数学教师KCS与学生认知的一致性研究——以“概率”内容为例

The Consistency between Mathematics Teacher' KCS and Students' Cognition——Take Probability Knowledge as a Case

以北京市28名七～九年级数学教师(教师端数据)及该市某校204名七～九年级学生(学生端数据)为被试,以"概率"内容为载体,通过对比学生的作答数据与教师对学生作答的预测数据,考察数学教师KCS与学生认知的一致性.结果表明:教师对学生作答的预测大都与学生的实际作答相去甚远,他们对学生概率认知的水平估计过高;鲜有教师给出的预测得分率排序与学生的实际作答完全一致;教师对学生在不同问题中可能出现的困难有不同的预测,而这些预测与教师对任务本身的认识有关.对教师的建议有:深入分析影响概率问题难度的潜在因素;站在学生的立场,了解学生概率思维的特征.

This study selected 28 teachers(teacher’s data)in grade seven and grade nine from Beijing and 204 7th to 9th students(student’s data)from one middle school in Beijing as the subjects and focused on teachers’knowledge on students’probability cognition through analyzing the consistency between the two set of data.The resulted shown that,teachers’prediction of students’performance was far away from students’performance,but they overestimated students’understanding of probability.Seldom teacher’s prediction of the relative sequence of difficulty of every items were consistent with that of students’.Teachers’predictions of the possible difficulties of different items were different and these predictions were related to their understanding of the tasks.Suggestions to teachers were:Analyzing the potential factors impacted the difficulty of the items;Studying the characteristics of students’probability thinking from their perspective.