摘要
问题图式的等级性可从解决问题所要求的表征关系复杂性、知识基础两方面来解释.将该解释模型用到关系结构更复杂的勾股定理问题图式的等级性研究中,一方面依据表征深度和知识基础的不同要求将问题图式分成6种形式的模版,另一方面对6个模版上的问题采用两种图式测量技术,以检验不同模版的图式水平.结果发现:(1)勾股定理问题图式具有等级性,且可以从表征深度和知识基础两方面来解释等级性的原因,但是这两项因素的解释作用需考虑问题解决者的已有水平.(2)表征深度除用表征关系最高层级数刻画之外,还与每级关系的表征难度有关,突出表现为表征关系所需的推理水平.
It is revealed that schematic knowledge relating to word problems was organized hierarchically. In fact, the essence of hierarchy has been interpreted by the integration of representational complexity and knowledge base. Evidences were provided in research of Area-of-rectangle problems schema. The paper further testified the effectiveness of the explanation when it comes to more complex problems. Using the empirical study method, we have assessed schematic knowledge relating to Pythagorean theorem problems by asking 1 068th students to judge the conditions on the calculation and classify problems in terms of whether the text of each problem provided insufficient, sufficient, or irrelevant information for solution. The results suggest that schematic knowledge relating to Pythagorean theorem problems involved with the latter four templates was hierarchically organized and the hierarchical ordering could be explained from depth of representation and knowledge base. Moreover, depth of representation is not only reflected by the number of represented hierarchical relations as stated in the previous study, but also is correlated with complexity inside a relational-representation and reasoning level required in a relational-representation.
出处
《数学教育学报》
北大核心
2009年第4期46-49,共4页
Journal of Mathematics Education
基金
全国教育科学“十一五”规划课题——回顾与反思:中国数学教育研究30年(DAA080080)
关键词
数学问题解决
图式等级
表征复杂性
mathematics problem-solving
hierarchical ordering of schematic knowledge
relational-representational complexity