Kelly Findley (University of Illinois Urbana-Champaign), Nicola Justice (Pacific Lutheran University), Christopher Kinson (University of Illinois Urbana-Champaign)
Abstract
Background. Many facets of statistics involve creativity, curiosity, and personal judgment to be exercised by the analyst (Wild & Pfannkuch, 1999), but little is known about how learners come to recognize and embrace these sides of data analysis. Previous research on students’ conceptions of statistics identify students falling along a general spectrum, with statistics as procedures on one end and statistics as meaning-making on the other (Bond et al., 2012; Justice et al., 2020). These studies, however, focus on cross-sectional perspectives, but questions remain as to how students’ perceptions of statistics change over time. Our study is guided by Greeno’s (1991) environment metaphor, where students’ knowledge is situated within a figurative physical environment. Knowing in an environment consists of understanding how to get around and where to find things. In our study, we frame students’ experiences learning statistics metaphorically as learning to navigate a new city. Gaining insights from data is akin to venturing out to explore new places and seeing the city from new perspectives. With this metaphor in mind, we ask: How do students come to navigate subjectivities inherent to data analysis? Moreover, what experiences help students develop the statistical thinking dispositions critical to engaging in authentic, open-ended analysis?
Methods. We conducted semi-structured interviews with three statistics majors at a large, midwestern university across 3 years. The interviews probed students’ perceptions of the discipline of statistics and students’ experiences with data analysis thus far. Several questions were repeated in interviews across different time points, allowing us to observe and probe changes over time. To guide our analysis, we coded each interview for the five markers of disciplinary appropriation documented by Levrini et al. (2015). Levrini and colleagues describe disciplinary appropriation as “transforming scientific discourse…so as to embody it in one’s own personal story, respecting disciplinary rules and constraints” (p. 99).
Findings. Our preliminary results map to the city metaphor in three ways. 1) An experienced data analyst recognizes numerous approaches to a data analysis task, much like an established resident compares several routes to a destination. 2) Data analysis does not always neatly proceed from start to finish; rather, it is often a cognitive process that continually seeks insights and explanations (Bailyn, 1977). Likewise, getting to know a city involves appreciating the journey between destinations and discovering new places. 3) Coding is an important medium through which students engage in data analysis, much like public transportation facilitates travel through a city.
Implications For Teaching and For Research. Students’ sense of agency in data analysis experiences seem key to supporting both an awareness of subjectivities and an acceptance of imperfection to data analysis. Moreover, the degree of structure and required deliverables in data analysis projects was an important factor that affected students’ data agency. Guided projects may be most effective for newcomers, but more open data projects seem critical for supporting students’ sense of ownership over their work and growth as statisticians. Ultimately, these findings may inform statistics educators to identify characteristics of projects or learning trajectories that support students in developing a sense of data agency.
Additional Information.
Bailyn, L. (1977). Research as a cognitive process: Implications for data analysis. Quality and Quantity, 11(2), 97–117. https://doi.org/10.1007/bf00151906.
Bond, M. E., Perkins, S. N., & Ramirez, C. (2012). Students’ Perceptions of Statistics: An Exploration of Attitudes, Conceptualizations, and Content Knowledge of Statistics. Statistics Education Research Journal, 11(2), 6–25. https://doi.org/10.52041/serj.v11i2.325
Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170-218.
Justice, N., Morris, S., Henry, V., & Fry, E. B. (2020). Paint-by-number or Picasso? A grounded theory phenomenographical study of students’ conceptions of statistics. Statistics Education Research Journal, 19(2). 76–102. https://doi.org/10.52041/serj.v19i2.111
Levrini, O., Fantini, P., Tasquier, G., Pecori, B., & Levin, M. (2015). Defining and Operationalizing Appropriation for Science Learning. Journal of the Learning Sciences, 24(1), 93–136. https://doi.org/10.1080/10508406.2014.928215
Wild, C., and Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–265. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x