Department Chair, University Of St. La Salle
Interesting discovery of metacognitive processes helpful in problem solving.
Problem solving has become the core value of 21st century mathematics learning but concern on improving one's capability in doing so is still a continued quest. In response to the need, this study aimed to determine possible presence and interrelationships of metacognitive processes in successful mathematical problem solving. Metacognitive processes are considered by this study as indicators of metacognition. Metacognition is known as 'thinking of thinking' or reflective thought processes responsible for regulating our own way of thinking. This study also sought to describe qualities of metacognitive solutions, identify factors that contribute to the emergence of these qualities, and determine stages of problem solving that require the said metacognitive processes. As guided by constructivist view in making new knowledge, the researcher found the covert cognitive phenomenon from 11 key informants. Corbin & Strauss (1990) grounded theory approach was modified to guide and attain this study's purpose through documents, interview, and observation data generation and coding analyses. Ethics requirement were addressed. Experts participation from the fields of mathematics, psychology, and education ensured the validity and trustworthiness of this study's methodology and results. Findings revealed that there are 3 clusters of metacognitive processes present in successful problem solving solutions. These are 1) metacognitive problem solving task-related knowledge, 2) metacognitive problem solving affect and motion experiences, and 3) metacognitve solution qualities manifested to be the 10 micro-metacognitive controls instrumental in achieving successful mathematical problem solving. The first two clusters of metacognitve processes is made up of the six emerging themes of metacognitive processes which are influential in the occurrence of the said 10 metacognitive controls. Results further revealed the emerging macro-metacognitive stages in problem solving, namely, 1) Big Understanding Process, 2) Conceptualization of Mathematical Solution Strategy, and 3) Execution of the conceptualized solution. Findings end with 6 propositions of the emerging grounded theory framework of metacognition in successful problem solving. Implication and recommendation emphasize on the integration of thinking skills and strategies, affect and bodily motion, micro and macro metacognitive experiences and exercises, curriculum review, and conduct of further studies and local researches.
Abstract: The present paper aims at building a fast and accurate phase transition solver dedicated to unsteady multiphase flow computations. In a previous contribution (Chiapolino et al. 2017), such a solver was successfully developed to compute thermodynamic equilibrium between a liquid phase and its corresponding vapor phase. The present work extends the solver’s range of application by considering a multicomponent gas phase instead of pure vapor, a necessary improvement in most practical applications. The solver proves easy to implement compared to common iterative procedures, and allows systematic CPU savings over 50%, at no cost in terms of accuracy. It is validated against solutions based on an accurate but expensive iterative solver. Its capability to deal with cavitating, evaporating and condensing two-phase flows is highlighted on severe test problems both 1D and 2D.
Pub.: 27 Mar '17, Pinned: 08 Oct '17
Abstract: •Numerical investigation of droplet migration in a macro and micro-channel flows.•Study of physical parameters impacts on equilibrium status of drops in channel flows.•Proposing a novel method for uncertainty quantification of two-phase channel flows.•Obtaining a faster convergence rate in comparison with Monte Carlo simulations.
Pub.: 01 Sep '17, Pinned: 08 Oct '17
Abstract: Piezoelectric fans have been studied extensively and are seen as a promising technology for thermal management due to their ability to provide quiet, reliable cooling with low power consumption. The fluid mechanics associated with a piezoelectric fan are similar to that for a flapping bird wing, which are known to be complex. This paper is the first to investigate the three-dimensional fluid mechanics of an unconfined fan operating in its first vibration frequency mode. A custom built experimental facility was developed to capture the fan's flow field using two-dimensional phase locked Particle Image Velocimetry (PIV). The fluid-structure interaction was also captured through unique two-way coupled three-dimensional simulations of an oscillating beam in which the beam is actuated by a shear force at its resonant frequency and interacts with the surrounding air. This forgoes the need for temporal beam displacement data from experiments as in previous studies, allowing the numerical technique to be used independently. A finite element method is used for the simulations which allows the two-way coupling while maintaining computational efficiency. A three dimensional λ2 criterion constructed from interpolated PIV measurements as well as numerical data was used to identify a horse shoe vortex in the vicinity of the fan and its evolution into a hairpin vortex before it breaks up due to a combination of vortex shedding and flow along the fan blade. The experimental and numerical data are comparatively in agreement, confirming that the methods presented are valid for capturing the complex flow fields generated by this fluid-structure interaction. The results provide both a fundamental understanding on the formation and break-up of vortices from an oscillating beam, and demonstrate a validated approach which can be applied in the development of high efficiency piezoelectrically driven air moving devices and extended to the study of flapping bird and UAV wings.
Pub.: 06 Mar '17, Pinned: 08 Oct '17
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