The Rationality of College Mathematics Instructors: The Choice to Use Inquiry-Oriented Instruction

Abstract

This study of inquiry-oriented instruction (IOI) explores what inquiry-oriented practices are used by college mathematics instructors, and what relationships there are between their use of those practices, their beliefs about students’ mathematics learning, and their recognition of professional obligations. I offer a conceptualization of inquiry-oriented instruction in which IOI practices documented in the literature are organized by the theory of the instructional triangle (Cohen, Raudenbush, & Ball, 2003), which pays particular attention to instruction as transactions of content between teacher and students. The INQUiry-Oriented Instructor REview (INQUIRE) instrument was developed on this conceptualization and used to gather data on the frequency that instructors report using inquiry-oriented practices. Professional obligations of mathematics teaching include the responsibilities that instructors have towards various stakeholders, including the institution, the individual student, mathematics as a discipline, and society (Herbst & Chazan, 2012) and instructors’ recognition of these obligations was hypothesized as playing a role in explaining the use of IOI practices. A modified version of the PRofessional Obligations Scenario Evaluation (PROSE) instrument, a scenario-based assessment, was created for this study to be used with college mathematics instructors. In addition to developing the INQUIRE and PROSE instruments, this study incorporated an existing beliefs instrument (Clark et al., 2014) to measure instructors’ beliefs on students’ mathematics learning. I used factor analyses to confirm the hypothesized inquiry-oriented practices in the instructional triangle framework and hierarchical cluster modeling to reveal patterns of inquiry-oriented practices among instructors. I found that instructors reported using seven distinct sets of practices, and instructors grouped into four different clusters based on their pattern of use of these practices – revealing different characterizations of IOI. This finding has implications for future research of IOI, showing that characterizing IOI as a singular pedagogy is problematic; rather, there are different types of IOI that are grounded in content-specific interactions. The first cluster includes participants that report the highest use of teacher-student and student-student interactions, but not the highest use of the student-content practices of giving students opportunities to construct and critique claims or write proofs. The second cluster includes participants that report the highest use of the aforementioned student-content practices, and second highest use of all five other inquiry-oriented practices. The third cluster included participants that reported low use of all inquiry-oriented practices except the teacher-content ones of interactive lecture and hinting without telling, which they use at levels comparable to other clusters. These three clusters or characterizations of IOI are all juxtaposed against the fourth cluster, which had the lowest reported use of all seven practices. I used structural equation modeling to explore the hypothesized relationships. Past studies have reported inconsistencies between beliefs and practice; instructors’ degree of recognition of the professional obligations helped explain why instructors may not always actualize their beliefs in the classroom. I found that learner-focused beliefs often predict the use of inquiry-oriented practices, but recognition of the disciplinary and interpersonal obligations can work in direct opposition of those beliefs – helping to explain why instructors sometimes do not instruct with IOI even if they believe it would be beneficial. These findings have practical implications for those wishing to shift trends in college mathematics instruction. Future work could use the INQUIRE instrument to link inquiry-oriented practices to student experiences.PHDEducational StudiesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155118/1/mollee_1.pd