This is a study of student engagement with computational labs in Calculus 2. The labs task students with using MATLAB to investigate contexts such as rocket science, disease modeling, and market economics forecasting by modifying and executing provided code, guided by questions that have students report the results of their simulations or observations of the model, as well as interpretive questions that ask them to make sense of their findings in the context of the realistic situation.Locally, the study is situated within an iterative design process with the goal of improving the labs and their implementation, meaning there are direct connections between the research and improvements to the written tasks or teaching practices. The goal of this dissertation, from a research perspective, is to examine student engagement to contribute to the development of theory about lab-type activities and the learning opportunities they facilitate. To accomplish both goals, this study follows a design-based research (DBR) methodology, which provides a structure to relate the local goal to inform practice to the broader research goal to develop theory that is useful broadly.The labs can be considered novel learning activities, with novel learning goals, in a novel teaching context. The labs were novel learning activities because they were the original product of the curriculum designers and they were still being substantially revised during the third year of the project, when this study took place. The learning goals were novel at the research site because they involved collaborative and higher-level objectives, a notable departure from the traditional emphasis on individual mastery of various rote calculation. The teaching context was novel because this research was conducted during the first time the labs were taught "at-scale", meaning it was the first time the labs were being led by graduate students during recitations connected to a multi-section large-lecture. In this novel context, studying engagement provides a way to understand how the labs facilitate students' attainment of those learning goals without attempting to measure students' individual attainment of those learning goals. Students learn through engagement, so understanding how students engage with the labs is a way to understand how students are learning-if students are engaged in the mathematical practices the labs are intended to facilitate, then they are learning those mathematical practices.This study examined engagement through interviews, classroom observations, and a post-course survey. Students were observed collaborating productively by discussing their thinking, tinkering with code, and co-authoring solutions. Rarely were off-task behaviors observed. Some interview participants identified intrinsic learning goals and other students were invested in completing the labs simply because they were a required, graded assignment. Some students found the labs to be interesting, challenging, and useful, but the broader sentiment was a more negative reaction that was especially pronounced in the post-course survey data. These negative feelings, however, did not appear to disrupt students' behavioral or cognitive engagement in the classroom, because students continued to put forward effort to complete the labs through the end of the semester, suggesting that negative emotional engagement does not necessarily lead to overall disengagement or undermine students' motivation. In other words, even though some students might not be trying to learn how to use MATLAB to model Calculus 2 concepts, they learn some of those skills anyway because they have to do the things they are supposed to learn.
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