Diophantine equations as a context for technology-enhanced training in conjecturing and proving

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification of this topic can provide a discovery experience for prospective secondary teachers and information technology students. Such experience can be extended to include a transition from a computationally driven conjecturing to a formal proof based on a number of simple yet useful techniques.

Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

Maternal concern about her toddler undereating and becoming underweight and use of feeding practices - analysis of the NOURISH and SAIDI cohorts using structural equation modeling

The chubby baby who eats well is desirable in our culture. Perceived low weight gains and feeding concerns are common reasons mothers seek advice in the early years. In contrast, childhood obesity is a global public health concern. Use of coercive feeding practices, prompted by maternal concern about weight, may disrupt a child’s innate self regulation of energy intake, promoting overeating and overweight. This study describes predictors of maternal concern about her child undereating/becoming underweight and feeding practices. Mothers in the control group of the NOURISH and South Australian Infants Dietary Intake studies (n = 332) completed a self-administered questionnaire when the child was aged 12–16 months. Weight-for-age z-score (WAZ)was derived from weight measured by study staff. Mean age (SD) was 13.8 (1.3) months, mean WAZ (SD), 0.58 (0.86) and 49% were male. WAZ and two questions describing food refusal were combined in a structural equation model with four items from the Infant feeding Questionnaire (IFQ) to form the factor ‘Concern about undereating/weight’. Structural relationships were drawn between concern and IFQ factors ‘awareness of infant’s hunger and satiety cues’, ‘use of food to calm infant’s fussiness’ and ‘feeding infant on a schedule’, resulting in a model of acceptable fit. Lower WAZ and higher frequency of food refusal predicted higher maternal concern. Higher maternal concern was associated with lower awareness of infant cues (r = −.17, p = .01) and greater use of food to calm (r = .13, p = .03). In a cohort of healthy children, maternal concern about undereating and underweight was associated with practices that have the potential to disrupt self-regulation.

A critical review of structural equation modeling applications in construction research

Structural equation modeling (SEM) is a versatile multivariate statistical technique, and applications have been increasing since its introduction in the 1980s. This paper provides a critical review of 84 articles involving the use of SEM to address construction related problems over the period 1998–2012 including, but not limited to, seven top construction research journals. After conducting a yearly publication trend analysis, it is found that SEM applications have been accelerating over time. However, there are inconsistencies in the various recorded applications and several recurring problems exist. The important issues that need to be considered are examined in research design, model development and model evaluation and are discussed in detail with reference to current applications. A particularly important issue concerns the construct validity. Relevant topics for efficient research design also include longitudinal or cross-sectional studies, mediation and moderation effects, sample size issues and software selection. A guideline framework is provided to help future researchers in construction SEM applications.