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反思能力是指自觉地对数学的认知活动进行考察、分析、总结、评价、反馈,控制和调节的能力。这种能力主要分为两大部分:一是认知过程中的自我监控能力,二是自我调节能力。培养学生的反思能力旨在用控制论原理剖析课堂信息交流的规律。荷兰著名数学家费赖·登塔尔指出:反思是数学活动的核心和动力。英国数学教育心理学家斯根普在《学习数学的心理学》一书中指出,在进行数学思考活动时,尽管有些结论和方法是显而易见的,但思维不能就此而止,还需要做进一步的逻辑分析,加以确认和证明。
Reflective ability refers to the ability to conscientiously study, analyze, summarize, evaluate, feedback, control and regulate cognitive activities in mathematics. This ability is mainly divided into two parts: First, cognitive process of self-monitoring capabilities, and second, self-regulation. The ability to develop students’ reflective ability aims to analyze the rules of classroom information exchange with the theory of cybernetics. The famous Dutch mathematician Feiradental pointed out: Reflection is the core and motivation of mathematical activities. In his book Psychology of Learning Mathematics, British mathematical education psychologist Sjppen pointed out that although some conclusions and methods are obvious in conducting mathematical thinking activities, thinking can not be stopped and more needs to be done Logic analysis, to confirm and prove.