Geology and its tangential studies, collectively known and referred to in this thesis as geosciences, have been paramount to the transformation and advancement of society, fundamentally changing the way we view, interact and live with the surrounding natural and built environment. It is important to recognize the value and importance of this interdisciplinary scientific field while reconciling its ties to imperial and colonizing extractive systems which have led to harmful and invasive endeavors. This intersection among geosciences, (environmental) justice studies, and decolonization is intended to promote inclusive pedagogical models through just and equitable methodologies and frameworks as to prevent further injustices and promote recognition and healing of old wounds. By utilizing decolonial frameworks and highlighting the voices of peoples from colonized and exploited landscapes, this annotated syllabus tackles the issues previously described while proposing solutions involving place-based education and the recentering of land within geoscience pedagogical models. (abstract)

This thesis is a supplement textbook designed with ASU’s MAT 370, or more generally, a course in introductory real analysis (IRA). With research in the realms of mathematics textbook creation and IRA pedagogy, this supplement aims to provide students or interested readers an additional presentation of the materials. Topics discussed include the real number system, some topology of the real line, sequences of real numbers, continuity, differentiation, integration, and the Fundamental Theorem of Calculus. Special emphasis was placed on worked examples of proven results and exercises with hints at the end of every chapter. In this respect, this supplement aims to be both versatile and self-contained for the different mathematics skill levels of readers.

Digital learning tools have become ubiquitous in virtual and in person classrooms as teachers found creative ways to engage students during the COVID 19 pandemic. Even before the pandemic and widespread remote learning, however, digital learning tools were increasingly common and a typical part of many classrooms. While all digital learning tools are worthy of study, math digital learning tools (MDLTs) designed for K - 8th grade in particular raise questions of efficacy and usefulness for classrooms. This paper shows that MDLTs are an effective tool to raise students’ math achievement across K - 8th grade, and that time spent on MDLTs can lead to better understanding of a topic than traditional, teacher led instruction. However, if the MDLT is being delivered in a language the student is not familiar with, that student will not be able to benefit from MDLTs in the way other students do. This is also true of students who receive Special Education services. Additionally, higher quality MDLTs that provide feedback that attaches meaning to students’ work creates a better learning environment for students than one with simpler feedback. Based on my experiences with student teaching this year and using the popular MDLT IXL frequently, I recommend that MDLTs not just be used for independent practice time, but for whole class, problem solving sessions where students have to use mathematical thinking in new content areas. This will build deeper conceptual learning and a greater sense of achievement in students.