图示化解答数学问题的异质分析及其应用启示
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摘要
智慧技能类知识的习得对青少年心智发展有重要作用。以数学为代表的智慧技能类知识在实际学习中实为难点。那么,图示在智慧技能类知识学习中将有怎样的影响,如何通过图示应用分析发现学生在智慧技能类知识学习中的弱点及其程度。在图示辅助的初中数学方程与函数知识学习情境下,通过数据收集、回归分析、聚类分析和异质组个案比较,结果表明:(1)图示化知识学习可以辅助理解与思考,对偏弱、中等水平的学生更有作用;(2)不同水平的学生对图示方式都有较高的倾向;良好水平学生融通图示与题意的能力较强,对图示材料依赖少而弱;而偏弱水平学生在信息整合、知识应用方面表现不力,对图示材料依赖多而强。研究认为,图示化知识习得与运用需要靶向主体异质因子;准确、恰当的图示设计与正确的图示运用是促进知识学习的重要条件;图示方式可辅助于分解理解过程,进而通过靶向增强图示效用。
The acquisition of intellectual skills plays an important role in the mental development of adolescents. The intelligent skills represented by mathematics are difficult in practical learning. Then, how does the diagram affect students' learning of intelligent skills, and how can we find out the weakness and degree of students in the learning of intelligent skills through analyzing the diagram? In the process of leaning Junior middle school mathematical equations and functions, through data collection, regression analysis, clustering analysis and case comparison of heterogeneous groups, it is found that:(1)diagrammatic knowledge can assist understanding and thinking, which is more useful for weak and average students.(2) Students of different levels have a higher tendency to the graphical representation; students of good level have strong ability to understand diagram and questions, and they are less dependent on graphical materials. However, the weak students show poor performance in information integration and knowledge application, and are more dependent on graphical materials. It is believed that acquisition and application of knowledge assisted with the diagram and graph need to target the heterogeneous factors of subjects. Accurate and appropriate graphic design and correct graphic application are important to promote knowledge learning. The graphic is helpful in understanding with its effects enhanced by targeting.
The acquisition of intellectual skills plays an important role in the mental development of adolescents. The intelligent skills represented by mathematics are difficult in practical learning. Then, how does the diagram affect students' learning of intelligent skills, and how can we find out the weakness and degree of students in the learning of intelligent skills through analyzing the diagram? In the process of leaning Junior middle school mathematical equations and functions, through data collection, regression analysis, clustering analysis and case comparison of heterogeneous groups, it is found that:(1)diagrammatic knowledge can assist understanding and thinking, which is more useful for weak and average students.(2) Students of different levels have a higher tendency to the graphical representation; students of good level have strong ability to understand diagram and questions, and they are less dependent on graphical materials. However, the weak students show poor performance in information integration and knowledge application, and are more dependent on graphical materials. It is believed that acquisition and application of knowledge assisted with the diagram and graph need to target the heterogeneous factors of subjects. Accurate and appropriate graphic design and correct graphic application are important to promote knowledge learning. The graphic is helpful in understanding with its effects enhanced by targeting.
引文
[1] WARE C. Visual queries:the foundation of visual thinking[M]//Knowledge and Information visualization:searching for Synergies.Berlin Heidelberg:Springer-Verlag, 2005:27-35.
[2]乔纳森D H.用于概念转变的思维工具:技术支持的思维建模[M].第三版.祝智庭,顾小清,译.上海:华东师范大学出版社,2007:164-170.
[3] SCHEITER K, GERJETS P, HUK T, et al. The effects of realism in learning with dynamic visualizations[J]. Learning&instruction,2009(6):481-494.
[4] FERGUSON E L, HEGARTY M. Learning with real machines or diagrams:application of knowledge to real-world problems[J].Cognition and instruction, 1995(1):129-160.
[5]加涅R M.学习的条件和教学论[M].皮连生,王映学,郑葳,等译.上海:华东师范大学出版社,1999:90-125,109-126.
[6]权国龙,冯园园,冯仰存,顾小清.面向知识的可视化技术分析与观察[J].远程教育杂志,2016(1):90-98.
[7] URSYN A. Handbook of research on maximizing cognitive learning through knowledge visualization[M]. Hershey, Penna.:Informationscience reference, 2015.
[8]权国龙,张茹,顾小清.面向“深阅读”的知识图示设计[J].电化教育研究,2015(11):13-19.
[9]权国龙,顾小清,姚媛媛,龚晋瑜.图解的设计与应用———可视技术辅助数学应用解答之行动研究[J].电化教育研究,2017(2):112-121.
[10]麻娟,张海,王以宁,多召军.移动技术辅助几何证明的多重表征系统设计与应用研究[J].电化教育研究,2014(5):66-69.
[2]乔纳森D H.用于概念转变的思维工具:技术支持的思维建模[M].第三版.祝智庭,顾小清,译.上海:华东师范大学出版社,2007:164-170.
[3] SCHEITER K, GERJETS P, HUK T, et al. The effects of realism in learning with dynamic visualizations[J]. Learning&instruction,2009(6):481-494.
[4] FERGUSON E L, HEGARTY M. Learning with real machines or diagrams:application of knowledge to real-world problems[J].Cognition and instruction, 1995(1):129-160.
[5]加涅R M.学习的条件和教学论[M].皮连生,王映学,郑葳,等译.上海:华东师范大学出版社,1999:90-125,109-126.
[6]权国龙,冯园园,冯仰存,顾小清.面向知识的可视化技术分析与观察[J].远程教育杂志,2016(1):90-98.
[7] URSYN A. Handbook of research on maximizing cognitive learning through knowledge visualization[M]. Hershey, Penna.:Informationscience reference, 2015.
[8]权国龙,张茹,顾小清.面向“深阅读”的知识图示设计[J].电化教育研究,2015(11):13-19.
[9]权国龙,顾小清,姚媛媛,龚晋瑜.图解的设计与应用———可视技术辅助数学应用解答之行动研究[J].电化教育研究,2017(2):112-121.
[10]麻娟,张海,王以宁,多召军.移动技术辅助几何证明的多重表征系统设计与应用研究[J].电化教育研究,2014(5):66-69.