Emerging multilingual students can develop the dimensions of Academic Literacy in Mathematics (ALM) in classroom discussions. But, there is a need for empirically-validated principles for fostering such discussions. This research used ALM as a framework to create a unit of instruction on linear rates of change for ninth grade mathematics in which multilingual students benefit from discussions. Project-specific design principles are presented along with qualitative analysis of classroom discussions from each phase of the project. The results illustrate how discussions in the redesigned lessons contributed to developing the interrelated dimensions of ALM among multilingual learners. The work concludes with a discussion of how the project-specific design principles can serve as a framework for fostering discussions in other multilingual secondary mathematics learning environments.

EQUIP is a free, customizable observation protocol for tracking patterns of student participation in STEM classrooms (https:// www. equip. ninja). EQUIP generates data analytics that are disaggregated by student social markers (e.g., race, gender), which makes it a useful tool for tracking patterns of inequity in student participation. However, prior studies have not yet established how many observations are needed to create a representative picture of instruction. In this study, we use g-theory and simulations with Cramer's V to analyze observations from 20 undergraduate mathematics instructors to determine how many classroom observations are needed, and how this differs by individual codes. We found that Gender could achieve stability in just a few observations, whereas codes such as Instructor Response, Instructor Solicitation Type, and Instructor Solicitation Method required nearly 20 observations. Thus, we recommend that users account for their specific context and needs with EQUIP when determining the ideal number of observations to conduct, using this research as a baseline. We also compare the g-study and simulations approaches, bringing up new methodological questions for the field.

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