Teaching square roots: conceptual complexity in mathematics language

The article presents strategies for communicating the concept of square roots to limited English-proficient students. Instead of using mathematical terminology, mathematics teachers could communicate the concept of square roots by integrating the literal concept of square to the actual meaning of a square root. Such approach addresses the learning difficulty experienced by limited English proficient students who tend to associate square roots to geometric concepts. Several strategies for illustrating the concept of a square root using square figures are presented.

A soil-free plant growth system to facilitate analysis of plant pathogen interactions in roots

Analysis of the interaction of pathogens with plant roots is often complicated by the growth of plants in a soil substrate. A soil-free plant growth system (SPS) was developed that removes the need for a substrate while supporting the growth of seedlings in a nutrient rich, oxygenated environment. The model legume Lupinus angustifolius was used to compare the growth of seedlings within soil and the SPS. Seedlings grown under both conditions were similar in morphology, anatomy and health (measured by leaf chlorophyll abundance) and importantly there was little difference in root growth and development although straighter and fuller root systems were achieved in the SPS. The ease of access to the root system proved efficient for the analysis of root and pathogen interactions with no interference from soil or adhering particulate matter. Following inoculation of L. angustifolius roots with Phytophthora cinnamomi the host/pathogen interaction was easily observed and tissues sampled undamaged.

Why do Australians, New Zealanders and Americans travel to Fiji? Evidence from cointegration, unit roots and parameter stability tests

The aim of this study was to estimate the demand for Fiji’s tourism from its three main source markets—Australia, New Zealand, and the US—using the bounds testing approach to cointegration. Our main finding was that visitor arrivals to Fiji and its key determinants are cointegrated over the 1970–2000 period. We then used the autoregressive distributed lag model to estimate short-run and long-run elasticities and found that income in origin countries, transport costs, and prices were significant determinants of Fiji’s tourism demand. We also found that coups negatively impact visitor arrivals from all markets. In testing for parameter stability, we established that the series were integrated of order one in the presence of a structural break. We then used the Hansen test for parameter stability and found that the parameters of our long-run model are stable over time.

Structural breaks and unit roots in Australian macroeconomic time series

We examine the unit root properties of 16 Australian macroeconomic time series using monthly data spanning the period 1960–2004. In addition to the standard Augmented Dickey Fuller (ADF) test, we implement one- and two-break endogenous structural break ADF-type unit root tests as well as one- and two-break Lagrange multiplier (LM) unit root tests. While the ADF test provides relatively little evidence against the unit root null hypothesis, once we allow for structural breaks we are able to reject the unit root null for just under half of the variables at the 10% level or better.

Profiling secondary metabolites of plant roots inoculated with Phytophthora cinnamomi

The soil-borne pathogen, Phytophthora cinnamomi, continues to cause severe dieback in Australian native forest species and is of great international significance due to its global distribution. This research established a protocol to successfully identify phyto-chemicals associated with the defense response of plants challenged by the disease caused by Phytophthora cinnamomi.

The historical roots of public diplomacy and their significance for India

Traces the evolution of the practice and conceptualisations of public diplomacy, especially with reference to India's recent ventures in this field