Future global challenges that engineering graduates face have placed demands on engineering education and how graduates develop competency in collaborative problem-solving. Such demand has seen an increase in the use of pedagogies like problem-based learning (PBL) that provide opportunities for developing collaborative problem-solving skills. PBL has been well studied however there is still much to understand about 'how' students solve problems collaboratively in PBL settings. This work investigates the processes taking place when students set out to solve problems in a group. Naturalistic data from video recordings of participants in chemical process design PBL sessions is used. Participants conversations were transcribed and their language analysed using qualitative content analysis to provide a description of 'what' strategies students use. The findings indicate that students tend to adhere to relatively rigid structures and minimize effort when tackling unfamiliar ill-defined problems. Additionally, students appear to struggle making connections between knowledge domains.
Foam drainage is considered in a froth flotation cell. Air flow through the foam is described by a simple two-dimensional deceleration flow, modelling the foam spilling over a weir. Foam microstructure is given in terms of the number of channels (Plateau borders) per unit area, which scales as the inverse square of bubble size. The Plateau border number density decreases with height in the foam, and also decreases horizontally as the weir is approached. Foam drainage equations, applicable in the dry foam limit, are described. These can be used to determine the average cross-sectional area of a Plateau border, denoted A, as a function of position in the foam. Quasi-one-dimensional solutions are available in which A only varies vertically, in spite of the two-dimensional nature of the air flow and Plateau border number density fields. For such situations the liquid drainage relative to the air flow is purely vertical. The parametric behaviour of the system is investigated with respect to a number of dimensionless parameters: K (the strength of capillary suction relative to gravity), α (the deceleration of the air flow), and n and h (respectively, the horizontal and vertical variations of the Plateau border number density). The parameter K is small, implying the existence of boundary layer solutions: capillary suction is negligible except in thin layers near the bottom boundary. The boundary layer thickness (when converted back to dimensional variables) is independent of the height of the foam. The deceleration parameter α affects the Plateau border area on the top boundary: weaker decelerations give larger Plateau border areas at the surface. For weak decelerations, there is rapid convergence of the boundary layer solutions at the bottom onto ones with negligible capillary suction higher up. For strong decelerations, two branches of solutions for A are possible in the K = 0 limit: one is smooth, and the other has a distinct kink. The full system, with small but non-zero capillary suction, lies relatively close to the kinked solution branch, but convergence from the lower boundary layer onto this branch is distinctly slow. Variations in the Plateau border number density (non-zero n and h) increase individual Plateau border areas relative to the case of uniformly sized bubbles. For strong decelerations and negligible capillarity, solutions closely follow the kinked solution branch if bubble sizes are only slightly non-uniform. As the extent of non-uniformity increases, the Plateau border area reaches a maximum corresponding to no net upward velocity of foam liquid. In the case of vertical variation of number density, liquid content profiles and Plateau border area profiles cease to be simply proportional to one another. Plateau border areas match at the top of the foam independent of h, implying a considerable difference in liquid content for foams which exhibit different number density profiles.PACS. 47.55.Dz Drops and bubbles -82.70.Rr Aerosols and foams
Puzzle-based Learning is under-used in the teaching of mathematics to engineers. It is argued here that embedding puzzles in the teaching of other subjects enhances students' learning by developing their problem-solving and independent-learning skills, whilst increasing their motivation to learn mathematics.The authors have defined a puzzle to be a problem that is perplexing and either has a solution requiring considerable ingenuity -perhaps a lateral thinking solution -or possibly results in an unexpected, even a counter-intuitive or apparently paradoxical solution.Engineering specific puzzle variants may help student learning, but specificity can also conflict with desirable simplicity, undermining the pedagogic value of a puzzle.It is not easy to categorize puzzles by level of difficulty, whether of the puzzle as a whole or the underlying mathematics, because this depends on the background and experience of the student.Classroom experiences of using puzzles in engineering teaching are described here, with some puzzles that illuminate these issues.
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