Detection of students' ability levels is one of the common aims in educational studies. Cognitive Diagnosis Modeling approach has been used recently for the purpose of ability level detection by defined Q-matrices. To evaluate students' strengths and weaknesses, determine their mastery skills, and design instructions and interventions in learning process, Cognitive Diagnosis Modeling approach can be helpful. Cognitive Diagnosis Modeling is an alternative approach to Item Response Theory, and provides more information using multiple fine-grained skills in problem solving process rather than order students on a latent proficiency continuum This paper aims to use Cognitive Diagnosis Modeling (CDM) in order to investigate the definition of a Q-matrix across the cognitive skills of different years and countries in Trends in International Mathematics and Science Study (TIMSS). There is a subjective way in defining Q-matrices, an intuitive definition of Q-matrices, for this purpose, an application of building Q-matrices under specific Cognitive Diagnosis Models, from a set of expert proposed attributes is examined. The proposed attributes are used to build Q-matrices for TIMSS mathematics questions across its cycles, and across different nations.