AHM Model on learning algebraic expressions with respect to knowledge components


  • Shiva Mafakheri
  • Ahmad Shahvarani Semnani
  • Mohammad Hassan Behzadi
  • Ali Barahmand


The purpose of this study is to apply the Attribute Hierarchy Method (AHM) in the cognitive domains of algebraic expressions to find cognitive inferences about students’ mathematical problem-solving skills. Initially, cognitive content techniques were developed to determine the knowledge and skills needed to solve mathematical assignments. Then, items were written specifically to assess skills in cognitive models. Finally, confirmatory psychometric analyses were used to evaluate students' response information by estimating the proportionality of the data model, attribute probabilities to report the diagnostic score and attribute validity. The first domain is concerned with the cognition and diagnosis of general polynomials and algebraic expressions and encompasses other areas. Therefore, the focus is on the precise definition of the basic concepts of the recognition of polynomials such as the polynomials and the number of very important terms and similar monomials and incorrect learning of algebra. Nevertheless, in the second domain, which focuses on simplification and related concepts, less emphasis has been placed on the seventh to ninth grades. The defect in the expression and practice of this field leads to weakness in solving and analyzing relevant mathematical problems. The third domain is related to the second domain and directly to the first domain. Factorization and distributive properties are often used without considering the rules of simplification by students. The weakness associated with the second domain causes the students not to be able to easily analyze and solve the problem in difficult polynomials in which the rules do not apply easily.

Author Biographies

Shiva Mafakheri

  Department of Mathematics , Science and Research Branch, Islamic Azad University, Tehran, Iran.

Ahmad Shahvarani Semnani

 Department of Mathematics , Science and Research Branch, Islamic Azad University, Tehran, Iran


Mohammad Hassan Behzadi

Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Ali Barahmand

 Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran