The influence of mathematics anxiety on pupils' choice of mental calculation strategies for two-digit addition and subtraction.

The ability to calculate mentally is a core skill in mathematics and is now a required feature of mathematics teaching. Mathematics anxiety is an established affective construct, associated with mathematical outcomes. The focus of this research is on the affective construct of mathematics anxiety and this may influence a pupil's choice of mental calculation strategy for two digit addition and subtraction. The main study (preceded by a pilot study) was divided into two parts and focused solely on Year 5 pupils; background data with permission, was obtained for each pupil. In the first part, pupils were given a mental calculation assessment, the Myself As Learner Scale (Burden, 1998) and the Mathematics Anxiety Scale for Children (Chiu Henry, 1990; Beasley, Long Natali, 2001). In the second part, the mental calculation strategies of pupils with either high or low mathematics anxiety was explored individually through a series of two digit addition and subtraction questions. Pupil responses were recorded, transcribed and classified. Strategy classification particularly distinguished pupils partitioning both two digit numbers and only one of the two digit numbers. Pupils with high mathematics anxiety tend to use lower order (less effective) strategies, whereas pupils with low mathematics anxiety tend to use higher order (more effective) strategies. No gender differences were found regarding strategy use. When controlled for mathematical competence, low mathematics anxious pupils produced more accurate mental calculation, whereas high mathematics anxious pupils produced less accurate mental calculations. Implications for Educational Psychologists and teachers in schools are discussed

Finite Density Fat QCD

Lattice formulation of Finite Baryon Density QCD is problematic from computer simulation point of view; it is well known that for light quark masses the reconstructed partition function fails to be positive in a wide region of parameter space. For large bare quark masses, instead, it is possible to obtain more sensible results; problems are still present but restricted to a small region. We present evidence for a saturation transition independent from the gauge coupling $\beta$ and for a transition line that, starting from the temperature critical point at $\mu=0$, moves towards smaller $\beta$ with increasing $\mu$ as expected from simplified phenomenological arguments.Comment: 14 pages, 10 figure

Quenched QCD at finite density

Simulations of quenched $QCD$ at relatively small but {\it nonzero} chemical potential $\mu$ on $32 \times 16^3$ lattices indicate that the nucleon screening mass decreases linearly as $\mu$ increases predicting a critical chemical potential of one third the nucleon mass, $m_N/3$, by extrapolation. The meson spectrum does not change as $\mu$ increases over the same range, from zero to $m_\pi/2$. Past studies of quenched lattice QCD have suggested that there is phase transition at $\mu = m_\pi/2$. We provide alternative explanations for these results, and find a number of technical reasons why standard lattice simulation techniques suffer from greatly enhanced fluctuations and finite size effects for $\mu$ ranging from $m_\pi/2$ to $m_N/3$. We find evidence for such problems in our simulations, and suggest that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte

Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems

Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the non-commutativity, which appears at the intermediate steps, cancels in the end results for physical observables.Comment: 7 pages, 9 figure

Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential

We simulate lattice QCD at non--zero baryon density and zero temperature in the quenched approximation, both in the scaling region and in the infinite coupling limit. We investigate the nature of the forbidden region -- the range of chemical potential where the simulations grow prohibitively expensive, and the results, when available, are puzzling if not unphysical. At weak coupling we have explored the sensitivity of these pathologies to the lattice size, and found that using a large lattice ($64 \times 16^3$) does not remove them. The effective potential sheds considerable light on the problems in the simulations, and gives a clear interpretation of the forbidden region. The strong coupling simulations were particularly illuminating on this point.Comment: 49 pages, uu-encoded expanding to postscript;also available at ftp://hlrz36.hlrz.kfa-juelich.de/pub/mpl/hlrz72_95.p

A deep dive into the ecology of Gamay (Botany Bay, Australia): current knowledge and future priorities for this highly modified coastal waterway

Context: Gamay is a coastal waterway of immense social, cultural and ecological value. Since European settlement, it has become a hub for industrialisation and human modification. There is growing desire for ecosystem-level management of urban waterways, but such efforts are often challenged by a lack of integrated knowledge. Aim and methods: We systematically reviewed published literature and traditional ecological knowledge (TEK), and consulted scientists to produce a review of Gamay that synthesises published knowledge of Gamay’s aquatic ecosystem to identify knowledge gaps and future research opportunities. Key results: We found 577 published resources on Gamay, of which over 70% focused on ecology. Intertidal rocky shores were the most studied habitat, focusing on invertebrate communities. Few studies considered multiple habitats or taxa. Studies investigating cumulative human impacts, long-term trends and habitat connectivity are lacking, and the broader ecological role of artificial substrate as habitat in Gamay is poorly understood. TEK of Gamay remains a significant knowledge gap. Habitat restoration has shown promising results and could provide opportunities to improve affected habitats in the future. Conclusion and implications: This review highlights the extensive amount of knowledge that exists for Gamay, but also identifies key gaps that need to be filled for effective management