Building and assessing subject knowledge in mathematics for pre-service students

In planning and teaching curriculum courses for pre-service primary teachers, both within a one-year Post Graduate Certificate of Education (PGCE) programme, and in a four-year undergraduate degree leading to Qualified Teacher Status (QTS), we have always been aware that mathematics presents particular problems because of the experiences and attitudes students bring to the subject. We have always tried to balance students’ learning about how children learn mathematics in school, with reflection on their own experiences as learners, and with understanding of the mathematical content of the curriculum. In the past, mathematical content has generally been approached indirectly through discussion of activities and materials appropriate for the primary classroom. However the recent introduction in the U.K. of a National Curriculum for Primary Mathematics in Initial Teacher Training (ITT) which places considerable emphasis on students’ subject knowledge, has meant that we have had to rethink the balance within courses, and to place much more overt emphasis on developing students’ mathematical knowledge. In this paper we describe the way in which we have approached building and assessing mathematical knowledge during the pilot phase of the ITT National Curriculum, examine some of the students’ responses to our approach, and discuss the issues this has raised

Twitter’s big hitters

We describe the results of a new computational experiment on Twitter data. By listening to Tweets on a selected topic, we generate a dynamic social interaction network. We then apply a recently proposed dynamic network analysis algorithm that ranks Tweeters according to their ability to broadcast information. In particular, we study the evolution of importance rankings over time. Our presentation will also describe the outcome of an experiment where results from automated ranking algorithms are compared with the views of social media experts

Upwelling, offshore transport, and the availability of rockfish in central California

EXTRACT (SEE PDF FOR FULL ABSTRACT): We used the diet of a seabird, the common murre (Uria aalge), nesting on Southeast Farallon Island and feeding in the Gulf of the Farallones, California, as an index to abundance of juvenile rockfish, then related fish abundance to indices of turbulence and upwelling over an 18-year period, 1973-1990. Strong, persistent upwelling or downwelling led to reduced availability of fish in the study area, in contrast to great abundance when upwelling was mild or pulsed. ... On the basis of our study, one effect might be that fishes thought strong enough to resist Ekman transport could be transported out of normal areas of recruitment

Chance Re-encounters: 'Computers in Probability Education' revisited

In recognition of Rolf Biehler’s contribution to probability and statistics education, we chose to re-visit his chapter in the edited book, Chance Encounters: Probability in Education. In particular, we examine three themes concerning the concept-tool gap, levels of access to concepts, which can be concealed by technology, and issues around demonstration and proof. We found many insights that resonate with current practice two decades later. Nevertheless, we argue that during that time, some progress has been made in how we can conceptualise the issues. For example, we discuss: (i) how it is now possible to unpick the metaphorical understanding that could emerge from the use of black boxes by reference to utility-based understanding; (ii) four principles that could inform how black boxes might be designed to support utility-based understanding; (iii) how the importance of explanation may overshadow a more traditional emphasis on proof

New Technologies Aid Understanding of the Factors Affecting Adélie Penguin Foraging

The Ross Sea (Figure 1) is home to 33% of the world’s Adélie penguins (Pygoscelis adeliae), as well as substantial numbers of Emperor penguins (Aptenodytes forsteri), Weddell seals (Leptonychotes weddellii), and pelagic birds (Smith et al., 2014). Among these, the Commission for the Conservation of Antarctic Marine Resources (CCAMLR) has designated the Adélie penguin an “indicator species” for monitoring ecosystem structure and function in the newly designated Ross Sea Region Marine Protected Area (RSR-MPA). This penguin, among the best-known seabirds, has been studied for decades at multiple locations with investigations that have delved into its population history (both recent and through thousands of years), survival strategies, responses to environmental changes, and feeding ecology (summarized in Ainley, 2002, with numerous papers published thereafter)

Physical and biological variables affecting seabird distributions during the upwelling season of the northern California Current

Author Posting. © The Authors, 2004. This is the author's version of the work. It is posted here by permission of Elsevier B. V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 52 (2005): 123-143, doi:10.1016/j.dsr2.2004.08.016.As a part of the GLOBEC-Northeast Pacific project, we investigated variation in the abundance of marine birds in the context of biological and physical habitat conditions in the northern portion of the California Current System (CCS) during cruises during the upwelling season 2000. Continuous surveys of seabirds were conducted simultaneously in June (onset of upwelling) and August (mature phase of upwelling) with ocean properties quantified using a towed, undulating vehicle and a multi-frequency bioacoustic instrument (38-420 kHz). Twelve species of seabirds contributed 99% of the total community density and biomass. Species composition and densities were similar to those recorded elsewhere in the CCS during earlier studies of the upwelling season. At a scale of 2-4 km, physical and biological oceanographic variables explained an average of 25% of the variation in the distributions and abundance of the 12 species. The most important explanatory variables (among 14 initially included in each multiple regression model) were distance to upwelling-derived frontal features (center and edge of coastal jet, and an abrupt, inshore temperature gradient), sea-surface salinity, acoustic backscatter representing various sizes of prey (smaller seabird species were associated with smaller prey and the reverse for larger seabird species), and chlorophyll concentration. We discuss the importance of these variables in the context of what factors may be that seabirds use to find food. The high seabird density in the Heceta Bank and Cape Blanco areas indicate them to be refuges contrasting the low seabird densities currently found in most other parts of the CCS, following decline during the recent warm regime of the Pacific Decadal Oscillation.Support from National Science Foundation Grant OCE-0001035, National Oceanic and Atmospheric Administration (NOAA)/Woods Hole Oceanographic Institution-CICOR Grant NA17RJ1223 is gratefully acknowledged