The Analysis of Students' Mathematics Achievement by Applying Cognitive Diagnostic Model

인지진단모형을 활용한 수학 학업성취 결과 분석 -2011년 국가수준 학업성취도 평가 자료를 중심으로-

Achievement profile by attribute in Korean students' mathematics was analyzed by applying cognitive diagnostic model, which is the newest measurement theory, to 2011 NAEA(National Assessment of Educational Assessment) results. The results are as follows. As the level of school is higher from 6th grade, 9th grade to 11th grade, the percentage of students mastering cognitive attribute 9(expressions using picture, table, graph, formula, symbol, writing, etc) drastically declined from 78%, 35% to 26%. It is necessary to have learning strategies to reinforce their abilities of expressing table, graph, etc. that higher graders in mathematics are more vulnerable to. Next, the property of mastering cognitive attributes according to gender, multi-cultural family was analyzed. In terms of mathematics, the percentage of girls mastering most of the attribute generally is higher than that of boys from 6th grade to 9th grade, however, boys show higher mastery in almost attributes than girls in the 11th grade. Compared to boys, the part where girls have the most trouble is attribute 9 in mathematics(expressions using picture, table, graph, formula, symbol, writing, etc). As international marriage, influx of foreign workers, etc. increase, the number of students from Korea's multi-cultural families is expected to be higher, therefore, identifying the characteristics of their educational achievement is significant in reinforcing Korea's basic achievement. In mathematics, gap of mastery level of attributes between multi-cultural group and ordinary group is more severe in higher grade and the type of multi-cultural group that needs supports for improving achievement most urgently changed in 6th grade, 9th grade and 11th grade respectively. In the 6th and 11th grade, migrant students from North Korea show the lowest level of mastering attributes, however, in the 9th grade, the mastery rate of immigrant students is lowest. Therefore, there is an implication that supporting plans for improving achievement of students from multi-cultural family should establish other strategies based on the characteristics of school level.

본 연구는 2011년 학업성취도 평가 결과를 Fusion 모형이라는 인지진단모형을 적용하여 수학교과에서 학교급별, 성취수준별, 성별에 따른 인지요소 숙달 양상과 다문화가정의 인지요소 숙달 양상을 분석하였다. 연구결과, 초6은 12개의 인지요소에서 '귀납적으로 추론하기', 중3은 10개의 인지요소에서 '연역적으로 정당화하기', 고2는 10개의 인지요소 중 '사칙계산'이 가장 높은 숙달 비율을 보였다. 성취수준별로 인지요소의 숙달 양상을 분석한 결과, 초 중 고 모두 우수학력 집단은 전체 인지요소에서 94%이상의 숙달률을 보였으나, 기초학력이하 집단 학생들은 거의 모든 인지요소에서 초6과 중3의 경우 미숙달 비율이 70%이상이었고 고2는 99%이상이었다. 또한, 초6, 중3까지는 전반적으로 여학생의 인지요소 숙달 비율이 남학생보다 높으나 고2에서는 대부분의 인지요소에서 남학생이 여학생보다 숙달 비율이 높게 나타났다. 다문화가정 학생 집단과 일반가정 학생 집단 간 인지요소의 숙달 양상은 학교급별로 상이하게 나타났다.