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When using mathematics to solve problems in everyday life, problem solvers must recognize and formulate problems by themselves because structured problems are not provided. Therefore, in general education, fostering learner problem posing is an important task. Because novice learners have difficulty in composing mathematical structures (solutions) in problem posing, learning support to improve the composition of solutions is required. Although learning by solving examples is adopted in general education, it may not be sufficiently effective in fostering learner problem posing because cognitive skills differ between problem solving and problem posing. This study discusses and experimentally investigates the effects of learning from examples on composing solutions when problem posing. We studied three learning activities: learning by solving an example, learning by reproducing an example, and learning by evaluating an example. In our experiment, undergraduates were asked to pose their own new, unique problems from a base problem initially presented after the students learned an example by solving, reproducing, or evaluating it. The example allowed the undergraduates to gain ideas for composing a novel solution. The results indicated that learning by reproducing the example was the most effective in fostering the composition of solutions.

SUMMARYIn this study, an e-learning system is developed to handle the e-learning environment based on the learning ecological model. In the learning ecological model, which represents the comprehensive e-learning environment, not only the contents of learning, but also the learning environment are managed and provided, based on the content, the goal, and the configuration of the learning. The major purpose of this study is to realize the function that can manage the diversified learning objects with various information granularities and representation formats, using the learning object metadata, so that each learner can utilize the learning object based on the learning scenario, which is matched to the individual learner. The learning scenario is constructed by sequencing the learning objects based on the learning necessity, the learning history information, and the curriculum information of the object of learning, according to the characteristics of the learning object. As the sequencing procedure, the sequencing of the learning objects is considered, by applying the optimization technique of the multi-objective optimization problem, so that multiple evaluation viewpoints are simultaneously satisfied. The genetic algorithm is used as the optimization procedure. The learning object metadata and the sequencing of the learning objects are discussed in detail in this paper. The evaluation of the developed e-learning system is also described.

In this research, a computational model that simulates the mental function of multicolor aesthetic evaluation through backpropagation neural networks was constructed. Helmut Leder's psychological model served as the theoretical framework. We determined the macro‐architecture of the computational model through two psychological experiments using the semantic differential (SD) method. The aesthetic score of a multicolor stimulus is defined as the inverse of its factor score on the factor “Pleasure” extracted in the first experiment, and each of the three factors extracted in the second experiment—i.e., “Stability,” “Heaviness,” and “Presence”—is regarded as a simple perceptual feature. The genetic algorithm was then employed to optimize the hidden layer node number, the learning rate, and the momentum constant of each neural network. In two simulation tests, this computational model exhibited some predictive power, implying that the model can be regarded as a relatively successful approximation of the psychological mechanism of multicolor aesthetic evaluation. In addition, the results of the second simulation also show that the perceptual feature “Heaviness” possesses the principal impact on the aesthetic evaluation of multicolor objects, whereas the other two perceptual features “Stability” and “Presence” have a minor influence. The heavier and/or more stable a multicolor object is perceived to be, the less aesthetically pleasing it is. Conversely, the stronger the sense of matter presence a multicolor object elicits, the more aesthetically appealing it is. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 216–235, 2017

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