Developing a structural model of the components influential on learning algebraic expressions at the new secondary school level using Attribute Hierarchy Method (AHM

In the process of teaching and learning basic mathematics, topics related to the algebraic expressions are the basis of many of the key topics at school and advanced mathematics, and especially they are used in teaching the topics related to the functions and operators. Therefore, it is important to find the relationships among the effective components and their dimensions at the level of knowledge and skills of students, as a model for mathematics educators. This research seeks to provide a structural model for the topic of algebraic expressions at secondary school level, using a mathematical test tool and then through analyzing data through the software R, applying Cognitive Diagnostic Assessment (CDA) to analyze data and then extracting the results using the Attribute Hierarchy Method (AHM). The results were examined in three content areas of “recognition and detection”, “simplification” and “factorization and distribution”. The structural model, based on the analysis of the results, showed a convergent and linear pattern for the model of the relationship among the components. And this model became fixed with the model of measurement to find the dimensions, validity, reliability and fit of the model.