5～7岁儿童数学过程性能力构成要素探索与模型建构

Factor Analysis on Mathematical Process Ability of Children Aged 5～7

为探索儿童数学过程性能力的构成要素,本研究通过对200名5～7岁儿童在数学运算和统计两个数学活动中的表现进行因素分析,构建了5～7岁儿童数学过程性能力要素模型。探索性因素分析结果显示,5～7岁儿童的数学过程性能力由数学交流、数学表征、数学推理与验证、数学关联四个要素构成;大班儿童和一年级儿童数学过程性能力的构成要素一致,表明数学过程性能力不存在年龄差异。验证性因素分析结果显示本研究构建的四因素模型具有良好的稳定性与科学性;5～7岁儿童数学过程性能力的构成要素不存在活动差异。政府应根据科学研究结果,对现行国家指导性文件做进一步完善,在其中增加有关数学过程性能力的内容;师资培养单位应在其开设的早期数学教育课程中增加有关数学过程性能力的内容,由此提高职前与在职幼儿园教师对儿童数学学习过程重要性的认识,从源头上遏制我国早期数学教育小学化倾向。

Early in the year 2000, NCTM put forward five mathematical process abilities in Principles and Standards for School Mathematics. Since then, empirical study on the return to process abilities has been internationally widespread, but in China such study is still in short supply. Through the methods of quantitative research, this paper evaluated 200 5-7-year-old children＇s behaviors in two mathematical activities named operation and statistics. Exploratory factor analysis found that： Process ability consisted of four elements called mathematical communication, mathematical representation, mathematical connection, mathematical reasoning and proof. There was no age difference on mathematical process ability between children aged 5-6 and 6-7. Confirmatory factor analysis found that there was no activity difference on mathematical process ability which also indicated that the model with four elements is stable and scientific. These findings suggested that governments and authorities should revise some of our documents to include contents about mathematical process ability based on scientific researches. Also teacher training about process ability must be a matter bf great urgency because it＇s an efficient way to improve the quality of mathematical education.