Estrella Johnson

Inquiry-Oriented Instruction: A Conceptualization of the Instructional Principles

Abstract Research has highlighted that inquiry-based learning (IBL) instruction leads to many positive student outcomes in undergraduate mathematics. Although this research points to the value of IBL instruction, the practices of IBL instructors are not well-understood. Here, we offer a characterization of a particular form of IBL instruction: inquiry-oriented instruction. This characterization draws on K-16 research literature in order to explicate the instructional principles central to inquiry-oriented instruction. As a result, this conceptualization of inquiry-oriented instruction makes connections across research communities and provides a characterization that is not limited to undergraduate, secondary, or elementary mathematics education.

A structural equation model looking at student’s participatory behavior and their success in Calculus I

BackgroundGovernment projections in the USA indicate that the country will need a million more science, technology, engineering, and mathematics (STEM) graduates above and beyond those already projected by the year 2022. Of crucial importance to the STEM pipeline is success in Calculus I, without which continuation in a STEM major is not possible. The STEM community at large, and mathematics instructors specifically, need to understand factors that influence and promote success in order to mitigate the alarming attrition trend. Previous work in this area has defined success singularly in terms of grades or persistence; however, these definitions are somewhat limiting and neglect the possible mediating effects of affective constructs like confidence, mindset, and enjoyment on the aforementioned markers of success. Using structural equation modeling, this paper explored the effect of participation on grades in freshman college calculus and investigated whether these effects were mediated by affective variables.ResultsResults indicated that participation had no significant direct effect on any of the success components in the final model—a finding that was not only counterintuitive but actually contradicted previous research done on this data. Participation was however highly correlated with two other exogenous variables indicating it would be inappropriate to dismiss it as being unrelated to success. Furthermore, the results suggested a cluster of affective success components and an achievement component with confidence being the intermediary between the two.ConclusionsThis paper extends upon previous work with this data set in which the effect of participatory behaviors on success was investigated wherein success was measured singularly with expected course grade and affective components of success were not considered. The limited explanatory power of the model, coupled with the seemingly contradictory results, indicates that participatory behaviors alone might be insufficient to capture the complexity of the success response variable.

Factors contributing to students and instructors experiencing a lack of time in college calculus

BackgroundCalculus is a foundational course for STEM-intending students yet has been shown to dissuade students from pursuing STEM degrees. In this report, we examine factors related to students and instructors reporting a lack of time in class for students to understand difficult ideas and relate this to students’ and instructors’ perceptions of opportunities to learn using a hierarchical linear model. This work is part of the US national study on college calculus, which provides an ideal landscape to examine these questions on a large scale.ResultsWe find a number of student factors associated with students experiencing negative opportunities to learn, such as student gender, lacking previous calculus experience, and reports of poor and non-student-centered teaching. Factors weakly associated with instructor reports of lack of time were a common final and reporting that approximately half of the students lacked the ability to succeed in the course.ConclusionsThis analysis offers insight into how we might create more positive opportunities to learn in our own classrooms. This includes preparing students before they enter calculus, so they feel confident in their abilities, as well as weakening the internal framing of the course by engaging in teaching practices that provide students opportunities to communicate and influence their learning (e.g., discussion and group work). We argue that this is especially important in introductory college calculus courses that are packed with material, taught to a diverse population of students in terms of demographics, mathematical preparation, and career goals.

It's about time: the relationships between coverage and instructional practices in college calculus

This paper is based on a large-scale empirical study designed to investigate Calculus I programmes across the United States to better understand the relationship between instructors concerns about coverage, instructional practices, and the nature of the material covered. We found that there was no association between instructors feeling pressured to go through material quickly to cover all the required topics and intended pacing. Furthermore, our results suggest that both intended pacing and feelings of pressure are poor indicators of instructional practices.