In this paper we discuss a study on the approaches to modeling of students of the 4-year elementary school teacher program at the University of Palermo, Italy. The answers to a specially designed questionnaire are analyzed on the basis of an a priori analysis made using a general scheme of reference on the epistemology of mathematics and physics. The study is performed by using quantitative data analysis methods, i.e. factorial analysis of the correspondences and implicative analysis. A qualitative analysis of key words and terms used by students during interviews is also used to examine some aspects that emerged from the quantitative analysis. The students have been classified on the basis of their different epistemological approaches to knowledge construction, and implications between different conceptual strategies used to answer the questionnaire have been highlighted. The study's conclusions are consistent with previous research, but the use of quantitative data analysis allowed us to classify the students into three "profiles" related to different epistemological approaches to knowledge construction, and to show the implications of the different conceptual strategies used to answer the questionnaire, giving an estimation of the classification or implication "strength." Some hints on how a course for elementary school physics and mathematics education can be planned to orient the future teachers to the construction of models of explanation are reported.