Using simulation approaches when conducting randomization tests for comparing two groups in the context of experimental studies has been promoted as a beneficial approach for supporting student learning of statistical inference. Many researchers have suggested that the data production process in simulations for the randomization test intuitively connects to the random assignment used in the original study design, thus supporting students' understanding of the logic of inference. Yet, there is little empirical research on how students initially think about the concepts and processes underlying the randomization test as they engage in constructing and using probability models to solve a problem. This work makes a contribution by deepening our understanding of students' reasoning about randomization tests by focusing on a group of three students as they create and use a TinkerPlots model to simulate data and use this data to make a statistical inference. This work adopts a narrative lens through which to view these students' reasoning and modeling activity. We compare and contrast the narratives we constructed for these students along with a narrative we constructed for a statistician. We discuss possible implications for teaching randomization tests for comparing two groups using a modeling and simulation approach.

Initial research has shown that simulating data from models created with computer software may enhance students' understanding of concepts in introductory statistics; yet, there is little research investigating students' development of statistical models. The research presented here examines small groups of students as they develop a model for a situation where a music teacher plays ten notes for a student who tries to guess each of the notes correctly. As students constructed their models and described their thinking, their descriptions were narrative in nature, focusing on the story of notes played and guessed. In this context, their focus on narrative appeared to support the development of productive statistical models. In addition, when students investigated pre-built TinkerPlots models, they preferred models that they perceived as more communicative or narrative in nature. These results have important pedagogical implications in terms of designing modeling curriculum.

Teaching introductory statistics using curricula focused on modeling and simulation is becoming increasingly common in introductory statistics courses and touted as a more beneficial approach for fostering students' statistical thinking. Yet, surprisingly little research has been conducted to study the impact of modeling and simulation curricula on student thinking, nor is there much research on how students make sense of the computer models they construct. The work presented here utilizes a framework developed by Biehler, Frischemeier, and Podworny (2015) for comparing two groups problems via a modeling and simulation approach using TinkerPlotsTM. Our work makes a contribution to the field by delving deeper into student reasoning as students create TinkerPlotsTM models to solve a comparing two groups problem. © International Association for Statistical Education (IASE/ISI), November, 2017.