The coherence of enactivism and mathematics education research: A case study

This article addresses the question of the coherence of enactivism as a research perspective by making a case study of enactivism in mathematics education research. Main theoretical directions in mathematics education are reviewed and the history of adoption of concepts from enactivism is described. It is concluded that enactivism offers a ‘grand theory’ that can be brought to bear on most of the phenomena of interest in mathematics education research, and so it provides a sufficient theoretical framework. It has particular strength in describing interactions between cognitive systems, including human beings, human conversations and larger human social systems. Some apparent incoherencies of enactivism in mathematics education and in other fields come from the adoption of parts of enactivism that are then grafted onto incompatible theories. However, another significant source of incoherence is the inadequacy of Maturana’s definition of a social system and the lack of a generally agreed upon alternative

Peruvian Beach Ridges: Records of Human Activity and Climate Change

Among the many unusual features of the desert coast of northern Peru are the five major beach-ridge sets: Santa (9˚S), Piura (5˚30\u27 S), Colán (5˚S), Chira (4˚50\u27 S), and Tumbes (3˚40’ S). These features of the landscape began forming after 5800 cal yr B.P., initiated by severe El Niño and seismic events. Archaeological remains on the beach-ridge sets of Santa, Colán, and Chira provide evidence of local prehistoric peoples. The extent of prehistoric occupation and utilization of beach ridges varied due to environmental limitations influenced by beach-ridge substrate material, local paleoenvironments, and climate-change events

Benthic Macrofauna of the New York Bight, 1979-89

The benthic macrofauna of the New York Bight has been monitored extensively, primarily to determine trends over space and time in biological effects of waste inputs. In the present study, from 44 to 48 stations were sampled each summer from 1980-1985. Data from other Bight benthic studies are included to· extend the temporal coverage from 1979 to 1989. Numbers of species and amphipods per sample, taken as relatively sensitive indicators of environmental stress, showed consistent spatial patterns. Lowest values were found in the Christiaensen Basin and other inshore areas, and numbers increased toward the outermost shelf and Hudson Shelf Valley stations. There were statistically significant decreases in species and amphipods at most stations from 1980 to 1985. (Preliminary data from a more recent study suggest numbers of species increased again between 1986 and 1989.) Cluster analysis of 1980-85 data indicated several distinct assemblages-sewage sludge dumpsite, sludge accumulation area, inner Shelf Valley, outer Shelf Valley, outer shelf-with little change over time. The "enriched" and "highly altered" assemblages in the Basin appear similar to those reported since sampling began there in 1968. No consistently defaunated areas have been found in any sampling programs over the past 20 years. On a gross level, therefore, recent faunal responses to any environmental changes are not evident, but the more sensitive measures used, i.e. numbers of species and amphipods, do indicate widespread recent effects. Causes of the faunal changes are not obvious; some possibilities, including increasing effects of sewage sludge or other waste inputs, natural factors, and sampling artifacts, are discussed. (PDF file contains 54 pages.

Molecular electrostatic potentials by systematic molecular fragmentation

A simple method is presented for estimating the molecular electrostatic potential in and around molecules using systematic molecular fragmentation. This approach estimates the potential directly from the electron density. The accuracy of the method is established for a set of organic molecules and ions. The utility of the approach is demonstrated by estimating the binding energy of a water molecule in an internal cavity in the protein ubiquitin

Flux calibration of the AAO/UKST SuperCOSMOS H-alpha Survey

The AAO/UKST SuperCOSMOS H$\alpha$ Survey (SHS) was, when completed in 2003, a powerful addition to extant wide-field surveys. The combination of areal coverage, spatial resolution and sensitivity in a narrow imaging band, still marks it out today as an excellent resource for the astronomical community. The 233 separate fields are available online in digital form, with each field covering 25 square degrees. The SHS has been the motivation for equivalent surveys in the north, and new digital H$\alpha$ surveys now beginning in the south such as VPHAS+. It has been the foundation of many important discovery projects with the Macquarie/AAO/Strasbourg H$\alpha$ planetary nebula project being a particularly successful example. However, the full potential of the SHS has been hampered by lack of a clear route to acceptable flux calibration from the base photographic data. We have determined the calibration factors for 170 individual SHS fields, and present a direct pathway to the measurement of integrated H$\alpha$ fluxes and surface brightnesses for resolved nebulae detected in the SHS. We also include a catalogue of integrated H$\alpha$ fluxes for $>$100 planetary and other nebulae measured from the SHS, and use these data to show that fluxes, accurate to $\pm$ 0.10 - 0.14 dex ($\sim$25-35 per cent), can be obtained from these fields. For the remaining 63 fields, a mean calibration factor of 12.0 counts pix$^{-1}$ R$^{-1}$ can be used, allowing the determination of reasonable integrated fluxes accurate to better than $\pm$0.2 dex ($\sim$50 per cent). We outline the procedures involved and the caveats that need to be appreciated in achieving such flux measurements. This paper forms a handy reference source that will significantly increase the scientific utility of the SHS.Comment: 14 pages, 12 figures, 2 tables (plus 7 pp. of supplementary online information). Version to appear in MNRA

How are proof and proving conceptualized in mathematics curriculum documents in the USA and Japan?

Only a few international comparative studies have reported on proof and proving in curriculum documents. This report proposes a method of comparing the meaning of proof-related words in two specific countries’ curriculum documents (the USA and Japan) through quantitative and interpretative analyses. Using a text mining approach to explore text data, we found that the co-occurrence network of the words “proof” and “prove” in curriculum documents from the two countries is quite different. In the USA, the word “proof” is concerned with justification and “prove” is used as a general process, while in Japan “proof” is more related to discovery and “prove” is more associated with specific theorems.This research was supported by JSPS KAKENHI (JP20KK0053, JP20K14013)

Letter. On the activation of [CrCl3{R-SN(H)S-R}] catalysts for selective trimerization of ethene: a freeze-quench Cr K-edge XAFS study

Homogeneous chromium catalysts for the selective conversion of ethene to hex-1-ene are formed from Cr(III) reagents, amino-thioether ligands of the type HN(CH2CH2SR)2, and aluminum reagents. In this study the early activation steps are investigated by EPR, UV-visible and Cr K-edge XAFS spectroscopy; rapid stopped-flow mixing and a freeze-quench allows good quality EXAFS analysis of a species formed in ~ 1 second of reaction. This is shown to involve reduction to Cr(II) and deprotonation of a NH group of the auxiliary ligand. This 4-coordinate metal-center may act as precursor for the coordination of ethene and subsequent selective oligomerization

Hydrothermal activity lowers trophic diversity in Antarctic sedimented hydrothermal vents

Sedimented hydrothermal vents are those in which hydrothermal fluid vents through sediment and are among the least studied deep-sea ecosystems. We present a combination of microbial and biochemical data to assess trophodynamics between and within hydrothermally active and off-vent areas of the Bransfield Strait (1050–1647 m depth). Microbial composition, biomass and fatty acid signatures varied widely between and within vent and non-vent sites and provided evidence of diverse metabolic activity. Several species showed diverse feeding strategies and occupied different trophic positions in vent and non-vent areas and stable isotope values of consumers were generally not consistent with feeding structure morphology. Niche area and the diversity of microbial fatty acids reflected trends in species diversity and was lowest at the most hydrothermally active site. Faunal utilisation of chemosynthetic activity was relatively limited but was detected at both vent and non-vent sites as evidenced by carbon and sulphur isotopic signatures, suggesting that the hydrothermal activity can affect trophodynamics over a much wider area than previously thought