Composition of functions are important tool for producing associativity in mathematical model. However it is not properly treated in dealing together with the other operation, the addition +, of functions defined on real numbers. In this note, we will study mathematization of the construction of nearring axiom from relationships between the addition + and the composition $circ$ of functions, comparing with those between the addition + and the multiplication of functions. Furthermore, we will suggest some helpful teaching methods of these mathematization in the secondary school mathematics.