A teaching experiment to foster the conceptual understanding of multiplication based on children's literature to facilitate dialogic learning

The importance of conceptual understanding as opposed to low-level procedural knowledge in mathematics has been well documented (Hiebert & Carpenter, 1992). Development of conceptual understanding of multiplication is fostered when students recognise the equal group structure that is common in all multiplicative problems (Mulligan & Mitchelmore, 1996). This paper reports on the theoretical development of a transformative teaching experiment based on conjecture-driven research design (Confrey & Lachance, 1999) that aims to enhance Year 3 students’ conceptual understanding of multiplication. The teaching experiment employs children’s literature as a motivational catalyst and mediational tool for students to explore and engage in multiplication activities and dialogue. The SOLO taxonomy (Biggs & Collis, 1989) is used to both frame the novel teaching and learning activities, as well as assess the level of students’ conceptual understanding of multiplication as displayed in the products derived from the experiment. Further, student’s group interactions will be analysed in order to investigate the social processes that may contribute positively to learning

Transient technique for measuring heat transfer coefficients on stator airfoils in a jet engine environment

A transient technique was used to measure heat transfer coefficients on stator airfoils in a high-temperature annular cascade at real engine conditions. The transient response of thin film thermocouples on the airfoil surface to step changes in the gas stream temperature was used to determine these coefficients. In addition, gardon gages and paired thermocouples were also utilized to measure heat flux on the airfoil pressure surface at steady state conditions. The tests were conducted at exit gas stream Reynolds numbers of one-half to 1.9 million based on true chord. The results from the transient technique show good comparison with the steady-state results in both trend and magnitude. In addition, comparison is made with the STAN5 boundary layer code and shows good comparison with the trends. However, the magnitude of the experimental data is consistently higher than the analysis

Combustor flame flashback

A stainless steel, two-dimensional (rectangular), center-dump, premixed-prevaporized combustor with quartz window sidewalls for visual access was designed, built, and used to study flashback. A parametric study revealed that the flashback equivalence ratio decreased slightly as the inlet air temperature increased. It also indicated that the average premixer velocity and premixer wall temperature were not governing parameters of flashback. The steady-state velocity balance concept as the flashback mechanism was not supported. From visual observation several stages of burning were identified. High speed photography verified upstream flame propagation with the leading edge of the flame front near the premixer wall. Combustion instabilities (spontaneous pressure oscillations) were discovered during combustion at the dump plane and during flashback. The pressure oscillation frequency ranged from 40 to 80 Hz. The peak-to-peak amplitude (up to 1.4 psi) increased as the fuel/air equivalence ratio was increased attaining a maximum value just before flashback. The amplitude suddenly decreased when the flame stabilized in the premixer. The pressure oscillations were large enough to cause a local flow reversal. A simple test using ceramic fiber tufts indicated flow reversals existed at the premixer exit during flickering. It is suspected that flashback occurs through the premixer wall boundary layer flow reversal caused by combustion instability. A theoretical analysis of periodic flow in the premixing channel has been made. The theory supports the flow reversal mechanism

The Early Promise of TBRI Implementation in Schools

The program known as Trust Based Relational Intervention® (TBRI®) began as an exploration into the detrimental behaviors of foster and adopted children placed in homes with unsuspecting caregivers who assumed their living environment would result in positive results rather than fear based emotions and behaviors. The researchers at the Karyn Purvis Institute of Child Development (KPICD) at Texas Christian University held summer camps for adopted children and through that work developed an intervention to meet the needs of children who had experienced trauma. KPICD identifies these young people as “children from hard places” (Purvis & Cross, 2005). Copeland et al (2007) reported that an estimated 68% of children in the United States have experienced some sort of trauma. This astounding statistic holds great meaning for teachers and administrators, because these children from hard places routinely manifest aggressive and undesired behaviors due to an altering of their physiology. The literature on TBRI® at this point mostly has chronicled success with families, group homes and summer camps (McKenzie, Purvis, & Cross, 2014; Howard, Parris, Neilson, Lusk, Bush, Purvis & Cross, 2014; Purvis & Cross, 2006). TBRI® has only recently been implemented in school settings. This report provides an overview of the impacts of trauma, trauma related work in schools, and the four articles published to this point related to the use of TBRI® in schools

Mean flow instabilities of two-dimensional convection in strong magnetic fields

The interaction of magnetic fields with convection is of great importance in astrophysics. Two well-known aspects of the interaction are the tendency of convection cells to become narrow in the perpendicular direction when the imposed field is strong, and the occurrence of streaming instabilities involving horizontal shears. Previous studies have found that the latter instability mechanism operates only when the cells are narrow, and so we investigate the occurrence of the streaming instability for large imposed fields, when the cells are naturally narrow near onset. The basic cellular solution can be treated in the asymptotic limit as a nonlinear eigenvalue problem. In the limit of large imposed field, the instability occurs for asymptotically small Prandtl number. The determination of the stability boundary turns out to be surprisingly complicated. At leading order, the linear stability problem is the linearisation of the same nonlinear eigenvalue problem, and as a result, it is necessary to go to higher order to obtain a stability criterion. We establish that the flow can only be unstable to a horizontal mean flow if the Prandtl number is smaller than order , where B0 is the imposed magnetic field, and that the mean flow is concentrated in a horizontal jet of width in the middle of the layer. The result applies to stress-free or no-slip boundary conditions at the top and bottom of the layer

Magnetic buoyancy instabilities in the presence of magnetic flux pumping at the base of the solar convection zone

We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer (‘the convection zone’) on magnetic buoyancy instabilities in a lower layer (‘the upper parts of the radiative interior – including the tachocline’), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfvén speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer. In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior

How can large-scale twisted magnetic structures naturally emerge from buoyancy instabilities?

We consider the three-dimensional instability of a layer of horizontal magnetic field in a polytropic atmosphere where, contrary to previous studies, the field lines in the initial state are not unidirectional. We show that if the twist is initially concentrated inside the unstable layer, the modifications of the instability reported by several authors (see e.g. Cattaneo et al. (1990)) are only observed when the calculation is restricted to two dimensions. In three dimensions, the usual interchange instability occurs, in the direction fixed by the field lines at the interface between the layer and the field-free region. We therefore introduce a new configuration: the instability now develops in a weakly magnetised atmosphere where the direction of the field can vary with respect to the direction of the strong unstable field below, the twist being now concentrated at the upper interface. Both linear stability analysis and non-linear direct numerical simulations are used to study this configuration. We show that from the small-scale interchange instability, large-scale twisted coherent magnetic structures are spontaneously formed, with possible implications to the formation of active regions from a deep-seated solar magnetic field