中国小学生基本数学能力测试量表常模的建立

背景:数学能力是人类智能结构中重要的基础能力之一,数学学习不良是掌握数学概念、进行抽象运算以及开始形成综合数学能力的关键期的学龄期儿童普遍的学习不良类型,但缺乏专用的筛查量表和参照常模。目的:建立适合中小学生基本数学能力测试量表的评定常模。设计:多阶段分层整群随机抽取横断面调查。单位:由华中科技大学同济医学院主持,北京市疾控中心、河北省疾控中心、哈尔滨医科大学、安徽医科大学、江苏省疾控中心、山东省疾控中心、湖南冷水江市疾控中心、中山医科大学、海南省疾控中心、华西医科大学、贵阳医学院、兰州医学院等单位协作完成。对象:在全国范围内共调查样本22039人,整群随机抽取城区和农村普通小学1～6年级的学生,共14693人,其中城市学生7377人,农村学生7316人。方法:于2003-06/09以普通小学1～6年级的学生为对象完成抽样调查。参照2000年第五次全国人口普查资料,以性别,民族,地域,城乡为标准,采用多阶段分层整群抽样方法,用《中国小学生数学基本能力测试量表》,对整群抽取的班级学生的数学能力进行团体测试。主要观察指标:数学运算能力、逻辑思维能力、空间-视觉能力等。结果:常模样本共14693人,其中城市学生7377人,农村学生7316人,全部进入结果分析。①城乡两样本儿童在本量表的各分测试得分均值均随年级而呈阶梯性增高,城乡样本各年龄组间测试得分比较(两两比较)差异有显著性意义(P<0.05);城区样本各年级组的测试得分高于相应年级组的农村样本(t=2.234～11.766,P<0.05)。分别建立城区(n=7377)和农村(n=7316)两套常模。②参照常模由转换T分及百分位P构成,估算了每一学期中和学期末的T分,并根据T分计算Z分,再求得正态分布下的概率函数P。③数学能力等级评价分为5等,即得分在x±s(P=16%～84%)的范围者为中等,得分在x s与x 2s之间者(P=84%～97.5%)为中上,得分超过x 2s者(P>97.5%)为优秀,得分在x-s与x-2s之间者(P=16%～2.5%)为中下,得分低于x-2s者(P<2.5%)为较差。结论:常模样本构成比例与人口资料基本吻合,样本在各年级、男女性别分布基本均衡;城乡儿童的数学能力测试得分在大部分分测试中差异存在显著性意义有必要分别建立城区和农村两套常模。

Norm establishment for Chinese Rating Scale of Pupil''''s Mathematics Abilities

BACKGROUND: Mathematics ability is one of the basic abilities in human intelligence and mathematics disability is a universal type in key period of school-age children to master the mathematical concepts, perform the abstract calculation and form comprehensive mathematics ability, which is lack of a special rating scale and reference norm.OBJECTIVE: To establish a suitable evaluated norm for rating scale of pupil's basic mathematical abilities.DESIGN: Cross-sectional study of multi-phase stratified cluster random sampling.SETTING: The experiment was presided by Tongji Medical College collaborating with the Centers for Disease Prevention and Control of Beijing,Hebei province, Jiangsu province, shangdong province, Lengshuijiang,Hainan province and Hainan province, Herbin Medical University, Anhui Medical University, Sun Yat-sen University of Medical Sciences, West China University of Medical Sciences, Guiyang Medical College, Lanzhou Medical College and other units.PARTICIPANTS: Totally 22 039 people were investigated in nationwide,including 14 693 students (7 377 urban ones and 7 316 ones, respectively), who were randomly selected from Grade One to Six of urban and rural general elementary schools.METHODS: Between June and September 2003, students from Grade One to Six of general elementary schools were sampled. According to the Fifth National Population Census in 2000 and based on sex, nation, area and city or count, the Chinese Rating Scale of Pupil's Mathematic Abilities was applied in group-test on mathematic abilities of the cluster-selected students with multi-phase-stratified sampling method.MAIN OUTCOME MEASURES: Calculative ability, logical thinking and spatial-visual abilities and so on.RESULTS: The norm samples of 14 693 subjects including 7 377 urban students and 7 316 rural students all entered the result analysis. ①The mean scores of each sub-test for the two sampled subjects gradiently increased along with grades rising; the scores of subtests among various ages from urban and rural samples (paired comparison) had significant differences (P ＜ 0.05); the scores of sub-tests of urban samples in various grades were higher than those of rural samples (t=2.234-11.766, P ＜ 0.05). The urban (n=7 377) and rural (n=7 316) norms were established, respectively.②The reference norm was composed of converted T score and percentile P,the T scores in every mid-term and final-term were estimated to calculate Z scores; finally, the probability function P under normal distribution was achieved. ③The evaluation of mathematics abilities were classified into 5 grades: it was average with the scores of (-x)±s (P=16%-84%); good if between (-x)+s and (-x)+2s (P=84%-97.5%); excellent if exceeded (-x)+2s(P ＞ 97.5%); inferior if between (-x)-s and (-x)-2s(P=16%-2.5%); worse if lower than (-x)-2s (P ＜ 2.5%).CONCLUSION: The constituent ratio of normal samples is basically consistent with the data of total population and the distribution of samples in various grades and sexes is nearly equilibrate; there are significant differences in scores of most subtests on mathematics abilities between urban and rural children, which suggest that it is necessary to establish urban and rural norm, respectively.