What may be neglected by an application-centred approach to mathematics education?

It seems that an ongoing discussion of why modelling and applications should be part of mathematics education has mostly centred around utilitarian argument. In my opinion, such an attitude may produce an unbalanced view on the reasons for including modelling and applications in mathematics education, which, in turn, may result in a neglect of the following important issues of mathematical modelling: – the complexity of the modelling process; – the distinction between the perspective of model builders and that of model users – the necessity of a demanding interplay among students' cognitive, metacognitive and affective domains in the modelling process. The article briefly presents the application-centred approach to mathematics education, examines these neglected issues, and suggests how the teaching of modelling and applications may thus be utilised.