Abstract
Assessment is a topic of concern to teachers, students, administrators, parents, and all stakeholders in our educational system. Many current standardized assessments have been criticized for their limited ability to address issues of validity, equity, and usefulness in teaching and learning. One alternative assessment methodology, pattern-based questions, shows promise in addressing issues of equity and usefulness in teaching and learning but has not yet established a sense of validity. This grounded theory study explores developmental university students' understanding of four Pattern-Based questions (PBQs) through clinical interviews. This research found multiple, identifiable and coherent ways of thinking for each of four PBQs. A correspondence graph was developed to investigate the correspondences between student response patterns and the students’ expressed ways of thinking. A plurality of correspondences was found for all four PBQs. A nascent theory of validity for PBQs suggests that the validity of PBQs should be evaluated first, on if the question illuminates ways of thinking and second on if the correspondence graph displays correspondences between common response patterns (modes) and students' ways of thinking about the mathematical content of the question. This research also has implications for mathematics education in the classroom and across all classrooms. Keywords: assessment, validity, pattern-based questions, clinical interviews, grounded theory, ways of thinking, correspondences, algebra, fractions.