【作者】 刘燕；

【导师】 范晓玲；

【作者基本信息】 湖南师范大学 ， 心理学， 2018， 硕士

【摘要】 目的:(1)编制一套小学生小数除法认知诊断测验(A、B卷),为小数除法学习困难儿童的筛查提供有效、可行的工具。(2)在认知诊断的基础之上,构建小学生小数除法计算的认知模型,为小学生提升除法计算能力提供理论依据。(3)对小数除法学习困难儿童的反应模式和错误规则进行分析,为认知模型的建构和应用提供数据上的支持。方法:采用认知设计系统(CDS)方法,以McCloskey等人的语义表征中心理论为认知理论基础,以CTT和IRT参数和小数除法错误类型为选题依据,编制小数除法认知诊断测验。本研究析出小数除法共有7个认知属性,并建构其属性层级关系,通过专家评定法和口语报告法验证其属性层级关系。本测验分为A、B卷,每套试卷有27道题。通过专家评定法与ROC曲线法确定测验的划界分。前后共经过3次施测,正式施测共发放1435份问卷,有效问卷共1294份(男生725人,女生569人),有效率达到90.17%。基于DINA模型对小数除法学习困难儿童的属性反应模式和错误规则进行分析。结果:(1)项目质量:A卷难度参数在[-3.309,0.507]之间,平均难度系数为-1.134;B卷难度参数在[-3.413,1.701]之间,平均难度系数为-1.084。A卷区分度参数在[0.478,2.241]之间,平均区分度系数为0.903>0.7,B卷区分度参数在[0.435,1.938]之间,平均区分度系数为0.860>0.7。(2)测验信效度:A卷最大信息函数为20,Cronbachα系数为0.807,分半信度为0.670,基于认知诊断测验信度为0.72;B卷最大信息函数为15,Cronbach α系数为0.821,分半信度为0.625,基于认知诊断测验信度为0.80;内容效度表明正常儿童得分显著高于困难儿童;结构效度表明,A、B卷的HCI值分别为0.63和0.57,均大于0.3;外部效度表明,学校类型(好,中,差)在各个属性上的通过率差异显著。(3)划界分与检出率:A卷划界分为14分;B卷划界分为13分;总体检出率为8%;(4)基于DINA模型的认知诊断结果:得出14种典型考核模式,15种理想掌握模式;由DINA模型诊断出的项目参数有猜测参数和失误参数,A卷猜测参数在[0.1260,0.5660]之间,失误参数在[0.0067,0.2590]之间;B卷猜测参数在[0.0587,0.5398]之间,失误参数在[0.0335,0.3900]之间;被试对属性Al、A2掌握概率在90%以上,对A5、A6、A7的掌握概率低于80%;A卷共563人,有388人被归入到理想掌握模式中,归入率为68.9%;B卷共731人,有567人被归入到理想掌握模式中,归入率为77.6%,总体归入人数为955人,73.8%的被试能够被合理归类;筛选出79名小数除法学习困难儿童,均被成功归类,54名归到7种典型反应模式,25名归到剩余9种非理想掌握模式中。结论:(1)项目参数基本符合认知诊断测验的要求,测验的信度、效度良好,各项指标基本达到测量学的要求。(2)小学生小数除法的认知属性模型合理有效。(3)儿童在小数除法学习中对计算程序的执行(属性A5、A6、A7)上表现更差。(4)认知诊断实现了对小数除法学习困难儿童的归类以及错误规则的分析。更多还原

【Abstract】 Objectives:(1)To develop a set of test papers(Scale A and B)for cognitive diagnostic assessment of decimal division towards pupils,aiming at providing an effective and feasible tool for screening the children who may have difficulty in learning decimal division.(2)To build a cognitive model of decimal division for pupils(based on the results of the cognitive diagnostic assessment),which can provide a theory basis for improving their ability in decimal division.(3)To analyze the response pattern and error type the children have in learming decimal division,which can support the construction and application of the model from the perspective of data.Methods:With the Cognitive Design System(CDS)as the compilation method,McCloskey’s theory of semantic representation as the theoretical basis for cognition,and CTT/IRT parameters and decimal division error types as the basis to select items,a cognitive test for decimal division was drew up.In this resaerch,seven cognitive attributes as well as the logical relationship were developed,which could be confirmed by expert evaluation and oral report.The test papers we proposed are divided into Scale A and B,each of which has 27 items.And the cutoff score was determined by combining expert evaluation method and ROC curve method.After 3 surveys,1294 valid samples(725 boys and 569 girls)were collected out of 1435 questionnaires with effective return-ratio 90.17%.Finally,the analysis of response pattern and error type they have in learning decimal division was carried out based on DINA model.Results:(1)The quality analysis of the item revealed that the difficulty indexs of Scale A and B were[-3.309,0.507]and[-3.413,1.701],the average values of which were-1.134 and-1.084,respectively.On the other hand,the discrimination index of Scale A was[0.478,2.241]with the average value of 0.903>0.7,while the discrimination index of Scale B was[0.435,1.938]with the average value of 0.860>0.7.(2)The Maximum information fiunction of Scale A(B)was 20(15),the Cronbach a coefficient was 0.670(0.821),the split-half reliability was 0.670(0.625),and the reliability based on the cognitive diagnostic test was 0.72(0.80).The content validity showed that the normal children’s scores were significantly higher than the difficult pupils;the construct validity revealed the HCI value of the Scale A(B)was 0.63(0.57),both were more than 0.3;the external validity showed that the passing rate of the school types(good,middle,poor)differ significantly in each attribute.(3)The cutoff scores of Scale A and B were 14 and 13,respectively,the overall detection rate of which was 8%.(4)The results of cognitive diagnosis based on DINA model:14 typical assessment models and 15 ideal master models were obtained.From DINA model,the guessing parameters of Scale A and B were[0.1260,0.5660]and[0.0587,0.5398],respectively;and the error parameters of Scale A and B were[0.0067,0.2590]and[0.0335,0.3900],respectively.The probabilities of attribute Al,A2 subjects mastered was more than 90%,that of A5,A6,A7 were less than 80%;In Scale A(B),388(567)children were assigned to the ideal master model among 563(731)children,and the rate is 68.9%(77.6%).955 children were reasonably classified,which accounts for 73.8%;79 children who have learning difficulties with decimal fractions were successfully classified.54 of them were discriminated among 7 typical response patterms,the rest were discriminated among 9 Non-ideal patterns.Conclusions:(1)The item parameters basically accommodated the requirements of cognitive diagnostic test,the reliability and validity of the test were good,and all indicators also reached the surveying demands;(2)The cognitive attribute model of primary division of students is reasonable and effective;(3)Children perfodrm poorly on calculation program execution in fractional division learning;(4)the cognitive diagnosis realized the classification of the children who have difficulty in learning decimal division as well as the analysis of error rules.更多还原