Implementation and evaluation of a method to support learning of a production task for generation of creativity in mathematical learning

为了在数学教育中促进创造力的产生，我们实现了一种产生式任务的智能学习支持方法，并对该方法进行了实证评估。为了产生创造力，除了解决给定问题的常见活动外，还需要为学习者提供一项需要学习者自己产生想法的活动。虽然常见的问题解决学习活动通常使用示例，但在生产任务的学习中还没有建立这样的常规方法。我们首先提出了一种在问题提出中使用实例及其支持方法的学习活动，即学习者将自己的问题作为产出性任务提出。学习活动的基本框架如下。学习者被给予一个问题作为提出问题的例子，以及指示该例子是如何产生的规范过程的信息。信息是自动生成的。学习者复制…更多的例子是通过遵循过程信息。这有望帮助学习者理解在生成示例时使用的深层思想。然后，我们实现了一个智能支持系统，该系统提供了所提出的学习活动，并通过实验验证了该系统是否能够改善学习者的问题提出。我们首先证实，初学者很少通过改变给定问题的结构来提出新问题，而且他们自己组成的问题结构大多是简单的或不合适的。实验结果证明，通过使用该系统再现一个例子进行学习，可以促进通过改变问题结构和例子中使用的想法来合成问题。进一步的实验研究证明，再生式学习可以促进学习者用自己的新想法提出问题。然而，研究也表明，一些学习者未能成功地再现一个给定的例子，他们的问题提出没有得到改善。我们相信，我们的研究成功地为数学创造力教育中的学习活动提供了一种基本的支持方法。然而，为了使这种方法适用于普通教育，我们必须引入一种额外的方法来帮助那些通过复制学习失败的学习者。较少

To contribute to generation of creativity in mathematical education, we implemented an intelligent learning supporting method for a production task and empirically evaluated the method. To generate creativity, it is necessary to provide learners with an activity which requires production of ideas by the learners themselves, in addition to the common activity to reach answers of given problems. Although the common learning activity of problem solving conventionally uses examples, no such conventional method has been established in learning of a production task. We first proposed a learning activity by using examples and its supporting method in problem posing where learners pose their own problems as a production task. The basic framework of the learning activity is as follows. A learner is given a problem as an example of problem posing and information of normative processes indicating how the example is generated. The information is automatically generated. The learner reproduces the … More example by following the process information. That is expected to help the learner in understanding deep ideas used in generation of the example. We then implemented an intelligent support system which provides the proposed learning activity and experimentally confirmed whether the system could improve problem posing by learners. We precedently confirmed that novice learners hardly posed novel problems by altering structures of given problems, and that problem structures composed by themselves were mostly simple or inappropriate. The experimental results proved that learning through reproducing an example by using the system facilitated generation of problems composed by altering problem structures with ideas used in the example. Further experimental study proved that learning by reproduction can facilitate problem posing by novel ideas of learners themselves. However, it also revealed that some of the learners failed reproduction of a given example and their problem posing was not improved. We believe that our studies successfully established a basic method to support learning activities in creativity education for mathematics. To adapt the method to general education, however, we must introduce an additional method to help learners who fail learning by reproduction. Less