous research, however, indicates that undergraduate students tend to hold various misconceptions about histograms (delMas, Garfield & Ooms, 2005;Kaplan, Gabrosek, Curtiss, & Malone 2014;Meletiou-Mavrotheris & Lee, 2010). For example, students may view all graphs with bars as bar graphs or case value graphs (see Kaplan et al, 2014 for discussion), not distinguishing the difference between these graphs and histograms (delMas et al, 2005;Meletiou-Mavrotheris & Lee, 2010).…”

Section: The Importance Of Histogramsmentioning

confidence: 99%

“…Previous research, however, indicates that undergraduate students tend to hold various misconceptions about histograms (delMas, Garfield & Ooms, 2005;Kaplan, Gabrosek, Curtiss, & Malone 2014;Meletiou-Mavrotheris & Lee, 2010). For example, students may view all graphs with bars as bar graphs or case value graphs (see Kaplan et al, 2014 for discussion), not distinguishing the difference between these graphs and histograms (delMas et al, 2005;Meletiou-Mavrotheris & Lee, 2010). Confusing histograms and case value graphs, thinking that each bar represents one observation instead of the aggregate of all observations that take certain values, can lead to confusion between what is represented by the horizontal and vertical axes in a histogram (Bright & Friel, 1998;Friel, Curcio, & Bright, 2001).…”

Section: The Importance Of Histogramsmentioning

confidence: 99%

“…This is one of the future directions associated with the project. A second future direction is the investigation of the interaction between misconceptions about histograms held by a student and that student's ability to describe a histogram, particularly given the literature on student misconceptions of histograms (see, for example, delMas et al, 2005;Kaplan et al, 2014;Meletiou-Mavrotheris & Lee, 2010). The research team is currently analyzing data that included both items to assess student misconceptions about histograms and student descriptions of histograms in an effort to shed light on this second direction for research.…”

Section: Implications For Researchmentioning

confidence: 99%

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Effects of Question Stem on Student Descriptions of Histograms

Kaplan¹,

Lyford

Jennings³

2018

SERJ

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Assessment is necessary, but difficult, in statistics education. Multiple choice assessments are common, particularly for research purposes. Open-ended assessments may be more adept at revealing student understanding, but ensuring their validity can be difficult. The study presented here examines differences in student descriptions of histograms for different question prompts and scenarios in order to understand how best to ask such questions in research and teaching situations. The results show that different ways of asking students to describe histograms and different scenarios and shapes of histograms lead to systematic differences in student descriptions of histograms. The paper concludes with suggestions for phrasing questions, both for research and classroom assessment, and provides directions for future research based on our results. First published May 2018 at Statistics Education Research Journal Archives

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“…It covers four main processes as follows: graph reading, graph interpretation, graph construction, and graph evaluation. More specifically, graph reading involves extracting data from a graphical display and generating information by operating on data shown in the graphical display (Meletiou-Mavrotheris & Lee, 2010). Graph interpretation involves gaining meaning and/or making inferences from a graph (Sharma, 2006).…”

Section: Mathematical Thinkingmentioning

confidence: 99%

The Thinking-About-Derivative Test for Undergraduate Students: Development and Validation

Aydın

Ubuz

2014

Int J of Sci and Math Educ

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Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test administration, generalizability analysis, confirmatory factor analysis, and subgroup validity analysis. Findings suggested that the 30-item multiple-choice TDT, which comprises 6 mathematical thinking aspects, enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking, demonstrates acceptable levels of reliability and validity. Followed by additional cross-validation studies, the TDT may be a useful tool for mathematics education researchers and mathematicians. Directions for future research and implications for educational practice are discussed.

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Investigating College-Level Introductory Statistics Students’ Prior Knowledge of Graphing

Cited by 8 publications

References 10 publications

Synergy between research on ensemble perception, data visualization, and statistics education: A tutorial review

Synergy between research on ensemble perception, data visualization, and statistics education: A tutorial review

Effects of Question Stem on Student Descriptions of Histograms

The Thinking-About-Derivative Test for Undergraduate Students: Development and Validation

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