# Reasoning from an Eikosogram: an Exploratory Study

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## Abstract

Although students’ understanding of frequency information presented in two-way tables was first explored in the 1990s, there is a surprising lack of research in this area. Furthermore, researchers and practitioners continue to highlight students’ difficulties in comprehending probability including concepts related to conditioning. Using an interactive eikosogram, a visual representation of a two-way table of information, we explore six introductory probability students’ reasoning, interaction and comprehension behaviours associated with the display. Our findings suggest that the eikosogram may have the potential to assist: proportional reasoning, ability to compare proportions, consideration of proportions in both the horizontal and vertical dimensions; the unlocking and verbalization of simple, conditional and joint probability stories from the data; and visualizing representations for independence. The students believed the eikosogram representation would be beneficial for learning probability. Improvements to the tool and task and implications of the research are discussed.

## Keywords

Introductory probability Interactive visualizations Graphicacy Conditioning Probability education## Notes

### Acknowledgments

This work is supported by a grant from the Teaching and Learning Research Initiative (http://www.tlri.org.nz/). We thank the anonymous reviewers of this paper for their very helpful comments.

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