• The Mathematical Education
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• v.49 no.2
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• pp.149-160
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• 2010

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.