The process of making meaning: The interplay between teachers\u27 knowledge of mathematical proofs and their classroom practices

The purpose of this study was to investigate and describe how middle school mathematics teachers make meaning of proofs and the process of proving in the context of their classroom practices. A framework of making meaning, created by the researcher, guided the data collection and analysis phases of the study. This framework describes the five central aspects of the process of making meaning: knowledge, beliefs, utilization of knowledge, interconnections of practice and knowledge, and making sense of past knowledge and current experiences. The utilization of a qualitative research methodology that combined ethnographic fieldwork and discourse analysis allowed the researcher to consider the interplay of individual knowledge and action with contextual influences. Data was gathered through participant observations, conducted in grade levels 5-8 classrooms, and interviews were conducted with teachers and administrators. The participants in the study include six middle grades teachers and two administrators from a New Hampshire public school. The teachers\u27 decision making processes, understandings of proofs, and the connections formed between their past knowledge and current experiences were analyzed. Data analysis was conducted using open coding, the creation of episodic threads, and the development and examination of themes. Findings from this study suggest that: (1) these teachers use proofs and the process of proving in their classrooms often and in meaningful ways, (2) the teachers hold a dual understanding of proofs and the process of proving: one related to their own education experiences and one related to their students\u27 education, (3) the teachers use alternative resources to make meaning of proofs and the process of proving in relation to their professional experiences, and (4) the use of alternative resources has allowed the teachers to disconnect their view of proofs and the process of proving in relation to their students education from their own past experiences, which they view as negative. Implications for future research related to teachers\u27 knowledge of proofs and the process of making meaning, as well as implications for the education and professional development of middle school mathematics teachers are presented and discussed

Early life-history studies of nearshore rockfishes and lingcod off Central California, 1987-92

This study focused on the physical and biological processes that influence the distribution, abundance, growth, and survival of young-of-the-year (YOY) rockfishes and lingcod along the central California coast. The annual somatic and reproductive condition of adult female blue rockfish corresponded to annual upwelling. Resulting larval production may correspond to the reproductive potential of adults; however, ultimate recruitment success of YOY is also effected by oceanographic conditions during their planktonic stage. Within a year, each species of settled YOY was observed concurrently and in relatively similar abundances at all study dive sites along the central coast. Most species of YOY exhibited similar growth patterns among stations and years. We found a high degree of interannual variability in the condition of adults and relative abundances of YOY. We believe a large part of this variability is due to annual oceanographic conditions, specifically upwelling. Marine reserves, which would protect populations of reproductively mature rockfishes and lingcod and insure 1arval production, have been suggested as an alternative to present management strategies for these species. However, a crucial question is whether or not larvae from adult fish in reserves would significantly contribute to replenishing stocks in other areas. This study was undertaken to assist in determining the feasibility of reserves to enhance nearshore rockfish and lingcod populations. (78pp.

Orbital parameters for the ogo-e geo-coronal hydrogen experiment

Geo-coronal hydrogen measurement experiment on OGO-E - methods of obtaining orbital and spacecraft parameters for data analysi

A Survey and an Annotated Bibliography of Fanny Burney Scholarship, 1920-1970

To provide a current survey of the scholarship and an annotated bibliography on Fanny Burney from 1920-1970 for scholars and students is the purpose of this paper

Simplification of Caribbean Reef-Fish Assemblages over Decades of Coral Reef Degradation

Caribbean coral reefs are becoming structurally simpler, largely due to human impacts. The consequences of this trend for reef-associated communities are currently unclear, but expected to be profound. Here, we assess whether changes in fish assemblages have been non-random over several decades of declining reef structure. More specifically, we predicted that species that depend exclusively on coral reef habitat (i.e., habitat specialists) should be at a disadvantage compared to those that use a broader array of habitats (i.e., habitat generalists). Analysing 3727 abundance trends of 161 Caribbean reef-fishes, surveyed between 1980 and 2006, we found that the trends of habitat-generalists and habitat-specialists differed markedly. The abundance of specialists started to decline in the mid-1980s, reaching a low of ~60% of the 1980 baseline by the mid-1990s. Both the average and the variation in abundance of specialists have increased since the early 2000s, although the average is still well below the baseline level of 1980. This modest recovery occurred despite no clear evidence of a regional recovery in coral reef habitat quality in the Caribbean during the 2000s. In contrast, the abundance of generalist fishes remained relatively stable over the same three decades. Few specialist species are fished, thus their population declines are most likely linked to habitat degradation. These results mirror the observed trends of replacement of specialists by generalists, observed in terrestrial taxa across the globe. A significant challenge that arises from our findings is now to investigate if, and how, such community-level changes in fish populations affect ecosystem function

Herbivory and the Resilience of Caribbean Coral Reefs: Knowledge Gaps and Implications for Management

Herbivory is a key process on coral reefs that can facilitate reef-building corals by excluding algae that otherwise negatively impact coral settlement, growth, and survivorship. Over the last several decades, coral cover on Caribbean reefs has declined precipitously. On many reefs, large structurally complex corals have been replaced by algae and other non-reef-building organisms, resulting in the collapse of physical structure and the loss of critical ecosystem services. The drivers of coral decline on Caribbean reefs are complex and vary among locations. On many reefs, populations of key herbivores have been greatly reduced by disease and overfishing, and this has resulted in the proliferation of algae that hinder coral recovery following major disturbances. Yet, evidence that increases in herbivory can promote coral recovery on Caribbean reefs has been mixed. Here, we discuss key contingencies that will modify the relationships between herbivores, algae, and corals and identify critical knowledge gaps that limit our ability to predict when and where herbivores are most likely to facilitate coral persistence and recovery. Impacts of herbivores on coral reef ecosystems will vary greatly in space and time and will depend on herbivore diversity and species identity. While there are still a large number of knowledge gaps, we make several management recommendations based on our current understanding of the processes that structure reef ecosystems. Reversing the fate of Caribbean coral reefs will require the development of integrated management strategies that simultaneously address multiple stressors in addition to the impacts of fisheries on herbivore assemblages

Brightness variation distributions among main belt asteroids from sparse light curve sampling with Pan-STARRS 1

The rotational state of asteroids is controlled by various physical mechanisms including collisions, internal damping and the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. We have analysed the changes in magnitude between consecutive detections of approximately 60,000 asteroids measured by the PanSTARRS 1 survey during its first 18 months of operations. We have attempted to explain the derived brightness changes physically and through the application of a simple model. We have found a tendency toward smaller magnitude variations with decreasing diameter for objects of 1 < D < 8 km. Assuming the shape distribution of objects in this size range to be independent of size and composition our model suggests a population with average axial ratios 1 : 0.85 \pm 0.13 : 0.71 \pm 0.13, with larger objects more likely to have spin axes perpendicular to the orbital plane.Comment: 10 pages, 10 figures, accepted by MNRA

Region-wide temporal and spatial variation in Caribbean reef architecture: is coral cover the whole story?

The architectural complexity of coral reefs is largely generated by reef-building corals, yet the effects of current regional-scale declines in coral cover on reef complexity are poorly understood. In particular, both the extent to which declines in coral cover lead to declines in complexity and the length of time it takes for reefs to collapse following coral mortality are unknown. Here we assess the extent of temporal and spatial covariation between coral cover and reef architectural complexity using a Caribbean-wide dataset of temporally replicated estimates spanning four decades. Both coral cover and architectural complexity have declined rapidly over time, with little evidence of a time-lag. However, annual rates of change in coral cover and complexity do not covary, and levels of complexity vary greatly among reefs with similar coral cover. These findings suggest that the stressors influencing Caribbean reefs are sufficiently severe and widespread to produce similar regional-scale declines in coral cover and reef complexity, even though reef architectural complexity is not a direct function of coral cover at local scales. Given that architectural complexity is not a simple function of coral cover, it is important that conservation monitoring and restoration give due consideration to both architecture and coral cover. This will help ensure that the ecosystem services supported by architectural complexity, such as nutrient recycling, dissipation of wave energy, fish production and diversity, are maintained and enhanced