The Study of Evolution of conceptual and procedural Knowledge of mathematics and the relationship between them

One of the factors affecting students’ mathematical performance is their mathematical knowledge. Like many other issues in mathematics education, mathematical knowledge, is developed in recent years. In this paper, some of important studies, researches and approaches on conceptual and procedural Knowledge of mathematics are analyzed and the result determined three main approaches in this area. First, one dimensional model of mathematical knowledge was illustrated. So that, according to type, this knowledge was classified into conceptual and procedural knowledge. After passing some time and based on the need for changing this model, a two dimensional model of knowledge based on type and quality of knowledge, and then a three dimensional model based on type, depth and readiness for learning were suggested. In addition to the models, diverse ideas regarding the relationship between these two types of knowledge are discussed. Some of important ideas are as fallows: Inactivation view, simultaneous activation view, dynamic interaction view, Genetic view and Iterative view. In-depth study of existing approaches and also the results of this research suggest that the three dimensional model of mathematical knowledge is the most significant, compared to other models. Also, iterative view about the relationship between conceptual and procedural Knowledge is the most significant view, compared to others.