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Although the paradigm wars between quantitative and qualitative research methods and the associated epistemologies may have settled down in recent years within the mathematics education research community, the high value placed on quantitative methods and randomized control trials remain as the gold standard at the policy-making level (USDOE, 2008). Although diverse methods are valued in the mathematics education community, if mathematics educators hope to influence policy to cultivate more equitable education systems, then we must engage in rigorous quantitative research. However, quantitative research is limited in what it can measure by the quantitative tools that exist. In mathematics education, it seems as though the development of quantitative tools and studying their associated validity and reliability evidence has lagged behind the important constructs that rich qualitative research has uncovered. The purpose of this study is to describe quantitative instruments related to mathematics teacher behavior and affect in order to better understand what currently exists in the field, what validity and reliability evidence has been published for such instruments, and what constructs each measure. 1. How many and what types of instruments of mathematics teacher behavior and affect exist? 2. What types of validity and reliability evidence are published for these instruments? 3. What constructs do these instruments measure? 4. To what extent have issues of equity been the focus of the instruments found? 

Engineering graduates need a deep understanding of key concepts in addition to technical skills to be successful in the workforce. However, traditional methods of instruction (e.g., lecture) do not foster deep conceptual understanding and make it challenging for students to learn the technical skills, (e.g., professional modeling software), that they need to know. This study builds on prior work to assess engineering students’ conceptual and procedural knowledge. The results provide an insight into how the use of authentic online learning modules influence engineering students’ conceptual knowledge and procedural skills. We designed online active learning modules to support and deepen undergraduate students’ understanding of key concepts in hydrology and water resources engineering (e.g., watershed delineation, rainfall-runoff processes, design storms), as well as their technical skills (e.g., obtaining and interpreting relevant information for a watershed, proficiency using HEC-HMS and HEC-RAS modeling tools). These modules integrated instructional content, real data, and modeling resources to support students’ solving of complex, authentic problems. The purpose of our study was to examine changes in students’ self-reported understanding of concepts and skills after completing these modules. The participants in this study were 32 undergraduate students at a southern U.S. university in a civil engineering senior design course who were assigned four of these active learning modules over the course of one semester to be completed outside of class time. Participants completed the Student Assessment of Learning Gains (SALG) survey immediately before starting the first module (time 1) and after completing the last module (time 2). The SALG is a modifiable survey meant to be specific to the learning tasks that are the focus of instruction. We created versions of the SALG for each module, which asked students to self-report their understanding of concepts and ability to implement skills that are the focus of each module. We calculated learning gains by examining differences in students’ self-reported understanding of concepts and skills from time 1 to time 2. Responses were analyzed using eight paired samples t-tests (two for each module used, concepts and skills). The analyses suggested that students reported gains in both conceptual knowledge and procedural skills. The data also indicated that the students’ self-reported gain in skills was greater than their gain in concepts. This study provides support for enhancing student learning in undergraduate hydrology and water resources engineering courses by connecting conceptual knowledge and procedural skills to complex, real-world problems. 

Climate change is likely to alter both flowering phenology and water availability for plants. Either of these changes alone can affect pollinator visitation and plant reproductive success. The relative impacts of phenology and water, and whether they interact in their impacts on plant reproductive success remain, however, largely unexplored. We manipulated flowering phenology and soil moisture in a factorial experiment with the subalpine perennial Mertensia ciliata (Boraginaceae). We examined responses of floral traits, floral abundance, pollinator visitation, and composition of visits by bumblebees vs. other pollinators. To determine the net effects on plant reproductive success, we also measured seed production and seed mass. Reduced water led to shorter, narrower flowers that produced less nectar. Late flowering plants produced fewer and shorter flowers. Both flowering phenology and water availability influenced pollination and reproductive success. Differences in flowering phenology had greater effects on pollinator visitation than did changes in water availability, but the reverse was true for seed production and mass, which were enhanced by greater water availability. The probability of receiving a flower visit declined over the season, coinciding with a decline in floral abundance in the arrays. Among plants receiving visits, both the visitation rate and percent of non-bumblebee visitors declined after the first week and remained low until the final week. We detected interactions of phenology and water on pollinator visitor composition, in which plants subject to drought were the only group to experience a late-season resurgence in visits by solitary bees and flies. Despite that interaction, net reproductive success measured as seed production responded additively to the two manipulations of water and phenology. Commonly observed declines in flower size and reward due to drought or shifts in phenology may not necessarily result in reduced plant reproductive success, which in M. ciliata responded more directly to water availability. The results highlight the need to go beyond studying single responses to climate changes, such as either phenology of a single species or how it experiences an abiotic factor, in order to understand how climate change may affect plant reproductive success. 

Flowering time may influence pollination success and seed set through a variety of mechanisms, including seasonal changes in total pollinator visitation or the composition and effectiveness of pollinator visitors.

We investigated mechanisms by which changes in flowering phenology influence pollination and reproductive success ofMertensia ciliata(Boraginaceae). We manipulated flowering onset of potted plants and assessed the frequency and composition of pollinator visitors, as well as seed set. We tested whether floral visitors differed in their effectiveness as pollinators by measuring pollen receipt and seed set resulting from single visits to virgin flowers.

Despite a five‐fold decrease in pollinator visitation over four weeks, we detected no significant difference in seed set among plants blooming at different times. On a per‐visit basis, each bumblebee transferred more conspecific pollen than did a solitary bee or a fly. The proportion of visits by bumblebees increased over the season, countering the decrease in visitation rate so that flowering time had little net effect on seed set.

This work illustrates the need to consider pollinator effectiveness, along with changes in pollinator visitation and species composition to understand the mechanisms by which phenology affects levels of pollination.

 

It remains unclear what sets the efficiency with which molecular gas transforms into stars. Here we present a new VLA map of the spiral galaxy M 51 in 33 GHz radio continuum, an extinction-free tracer of star formation, at 3″ scales (∼100 pc). We combined this map with interferometric PdBI/NOEMA observations of CO(1–0) and HCN(1–0) at matched resolution for three regions in M 51 (central molecular ring, northern and southern spiral arm segments). While our measurements roughly fall on the well-known correlation between total infrared and HCN luminosity, bridging the gap between Galactic and extragalactic observations, we find systematic offsets from that relation for different dynamical environments probed in M 51; for example, the southern arm segment is more quiescent due to low star formation efficiency (SFE) of the dense gas, despite its high dense gas fraction. Combining our results with measurements from the literature at 100 pc scales, we find that the SFE of the dense gas and the dense gas fraction anti-correlate and correlate, respectively, with the local stellar mass surface density. This is consistent with previous kpc-scale studies. In addition, we find a significant anti-correlation between the SFE and velocity dispersion of the dense gas. Finally, we confirm that a correlation also holds between star formation rate surface density and the dense gas fraction, but it is not stronger than the correlation with dense gas surface density. Our results are hard to reconcile with models relying on a universal gas density threshold for star formation and suggest that turbulence and galactic dynamics play a major role in setting how efficiently dense gas converts into stars. 

Species that persist in small populations isolated by habitat destruction may experience reproductive failure. Self‐incompatible plants face dual threats of mate‐limitation and competition with co‐flowering plants for pollination services. Such competition may lower pollinator visitation, increase heterospecific pollen transfer and reduce the likelihood that a visit results in successful pollination.

To understand how isolation from mates and competition with co‐flowering species contribute to reproductive failure in fragmented habitat, we conducted an observational study of a tallgrass prairie perennialEchinacea angustifolia. We quantified the isolation of focal individuals from mates, characterized species richness and counted inflorescences within 1 m radius, observed pollinator visitation, collected pollinators, quantified pollen loads on pollinators and onEchinaceastigmas, and measured pollination success. Throughout the season, we sampled 223 focal plants across 10 remnant prairie sites.

We present evidence that both co‐flowering species and isolation from mates substantially limit reproduction inEchinacea. As the flowering season progressed, the probability of pollinator visitation to focal plants decreased and evidence for pollen‐limited reproduction increased. Pollinators were most likely to visitEchinaceaplants from low‐richness floral neighbourhoods with close potential mates, or plants from high‐richness neighbourhoods with distant potential mates. Frequent visitation only increased pollination success in the former case, likely becauseEchinaceain high‐richness floral neighbourhoods received low‐quality visits.

Synthesis. InEchinacea,reproduction was limited by isolation from potential mates and the richness of co‐flowering species. These aspects of the floral neighbourhood influenced pollinator visitation and pollination success, although conditions that predicted high visitation did not always lead to high pollination success. These results reveal how habitat modification and destruction, which influence floral neighbourhood and isolation from conspecific mates, can differentially affect various stages of reproductive biology in self‐incompatible plants. Our results suggest that prairie conservation and restoration efforts that promote patches of greater floral diversity may improve reproductive outcomes in fragmented habitats.