六年级学生对高阶概率内容的认知:潜能与局限

Sixth Graders’ Cognition of High-Level Probability: Potential and Limitations

以64名六年级学生为被试,考察其在直观图示下对高阶概率内容的认知.结果表明,学生在＂理论计算＂任务上的表现差强人意,暴露出两类典型错误;＂理论计算＂能力是＂数量估计＂的先决条件,但对随机性的认知在此过程中也不可或缺;学生的概率直觉在＂数量估计＂任务中扮演着重要角色.对概率教学的启示和建议有：学生高阶概率内容认知的潜能与局限并存;教学应呵护学生的概率直觉,可通过计算机等直观模拟技术渗透概率思维.

This study selected 64 sixth graders as the subjects and explored their understanding of high-level probability in schema-based tasks. The results showed that, sixth graders＇ performance on calculation of theoretical probability were basically good but they also exhibited two typical erroneous cognition; their ability on calculation of theoretical probability was the prerequisite of probability evaluation but it their cognition of randomness was still necessary during this process; their probability intuition played important role in finishing probability calculation tasks. Implications and suggestions for mathematics education were： students＇ cognition of high-level probability in schema-based tasks exhibited some potentials accompanied with limitations; teachers should respect students＇ probability intuition and protect their good cognition of randomness, and cultivate their probability thinking by technology and other vivid ways.