有理数加法学习的认知模拟研究

A Cognitive Simulation Study of Rational Number Addition Learning

在有理数加法运算中,正、负两数相加且结果为负的情形是学生学习的难点.研究应用认知模拟方法探索有理数加法的盈亏模型和绝对值模型的认知过程及其差异,结果表明:当工作记忆能力较弱,表征用时较长时,运用绝对值模型计算有理数加法的用时超过盈亏模型.两模型的差异源于问题表征的次数、问题和知识的表征形式以及对前备知识的熟练程度3个方面.盈亏模型基于熟悉的现实背景,问题及知识表征的次数少、形式简单,减轻了学习的认知负荷.建议学生在初学阶段直接利用盈亏模型进行有理数加法运算,在理解的基础上逐步总结运算规律.

In the operation of rational number addition,it is difficult for students to learn the situation where positive and negative numbers are added and the result is negative.This study applies cognitive simulation methods to explore the cognitive processes and differences between the profit-and-loss model and the absolute value model of rational number addition.The results show that when the working memory capacity is weak and the representation takes longer,the use of the absolute value model to calculate the rational number addition takes longer than the profit-and-loss model.The differences between the two models stem from three aspects:the number of problem representation,the representation form of problems and knowledge,and the proficiency of prerequisite knowledge.The profit-and-loss model is based on a familiar real-life background,with fewer representations and simpler forms of representation,which reduces the cognitive load of learning.It is recommended that students use the profit-and-loss model to perform rational number addition operations directly at the beginning stage,and gradually summarize the operation rules on the basis of understanding.