Problem-solving model

Asieba, F.O. Egbugara, O.U. (1993). Evaluation of pupils chemical problemsolving skills using a problem-solving model. Journal of Chemical Education, 70, 38-39. 

Problem-Solving Model. Worked Examples are included in every chapter for students to rrse as... 

Problem solving, modelling and applications are not synonymous, although they are obviously related. For instance, the Discussion Document preparatory to the ICMI Study 14 (Blum et al., 2002), mentions that the term "modeUing" focuses in the direction that goes from the real world towards basic sciences, while the term "applications" goes in the... 

In this chapter we shall consider four important problems in molecular n iudelling. First, v discuss the problem of calculating free energies. We then consider continuum solve models, which enable the effects of the solvent to be incorporated into a calculation witho requiring the solvent molecules to be represented explicitly. Third, we shall consider the simi lation of chemical reactions, including the important technique of ab initio molecular dynamic Finally, we consider how to study the nature of defects in solid-state materials. 

In this section we consider the boundary value problem for model equations of a thermoelastic plate with a vertical crack (see Khludnev, 1996d). The unknown functions in the mathematical model under consideration are such quantities as the temperature 9 and the horizontal and vertical displacements W = (w, w ), w of the mid-surface points of the plate. We use the so-called coupled model of thermoelasticity, which implies in particular that we need to solve simultaneously the equations that describe heat conduction and the deformation of the plate. The presence of the crack leads to the fact that the domain of a solution has a nonsmooth boundary. As before, the main feature of the problem as a whole is the existence of a constraint in the form of an inequality imposed on the crack faces. This constraint provides a mutual nonpenetration of the crack faces ... 

Neural networks have the following advantages (/) once trained, their response to input data is extremely fast (2) they are tolerant of noisy and incomplete input data (J) they do not require knowledge engineering and can be built direcdy from example data (4) they do not require either domain models or models of problem solving and (5) they can store large amounts of information implicitly. 

Additionally, solutions to problems are presented in the text and the accompanying CD contains computer programs (Microsoft Excel spreadsheet and software) for solving modeling problems using numerical methods. The CD also contains colored snapshots on computational fluid mixing in a reactor. Additionally, the CD contains the appendices and conversion table software. 

The IMAS technique described above is useful, in that it addresses aspects of operational skills, that is, diagnostic and problem solving abilities, that are not covered by other techniques. To that extent it can be regarded as a method of cognitive task analysis. It is not essential to use a computer program to obtain useful results. The mental models produced by IMAS can be elicited by pencil and paper methods. Nevertheless interpretation and application of the results require some expertise. 

Notice that the only real dynamics going on here takes place between the A-units and R-units. The dynamical flow of information proceeds directly from input to output layers with no hidden units. We will follow the convention of calling perceptron models that have only input and output layers simple perceptrons. As we will shortly see, the absence of a hidden layer dramatically curtails the simple perceptron s problem solving ability. 

Two-dimensional compressible momentum and energy equations were solved by Asako and Toriyama (2005) to obtain the heat transfer characteristics of gaseous flows in parallel-plate micro-channels. The problem is modeled as a parallel-plate channel, as shown in Fig. 4.19, with a chamber at the stagnation temperature Tstg and the stagnation pressure T stg attached to its upstream section. The flow is assumed to be steady, two-dimensional, and laminar. The fluid is assumed to be an ideal gas. The computations were performed to obtain the adiabatic wall temperature and also to obtain the total temperature of channels with the isothermal walls. The governing equations can be expressed as... 

Bodner, G., Domirr, D. S. (2000). Mental models The role of representations in problem solving in chemistry. University Chemistry Education, 4(1), 22-28. 

Tsaparlis, G., Angelopoulos, V. (2000) A model of problem solving its operation, validity and usefulness in the ease of organie-synthesis problems. Science Education, 84, 131-153. 

Gabel, D. L., Briner, D., Haines, D. (1992). Modelling with magnets A unified approach to chemistry problem solving. The Science Teacher, 59(3), 58-63. 

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