Group work can become a powerful tool for teaching and learning of mathematics. Grouping strategy is one of the factors that determine the effectiveness of group work. In this paper, the researcher investigated the effectiveness of various strategies for grouping students in a maths class. Learners were placed in groups according to various strategies and given the same treatment under similar conditions. Afterward, a test was administered to gather the feedback of every grouping strategy and the results analyzed. Mixed-ability grouping based on academic achievement was observed to be the most effective grouping strategy.
Mathematics is the backbone of modern science, majorly used to solve world problems. Mathematical proficiency is thus very crucial. A math practice paper (MPP) can become a powerful tool for polishing student's mathematical knowledge and reasoning skills. This paper explores the usefulness of a math practice paper in the teaching and learning of mathematics. It also examines effectiveness of various differentiated strategies of implementing the use of a math practice paper in a diverse classroom. A class of 30 high school students was involved in this study. Students were introduced to math practice papers using various strategies during a term of 14 weeks. Classroom tests and questionnaires were used as instruments for data collection. Results were analyzed and compared. A math practice paper done individually, and then discussed in mixed-ability groups under the teacher intervention was observed to contribute significantly to student achievement. Constant use of MPPs resulted to a positive math trajectory.
We investigate shear banding phenomena in the plane Couette flow of viscoelastic fluids.The viscoelastic fluids are modelled via the Giesekus constitutive equations with stress diffusion. The nonlinear and coupled systems of equations, comprising the momentum equation and the constitutive equations, are solved numerically using semi-implicit finite difference methods. The effects of the fluid parameters on the flow variables are also investigated. Under certain values of the material parameters, we observe formation of shear bands in plane Couette flow.
This paper presents simulations of channelized dam-break flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the Shallow Water equations (SWEs). Particularly, the study aims at assessing the effects of rheological parameters: power-law index (n), consistency index (K) and yield stress (\tau_{c}), on the flow height and velocity over different topographies. Three practical examples of dam-break flow cases are considered: a dam-break on an inclined flat surface, a dam-break over a non-flat topography, and a dam-break over a wet bed. Effects of the bed slope and depth ratios between upstream and downstream fluid levels, on the flow behaviour are also analyzed. Numerical results are compared with experimental data from the literature, and are found to be in good agreement. Results show that for both dry and wet bed conditions, the fluid front position, the peak height, and mean velocity decrease when any of the three rheological parameters is increased. However, based on parametric sensitivity analysis, the power-law index appears to be the dominant factor in dictating the fluid behaviour. Moreover, increasing the bed slope and/or the depth ratio, the wave frontal position moves further downstream. Furthermore, the presence of an obstacle is observed to cause the formation of an upsurge that moves in the upstream direction; which increases by increasing any of the three rheological parameters. The study is useful for an in-depth understanding of the effects of rheology on catastrophic gravity driven flows of non-Newtonian fluids (like lava or mud flows) for risk assessment and mitigation.
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