Development and Analysis of Formative Assessment for Mathematics ‘Number and Operation’ in the First Grade of Middle School by the Cognitive Diagnosis Model

Abstract

본 연구는 검사의 교수· 학습적 기능을 극대화하기 위하여 인지진단모형을 적용한 형성평가 도구를 개발하여 실시하고 분석하는 절차와 방법을 제안하며 그에 따른 시사점을 제공하고자 하는 목적을 가진다. 검사도구 개발에 앞서 인지요소를 추출하여 Q행렬을 개발한 후, 학생들의 잘못된 인지구조를 분석하기 위하여 각 문항에 매력적인 오답지를 포함하여 검사를 제작하였다. 검사 실시 후 고전검사이론, 문항반응이론에 의한 분석을 통해 형성평가로서의 검사 특성을 지니는지 분석한 뒤 인지진단모형 중 DINA 모형에 의해 문항 모수, 인지요소별 숙달확률, 인지요소 프로파일 패턴을 분석하였다. 연구 결과 문항의 난이도는 쉬운 편이며 검사 정보 함수가 θ가 -1 지점에서 가장 높은 값을 가졌으며 모든 문항이 여러 개의 매력적 오답지를 가진 것으로 분석되어 형성평가 도구로서 적합하였다. 인지진단모형에 의한 문항별 실수 모수와 추측 모수, 학생 개개인의 인지요소 프로파일을 분석하여 특이한 인지요소 패턴을 발견하였다. 마지막으로 인지진단모형에 의한 형성평가 도구 제작 및 분석 절차를 제안하며 이를 학교 현장의 형성평가에 적용한다면 검사의 교수·학습 기능을 극대화할 수 있을 것으로 기대한다.The purpose of this study is to provide the implications and procedures for the development of the formative assessment with cognitive diagnosis through analyzing the response data based on classical test theory, item response theory, and cognitive diagnosis model to maximize the teaching and learning function of the test. Prior to the development of the test, the attributes were extracted and the Q matrix was developed and then the test was constructed in accordance with it. In order to analyze the students wrong cognitive structures and incorrect problem solving strategies, at least one of the attractive distracter were embeded in each item. After implementing the test, it was analyzed whether they had test characteristics as formative assessment through analysis by classical test theory and item response theory and then item parameters, mastery probability and attributes profile were analyzed by DINA model among cognitive diagnostic models. The results of the study showed that the difficulty of the item was easy, the test informative function had the highest at near of theta ability of -1, and all the items have more than one of attractive distractor. Therefore, this test was suitable as a formative assessment. By analyzing guessing parameters and slip parameters for each item and the attributes profiles of individual student by the cognitive diagnostic model, it can be found out what some kind of attributes profiles are having difficulty to understand a learning hierarchy. Finally, the development and analysis procedure of formative assessment by the cognitive diagnostic model is suggested and it is expected that the teaching and learning functions of the test can be maximized by applying it to the formative assessment at school site.