Jennifer L. Green’s research while affiliated with Michigan State University and other places

Assessment of similarity in species composition or abundance across sampled locations is a common goal in multi‐species monitoring programs. Existing ordination techniques provide a framework for clustering sample locations based on species composition by projecting high‐dimensional community data into a low‐dimensional, latent ecological gradient representing species composition. However, these techniques require specification of the number of distinct ecological communities present in the latent space, which can be difficult to determine in advance. We develop an ordination model capable of simultaneous clustering and ordination that allows for estimation of the number of clusters present in the latent ecological gradient. This model draws latent coordinates for each sample location from a Dirichlet process mixture model, affording researchers with probabilistic statements about the number of clusters present in the latent ecological gradient. The model is compared to existing methods for simultaneous clustering and ordination via simulation and applied to two empirical datasets; JAGS code to fit the proposed model is provided in an appendix. The first dataset concerns presence‐absence records of fish in the Doubs river in eastern France and the second dataset describes presence‐absence records of plant species in Craters of the Moon National Monument and Preserve (CRMO) in Idaho, USA. Results from both analyses align with existing ecological gradients at each location. Development of the Dirichlet process ordination model provides wildlife managers with data‐driven inferences about the number of distinct communities present across monitored locations, allowing for more cost‐effective monitoring and reliable decision‐making for conservation management.

Across recommendations for teaching undergraduate mathematics and statistics courses, instructors, including graduate student instructors (GSIs), are encouraged to implement techniques that actively engage students in the material. Despite these recommendations, GSIs’ adoption of active learning techniques remains limited. Research suggests that instructors’ knowledge about and emotions towards using active learning can promote or inhibit their use of active learning in the classroom. However, little is known about how GSIs’ knowledge about and emotions towards using active learning evolve over time. We present findings from a longitudinal case study following two GSIs within a department of mathematical sciences across four semesters and discuss observed breakthroughs regarding their knowledge of, emotions towards, and use of active learning techniques. Data from surveys, interviews, and classroom observations revealed that GSIs’ breakthroughs in their use of active learning only occurred after their increased knowledge about active learning aligned with their emotions towards it. This study further revealed that the GSIs needed to feel confident in and be challenged by their course structure, such as teaching in classrooms more suitable for active learning, before implementing such techniques. From these findings, we provide suggestions for professional development programs and discuss future research practice when investigating GSIs’ longitudinal development as instructors who use active learning techniques in the classroom.

An ongoing concern for researchers, policy makers, and educators is the contribution to student achievement of educational inputs such as individual schools and teachers, interventions, teaching practices, and school policies. Value-added modeling estimates such effects from longitudinal student achievement data. This article provides an overview of Value-Added Models (VAMs) by describing representative examples of econometric, statistical, and alternative approaches and their essential features. It also discusses the concerns that value-added modeling estimates may be biased or lack sufficient stability and precision to support desired inferences.

Descriptive statistics are used to summarize and explore characteristics of data. In this entry, we provide an overview of commonly used descriptive statistics for categorical and numerical data and how they are interpreted in summaries and analyses. We also present a practical example of how descriptive statistics may be used and interpreted in an educational context.

In K–12 statistics education, there is a call to integrate statistics content standards throughout a mathematics curriculum and to teach these standards from a data analytic perspective. Annotated lesson notes within a lesson plan are a freely available resource to provide teachers support when navigating potentially unfamiliar statistics content and teaching practices. We identified several types of annotated lesson notes, created two statistics lesson plans that contained various annotated lesson notes, and observed secondary mathematics teachers implement the lesson plans in their intermediate algebra courses. For this study, we qualitatively investigated how two teachers’ instructional actions compared to what was prescribed in the annotated lesson notes. We found ways in which the teachers’ instructional actions, across their differing contexts, aligned with, varied from, or adapted to the annotated lesson notes. From these results, we highlight affordances and limitations of annotated lesson notes for statistics instruction and offer recommendations for those who create statistics curricula with annotated lesson notes.