Abstracts Mathematics

Formative Assessment in Postsecondary Quantitative Reasoning Courses

by Deependra Budhathoki

Quantitative reasoning is an individual’s ability to understand quantitative information in context, represent and model such information in various forms, solve real-world problems using mathematical and statistical knowledge, and communicate ideas using quantitative arguments. Quantitative Reasoning (QR) courses are increasingly popular as gateway mathematics for students whose majors lie outside science, technology, engineering, and mathematics. Professional organizations and policy documents recommend incorporating innovative assessment approaches in QR courses, including continuous and formative assessment. However, many QR instructors are unsure about what types of assessments to use and how to implement such assessments to evaluate and support student learning. Moreover, previous studies, including my pilot research, have found that many QR instructors use traditional, summative assessments.In this dissertation study, I explored instructors’ intentions, behaviors, and reflections on formative assessment, aiming to answer two sets of research questions: (a) What kinds of assessments do QR instructors use? To what extent do the instructors use their assessments as stated in their course syllabus? (b) How do QR instructors implement their assessments to support student learning? In particular, how do instructors implement questioning, feedback, and peer- and self-assessment? What are their related perceptions and experiences?To examine these questions, I employed a collective case study design, recruiting 8 instructors from eight public postsecondary institutions in Ohio that offered Ohio Transfer 36–approved QR courses. The data sources included the instructors’ course documents, semistructured interviews of the instructors, and observations of their teaching. I used six Instructional Quality Assessment (IQA) rubrics for the class observations. I conducted individual and cross-case analyses to compare and contrast the instructors’ perceptions and practices of formative assessments.The individual case analyses revealed that the QR instructors planned and implemented several categories of assessments with a wide range of frequencies and weights. Also, the instructors generally implemented one or more categories of assessments differently from how they were explained in the course syllabus. The instructors’ implemented assessments were often innovative but not always collaborative. Still, there was a strong positive association between their collaborative and innovative assessments. After several failed attempts at discovering a key factor to use as the basis for grouping instructors for cross-case analysis, the post hoc individual case analyses revealed instructional autonomy as the critical variable for QR assessments. By instructional autonomy, I mean that the QR instructor had the freedom to select, develop, and implement assessments as they wished rather than being required to follow institutional or departmental mandates. Based on this variable, I placed each instructor into either the autonomous group or the…