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 (1南昌航空大学数学与信息科学学院, 南昌330063) (2江西师范大学计算机工程学院, 南昌330022)
(3江西省心理与认知科学重点实验室, 南昌 330022) (4 江西师范大学心理学院, 南昌330022)
Application of Rough Set Theory in Item Cognitive Attribute Identification
TANG Xiaojuan1; DING Shuliang2; YU Zonghuo3,4
 (1 School of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, China) (2 Computer Information Engineering College, Jiangxi Normal University, Nanchang 330022, China) (3 Jiangxi Key Laboratory for Psychology and Cognitive Science, Nanchang 330022, China) (4 School of Psychology, Jiangxi Normal University, Nanchang 330022, China)
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认知诊断是新一代测量理论的核心, 对形成性教学评估具有重要意义。项目认知属性标定是认知诊断中一项基础而重要的工作,现有的项目认知属性辅助标定方法的研究工作很少, 并且在应用上存在诸多局限。课堂评估是认知诊断应用的理想场所,但课堂评估中项目的选取具有随意性, 教师难以在短时间内准确标识项目认知属性。本研究首次提出采用粗糙集方法对项目认知属性进行标定, 该方法无需太多被试和项目, 亦无需已知项目参数, 且能当场诊断出结果, 适于采用纸笔测验的课堂评估。通过Monte Carlo模拟研究表明:采用粗糙集方法能迅速地对项目认知属性进行标定, 并具有较高的标定准确率; 而且, 项目认知属性越少、或被试估计判准率越高、或失误率越小则项目认知属性标定的准确率越高。粗糙集方法的引入, 对拓展认知诊断的应用范围, 真正实现其辅助性教学功能, 具有重要作用。

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关键词 粗糙集理论课堂评估认知属性辅助标定    

Item Cognitive Attribute Identification (ICAI) is the basis of Cognitive Diagnosis (CD), which is designed to measure specific knowledge structures and processing skills in students. According to the published documents, there are two methods used in ICAI.The one is to indentify item attributes by some experts of relative domains. When there are many items, it will be a huge burgen for experts to identify their attributes in the items. Especially, for some items, it’s difficult for experts to get a unified opinion about items’ attributes. As an assistant to this one, the other method is to identify items’ attributes by CD-CAT (Cognitive Diagnostic Computerized Adaptive Testing). Using CD-CAT in ICAI is an obvious breakthrough, for that it is not necessary totally depentant on manual labour. But using CD-CAT in ICAI has some heavy limitation. For example, if the items’parameters such as difficulty, are unknown, big samples of subjects and items are necessary for CD-CAT to identify item attributes. The second limit of CD-CAT is that it is based on item pool, and the development of item pool is very expensive that the cost of one item is about $1000. Cognitive diagnosis is designed to provide information about students’ cognitive strengths and weaknesses and to assist the teaching. So, the best place to use it is in classrooms. But cognitive diagnosis is just used in lager–scale examinations now for two reasons: First, most cognitive diagnosis models are based on probability models which need a large sample in estimating item parameters, and the using of these cognitive diagnosis models are also based on a large sample of subjects even the items’ parameters have been estimated. Secondary, even though the method of CD-CAT can be used in a small–scale examination once the item parameters are known, CAT has been prohibited in many kinds of examinations for other reasons. So, it is very necessary to find a new method to indentify item attributes when item parameters are unknown, examinees are less and feedbacks are timely. In the current studies, we apply a new method – Rough Set Theory (RST) to ICAI. RST can solve the uncertainty in CD caused by the size of knowledge granularity. It doesn’t require any priori knowledge. Through the knowledge reduction, RST induces decision or classification rules, and then classifies the object. At first, we verificate the application of RST in ICAI. Then, in Study One, we explore how the match ratio of subjects' knowledge states and the slippage in subjects' responses to items impact the match ratio of item attributes. The number of item attributes is a variable which impacts the accuracy of CD, so, we also examine how the number of cognitive contributes impact the match ratio of item attributes. The results show that: (1) In the absence of item parameters, the rough set theory of ICAI has fast diagnostic speed and good results even though the sample size is small. So RST can be applied to classroom assessment. (2) The lower examinee’s PMR, the lower PMR of item attribute identification is. And the higher slippage in examinee’s response, the lower item attribute identification’s PMR is. (3) The more the number of item attributes, the lower item attribute identification’s PMR is. (4) Both results are estimated by rough set software, and regardless of sample size and item number, the estimated speed is very fast (about 10 seconds). It shows the advantage of RST in ICAI.

Key wordsrough set theory    cognitive diagnosis    item attribute cognitive identification
收稿日期: 2014-07-25      出版日期: 2015-07-25

国家自然科学基金(30860084, 31160203, 31360237), 国家社科基金(12BYY055, 13BYY087), 教育部人文社科青年基金(13YJC790189), 江西省高校人文社科规划基金(XL1408), 南昌航空大学博士启动基金(EA201307354)和江西师范大学博士启动基金(12015786)的支持。

通讯作者: 丁树良, E-mail:   
唐小娟;丁树良;俞宗火. 粗糙集在项目认知属性标定中的应用[J]. 心理学报, 10.3724/SP.J.1041.2015.00950.
TANG Xiaojuan; DING Shuliang; YU Zonghuo. Application of Rough Set Theory in Item Cognitive Attribute Identification. Acta Psychologica Sinica, 2015, 47(7): 950-962.
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