基于关系—表征复杂性模型的有背景问题难度研究  

Solving Difficulty Relating to Pythagorean Theorem Problems with Backgrounds——the Explanation Based on Relational-Representational Complexity Model

作　　者：张夏雨[1] 

机构地区：[1]常州信息职业技术学院基础部

出　　处：《数学教育学报》2010年第3期46-49,共4页Journal of Mathematics Education

基　　金：江苏省教育科学“十一五”规划课题——本原性学科问题驱动课堂教学的理论建构与应用研究(D/2006/01/086)

摘　　要：包含现实情境的数学问题称之为有背景问题，去除背景后的问题称之为无背景问题，即一般意义上的数学问题．给问题加入背景会增加原有问题的难度．从表征复杂性和知识基础两方面可以解释问题难度级差的原因或本质，尝试对有背景问题难度做出解释．背景问题的难度可从两方面来解析：一是表征背景中关系的复杂程度，反映了从背景问题中抽象出无背景问题的难易；二是被抽象出的无背景问题的复杂性．给背景问题加入合适的提示后，会降低问题解决的难度，并且提示的作用在中等难度的背景问题中最为明显．The Relational-Representational Complexity Model refers to the depth and the width of representation, which can interpret the essence of solving difficulty of problems. Evidences were provided in research of Area-of-rectangle problems and Pythagorean theorem problems which are comparatively more comptex. Our concern in this study was the solving difficulty relating to Pythagorean theorem problems with backgrounds. It is indirectly examined according to the performances of the group which will accept implications based on the hypothesis of solving difficulty on problem-solving test, compared with the control group. Results show that after the problems are given with background, the solving difficulty will increase. If the implications are provided, the solving difficulty will be reduced and the effects of the implications are the most obvious on the problems of mid-difficulty with a background. The results identify indirectly the supposition on the background-oroblem-solving difficulty.

关 键 词：有背景问题 问题难度 表征复杂性 

分 类 号：G424.1[文化科学—课程与教学论]