Estrella Johnson

Calls to move away from traditional lecture-based instruction, and towards active learning, have been long been prevalent across K16 instruction. However, we know that not all active learning is equally beneficial. Thus, foundational to my research agenda is research that investigates, characterizes, and seeks to understand powerful instructional practices.

This work began under my advisor Sean Larsen’s NSF-funded project Teaching Abstract Algebra for Understanding (TAAFU). While his primary focus was on investigating student learning and making revisions to the student 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 pedagogical context for investigation, one in which I could identify and begin to understand the challenging work of utilizing student thinking and contributions to inform pedagogical decision-making in the moment (Johnson and Larsen, 2012; Johnson, 2013).

This work continued, when I transitioned to a faculty position at Virginia Tech, with my NSF-funded project “Collaborative Research: Teaching Inquiry-Oriented Mathematics: Establishing Supports.” (TIMES). This expanded context, with multiple sets of curricula materials and content areas, has allowed me to develop a characterization of, and measure for, inquiry-oriented instruction (Kuster, Johnson, Keene, Andrews-Larson, 2017; Kuster & Johnson, 2016). In the summer of 2017, my team scored instructional lessons from approximately 45 mathematicians. The results of this analysis will be used to continue my research on documenting and investigating powerful classroom instructional practices, while simultaneously contributing to my second research focus: developing and researching the impacts of instructional supports.

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 (the development of which is documented in Larsen, Johnson, Bartlo, 2013 and Lockwood, Johnson, Larsen, 2013). Our work on the instructor support materials for TAAFU served as a model for other curriculum innovations at the undergraduate level, including Inquiry Oriented Linear Algebra and Inquiry Oriented Differential Equations.

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 were insufficient for supporting meaningful instructional change. My TIMES grant 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 45 full research participants, i.e. “TIMES Fellows,” and another 50-60 in informal professional development settings (e.g., mini-courses at MathFest).

Currently, we are investigating the ways in which short-term professional development sessions can support mathematics instructors’ pedagogical reasoning (Andrews-Larson, Peterson, Johnson, & Keller, in preparation). 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 inquiry-oriented classes; and investigating the impacts of inquiry-oriented classes on student persistence in mathematics courses and STEM majors, measured using academic transcript data.

The 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 those that happen in the moment (e.g., the choice to explore an unexpected student question) and overarching propensities (e.g., the choice to incorporate small group work), one must understand the influence of individual and situational factors on teaching.

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), we first investigated the relationship between actual coverage expectations (Johnson, 2016) and reported instructional practices (Johnson, Ellis, Rasmussen, 2015). 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). We are currently drawing 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, under review).

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, 2017). A follow-up study was conducted in which we doubled our initial response rate. With this expanded data set we have conducted a comparison of teaching practices at “teaching” and “research” institutions (Keller, Johnson, Peterson, & Fukawa-Connelly, 2017) and are currently using the aggregate data to refine a theoretical model designed to coordinate individual characteristics, situational characteristics, and instructional practice (Johnson, Keller, Fukawa-Connelly, & Peterson, in preparation).

An additional source of data for this new line of inquiry is the TIMES project. A preliminary analysis of the data generated from the entrance interviews of the TIMES fellows suggests that there is much to be studied/learned in terms of the factors influencing individual pedagogical decision-making. An in-depth qualitative transcript analysis is planned in order to identify common contextual features that appear to support an instructor’s decision to implement inquiry-oriented instruction.

Finally, we recently we awarded an NSF grant to continue this line of research across multiple STEM disciplines. This study will investigate the knowledge about, and use of, research-based instructional strategies in mathematics, physics, and chemistry education. By involving multiple STEM disciplines, we will be better able to understand and untangle the influence(s) of institutions, discipline-specific departmental cultures, and individual instructors on pedagogical decision-making.