Fusion Model에 의한 수학 능력 진단을 위한 Q-행렬의 정교화

Refinement of Q-Matrix for Analysing students" mathematical skills via Fusion Model

  본 연구는 인지 진단 이론을 적용하여 학생들의 능력 진단을 위한 Q-행렬을 정교화하는 과정을 예시하고, 이를 토대로 산출한 능력 진단 결과를 제시하였다. 2003～2006년에 실시된 국가수준 학업성취도 평가의 중학교 3학년 수학 검사에서 30개의 선다형 문항을 선정하여 구성한 검사를 실시하고 Fusion Model을 적용하여 문항 모수 및 학생 모수를 추정하였다. 특히 Fusion Model의 중요한 요소 중의 하나인 Q-행렬을 구성하고 정교화하는 과정 및 정교화된 Q-행렬을 바탕으로 각 학생들의 수학적 속성을 진단한 결과를 보여주고 있다.

  Conventional assessments only provide a single summary score that indicates the overall performance level or achievement level of a student in a single learning area. For assessments to be more effective, test should provide useful diagnostic information in addition to single overall scores. Cognitive Diagnosis modeling provides useful information by estimating individual knowledge states by assessing whether an examinee has mastered specific attributes measured by the test (Embretson, 1990; DiBello, Stout, & Rousses, 1995; Tatsuoka, 1995). Attributes are skills or cognitive processes that are required to perform correctly on a particular item. If standardized testing could incorporate assessments of the various attributes constituting the item, then students, parents, and teachers would be able to see where a student stands with respect to mastering the item. Such information could be used to guide the learner and teacher toward areas requiring more study. By being able to assess where they stand in regard to the attributes that compose an item, students can plan a more effective learning path to be desired proficiency levels. It would be very helpful to the examinees if score reports can provide the scale scores as well as the skills profiles. When the scale scores are believed to provide students’ math ability by reporting only one score point, the skills profiles can offer a skill level of strong, weak or mixed for each student for each skill. This present study aims to investigate the possibility of providing student skill profile scores with the National Assessment of Educational Achievement (NAEA) in Korea. The NAEA is the nationally representative and continuing assessment of what Korean students know and can do in various subject areas. Also, the construction and specification of Q-matrix is discussed as very important aspect before analyzing the data. Fusion Model was used to assess examinee’s mastery of certain attributes in this study.