An analysis of 4th grade students' routine and non-routine problem-solving skills using cognitive diagnostic models

Abstract

Assessment is an important part of education that provides feedbacks to both students on their learning and educators on their instruction. Assessments enhance students’ learning when providing effective and immediate feedback to learners. In this study, Cognitive Diagnostic Assessments (CDAs) are used to give informative and in-depth feedback to teachers and students. CDAs provide cognitive data about students’ strengths and weaknesses in a particular ability. This study investigates routine and non-routine problem-solving attributes of grade 4 students with four operations (addition, subtraction, multiplication, and division) using CDA. The test used in the study is specifically developed with diagnostic purposes regarding 2021-2022 4th grade mathematics curriculum and analysed with Cognitive Diagnostic Models (CDMs). There are 6 attributes and 20 items in the test. A Q-matrix was constructed to show attribute-item relationship. Before administering the test, a group with 10 students were asked to answer the items and interviewed later to evaluate the timing and clarity of the items. The final form of CDA test was administered to 511 students in 4th grade, from various public and private schools. The responses were analysed by the GDINA package in R. As a result of the analysis, each participant was assigned to an attribute profile showing which skills they have mastered and which they have not. The results showed that 75% of the students have mastered routine problem-solving skills, while 17% of the students have mastered non-routine problem-solving skills. The most frequent attribute profiles in the study group are found as follows: 000010, 010010, 111111, 111110, 000000 and 110010.