从认知负荷理论看数学教材例题编写

Examples Compiled for Mathematical Textbooks in the View of Cognitive Load Theory

教材例题编写研究的一个重要基础:基于认知负荷理论.认知负荷理论强调在例题编写过程中应考虑认知资源的有限性和有助于学习者形成、发展问题图式.减负增效是教材例题编写应该遵守的基本原则,即优化内在负荷、降低外在负荷和增加关联负荷.其中,不完整例题因为包含了部分的解题步骤,所以它引起的外在认知负荷相对而言就较小一些,删除的解题步骤可增加关联认知负荷.对例题编写的解答步骤去设计一系列提示信息可减少内在与外在认知负荷,反思问题或暗示促进图式的建构与精致,可增加关联认知负荷.例题图表简洁、可视化,引起的内在、外在认知负荷相对较小.例题"1+n"型设计可促进学习者多角度的自我解释,提高关联认知负荷.例题设计中应排除多余的文字、图片及资源,消除相同内容重复形成不必要复本带来的冗余效应,可降低外在认知负荷.

As an important basis for compiling examples, cognitive load theory emphasizes that the limitations of cog-nitive resources should be considered to help learners develop problem schema. Compiling examples is basically to alleviate burdens for efficiency, which optimizes intrinsic cognitive load, reduces extraneous cognitive load and in-creases germane cognitive load. Incomplete examples, compared with the examples, include parts of the solutions, which reduce extraneous cognitive load but increase germane cognitive load. A series of information designed for the solutions to compiled examples decreases extraneous cognitive load but increases germane cognitive load. The con-cise and visual example design decreases both intrinsic and extraneous cognitive load. The pattern of“1+n”example design may promote students’self-explanation from different perspectives, and increase the germane cognitive load. If redundant words, pictures and resources are removed from examples, extraneous cognitive load will be decreased as well.