Research

My research agenda comprises a multi-faceted approach to investigating one large and critical question: How can we support high-quality, ambitious teaching in university mathematics classrooms? I address this question by: 1) researching the work of teaching, 2) developing and evaluating instructional supports, and 3) identifying individual and contextual factors that influence pedagogical decision-making. I have also have an emerging research interest in equitable teaching practices – that has been spurred by my own recent research findings.  

Classroom Instructional Practice Calls to move away from traditional lecture-based instruction, and towards active learning, have been long been prevalent across K-16 instruction. However, we know that not all forms of active learning are equally beneficial for students. Thus, foundational to my research agenda is research that investigates, characterizes, and seeks to understand powerful instructional practices.

This work began under my doctoral advisor Sean Larsen’s NSF-funded project Teaching Abstract Algebra for Understanding (TAAFU). While his primary focus was on investigating student learning and developing curricular materials, I led the investigation into the pedagogical challenges and activities involved with the implementation of the materials. This proved to be a rich context for investigation, one in which I was able to identify and begin to understand the challenging work of utilizing student thinking and contributions to inform pedagogical decision-making in the moment (Johnson & Larsen, 2012; Johnson, 2013).

This work continued, when I transitioned to my faculty position at Virginia Tech, with my NSF-funded project “Teaching Inquiry-Oriented Mathematics: Establishing Supports” (TIMES). The TIMES project enabled me to continue my research in an expanded context, involving many more institutions and curricula in three different content areas. This has allowed my research team to develop a characterization of, and measure for, inquiry-oriented instruction (Kuster, Johnson, Keene, & Andrews-Larson, 2018, Kuster, Johnson, Rupnow, & Wilhelm, 2019). We used the measurement tool we developed to score instructional units taught by approximately 45 mathematicians. I continue to draw on the results of these analyses to inform my second focus of my research: developing and researching the impacts of instructional supports.

Developing and Researching the Impacts of Instructional Support. The articulation of inquiry-oriented instruction, as well as the identification of powerful, in-the-moment instructional practices, has provided a research-based goal for my work to support instructional change. Within the context of the TAAFU curriculum, my research informed a set of freely available, online instructional support materials (Larsen, Johnson, & Scholl, 2016), the development of which is documented in Larsen, Johnson, & Bartlo, 2013 and Lockwood, Johnson, & Larsen, 2013. This work has served as a model for others in the field, including two other reform curricula developed for undergraduate mathematics courses.

Research into the implementation of these three curricula in general, and into TAAFU in particular (e.g., Johnson et al., 2013), suggested that the online support materials alone are insufficient for supporting meaningful instructional change. My TIMES project takes seriously the practical challenges of supporting instructional change: it was developed to design, investigate, and evaluate a system of instructional supports. To date, we have worked with approximately 100 undergraduate mathematics instructors: 45 full research participants and another 50-60 in informal professional development settings.

Currently, we are investigating the ways in which short-term professional development sessions can support mathematics instructors’ pedagogical reasoning (Andrews-Larson, Johnson, Peterson, & Keller, 2019). Future research planned in this area includes: investigating relationships between online working groups and classroom instructional practices (as assessed by the inquiry-oriented instructional measure); analyzing and comparing student assessment scores and reports of learning gains for students in traditional and in inquiry-oriented classes; and investigating the impacts of inquiry-oriented classes on student persistence in mathematics courses and STEM majors, as measured by academic transcript data.

Identifying Factors and Influences that Shape Pedagogical Practice. This last strand, identifying factors and influences that shape pedagogical practice, reflects the fact that teaching is influenced by more than what happens in the classroom. In order to understand pedagogical decisions, both in the moment decisions (e.g., the choice to explore an unexpected student question) and broader propensities (e.g., the choice to incorporate small group work), we must understand the influence of individual and situational factors on teaching.

I have been investigating these influences using a variety of data sources and methodological approaches. Using data from a national survey of Calculus I instructors (gathered through the NSF-funded project Characteristics of Successful Programs in College Calculus NSF DRL #0910240, for which I served as a graduate research assistant and a consultant after graduation), we first investigated the relationship between actual coverage expectations and reported instructional practices (Johnson, 2016; Johnson, Ellis, & Rasmussen, 2016). Next, we analyzed how external pressures, characteristics of teachers and students, and teaching practices impacted instructional quality, as measured by the opportunities to learn reported by both instructors and students (Hagman, Johnson, & Fosdick, 2017). Most recently, we drew on this data set to develop a hierarchical linear model that allows us to better understand, and tease apart, the influence of individual and institutional characteristics on teaching practices (Keller & Johnson, 2019).

To further investigate influences on pedagogical practice, we developed and administered a survey for mathematicians teaching abstract algebra. This survey was used to understand if/how mathematics education research influences teaching practices (Fukawa-Connelly, Johnson, & Keller, 2016), and to develop a logistic regression model to identify factors that are predictive of the use of non-lecture pedagogy (Johnson, Keller, & Fukawa-Connelly, 2018). We have also conducted a comparison of teaching practices at “teaching” and “research” institutions (Keller, Johnson, Peterson, & Fukawa-Connelly, 2017) and published a recent article on the aggregate data that looks at the individual bounds, and situational factors, that influence instructional practice (Johnson, Keller, Fukawa-Connelly, & Peterson, 2019).

Finally, I was awarded an NSF grant to continue this line of research across multiple STEM disciplines. The “Evaluating the Uptake of Research-Based Instructional Strategies in Undergraduate Chemistry, Mathematics, & Physics” project investigates knowledge about, and the use of, research-based instructional strategies in first-year undergraduate courses. By involving multiple STEM disciplines, we will be better able to understand and tease apart the influences of institutions, discipline-specific departmental cultures, and individual instructors on pedagogical decision-making. Survey data collection for this project has just been completed. With more than 3,750 responses, we anticipate this study will generate significant findings for the field.

Equitable Teaching Practices. As part of the evaluation of our TIMES project we discovered a finding that warrants additional research. Our analysis of 522 student content assessments revealed that, while the performance of students in inquiry-oriented classrooms and those who were in more traditional settings was not significantly different, there was a gender performance difference (men out-performing women) in the inquiry-oriented classes that was not present in the traditional classes. This difference was large, with men on average scoring 13 percentage points higher than women, and remained significant even after we ran a hierarchical linear model to account for the instructor and institutional differences (Johnson et al., in press).

In reaction to this finding, my current analysis of the TIMES data is focused on understanding the gendered experiences of students in the inquiry-oriented setting promoted by the TIMES project. Additionally, I submitted an NSF grant proposal in Oct 2019 with two main goals: 1) develop methodologies for investigating marginalizing experiences of students in undergraduate mathematics classes – attending to how different learning environments (e.g., lecture, IBL, IOI) may have different impacts on different student groups, and 2) develop theories to understand how different active learning approaches are (not) linked to more equitable outcomes for different student populations.