Search

The effects of wildfire on the power grid are a recurring concern for utility companies who need reliable information about where to prioritize infrastructure hardening. Though there are existing data layers that provide measures of burn probability, these models predominately consider long-term climate variables, which are not helpful when analyzing current season trends. Utility companies need data that are temporally and locally relevant. To determine the primary drivers of burn probability relative to power grid vulnerability, this study assessed potential wildfire drivers that are both readily accessible and regularly updated. Two study areas in Idaho, USA with contrasting burn probabilities were compared. Wildfire drivers were obtained and differentiated between the study areas across the 2018–2021 growing seasons. This study determined that mean wind speed, cumulative growing season precipitation, and the mean Normalized Difference Vegetation Index (NDVI) for an area of interest may be reliable indicators of burn probability on a temporally relevant scale. This assessment demonstrates a method and variables that may be utilized by municipal electric utilities, electric cooperatives, and other power utilities to determine where to harden power grid infrastructure within wildfire-prone areas.

Students often have difficulty understanding the proofs that they read. Some mathematics educators have suggested using generic proofs to improve students' proof comprehension. However, few empirical studies about students' perceptions of generic proofs or whether students understand generic proofs better than traditional proofs have been conducted. In this paper, we describe a qualitative interview study and a quantitative experimental study exploring these issues. Our first finding is that generic proofs are popular with students, who believe they have the potential to improve proof comprehension. Our second finding is that in a randomized controlled experiment, students did not learn more from reading a generic proof than a traditional proof. The significance of these findings is discussed at the end of the paper.

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition.