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

为了促进数学教育中创造力的产生，我们实施了一个智能学习支持方法的生产任务和实证评估的方法。为了产生创造力，有必要为学习者提供一种活动，这种活动要求学习者自己产生想法，除了共同的活动来解决给定的问题。虽然通常的问题解决的学习活动通常使用示例，但是在生产任务的学习中还没有建立这样的传统方法。我们首先提出了一个学习活动，通过使用的例子和它的支持方法，在问题提出学习者提出自己的问题作为一个生产性的任务。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和指示例子是如何产生的规范过程的信息。信息是自动生成的。学习者再现了 ...更多信息 以过程信息为例。这有助于学习者理解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，它提供了建议的学习活动，并通过实验证实了该系统是否可以提高学习者提出的问题。我们在前人的研究中证实，初学者很少通过改变问题的结构来提出新问题，而他们自己提出的问题结构大多是简单的或不合适的。实验结果表明，通过使用该系统再现一个例子的学习促进了通过改变问题结构与例子中使用的想法组成的问题的生成。进一步的实验研究证明，再现式学习可以促进学习者通过自己的新颖想法提出问题。然而，它也揭示了一些学习者未能再现给定的例子，他们的问题提出并没有改善。我们相信，我们的研究成功地建立了一个基本的方法来支持数学创造教育的学习活动。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。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