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Abstract Hyporheic zones regulate biogeochemical processes in streams and rivers, but high spatiotemporal heterogeneity makes it difficult to predict how these processes scale from individual reaches to river basins. Recent work applying allometric scaling (i.e., power‐law relationships between size and function) to river networks provides a new paradigm for understanding cumulative hyporheic biogeochemical processes. We used previously published model predictions of reach‐scale hyporheic aerobic respiration to explore patterns in allometric scaling across two climatically divergent basins with differing characteristics in the Pacific Northwest, United States. In the model, hydrologic exchange fluxes (HEFs) regulate hyporheic respiration, so we examined how HEFs might influence allometric scaling of respiration. We found consistent scaling behaviors where HEFs were either very low or very high, but differences between basins when HEFs were moderate. Our findings provide initial model‐generated hypotheses for factors influencing allometric scaling of hyporheic respiration. These hypotheses can be used to optimize new data generation efforts aimed at developing predictive understanding of allometries that can, in turn, be used to scale biogeochemical dynamics across watersheds. 

Can fostering mathematical creativity explicitly in a calculus I course impact students’ mathematical identity? As a part of a larger research project exploring this question, a quantitative research study was developed to explore six aspects of student mathematical identity along with student perception of creativity-fostering instructor behavior. Analysis of pre- and post-semester survey data indicated that the instruments measuring aspects of student identity had strong reliability and good structure validity. Correlational analysis of the six aspects of student identity provided evidence that students’ views of mathematics as a creative endeavor impacted the formation of self-efficacy in mathematics. The instrument measuring creativity-fostering instruction demonstrated low reliability and internal inconsistencies. Methodological issues related to measuring creativity-fostering instruction and directions for future research studying creativity-fostering and student identity are discussed. 

Through participation in a research project on fostering creativity in calculus, two instructors showed shifts in their beliefs on teaching. Participation in the project entailed creating mathematical tasks designed to elicit creative responses from students. Support for task development included participation in weekly online professional development sessions. In this paper, we share one instructor’s shifts in beliefs as well as alignment of her pre-existing beliefs with pedagogical actions. Preliminary analysis of her entrance tickets to the professional development sessions and her exit interview indicates that this instructor a) shifted her previous beliefs about a perceived time pressure and b) manifested her existing beliefs into actions regarding multiple-approach tasks. 

Fostering students’ mathematical creativity necessitates certain instructional actions - one of which is designing and implementing tasks that foster creativity. Drawing on the literature on mathematical creativity, we describe existing research-based features of tasks for eliciting student creativity, or creativity-based tasks, and provide suggestions for implementation of such tasks. Based on these features, we analyzed two instructors’ first experiences designing and implementing creativity-based tasks in Calculus I. Both instructors’ frequent use of the multiple- solutions feature suggests that this feature could be an entry-point for designing and implementing creativity-based tasks for other instructors seeking to foster creativity.