Research on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the presence of words and expressions having many and sometimes opposite meanings. Significant examples are the terms 'realistic' and 'modeling' associated with word problems in school. Understanding how these terms are used is important in research, because this issue relates to the design of several studies and to the interpretation of a large number of phenomena, such as the well-known phenomenon of students' "suspension of sense making" when they solve mathematical problems. In order to deepen our understanding of this phenomenon, we describe a large empirical and qualitative study focused on the effects of variations in the presentation (text, picture, format) of word problems on students' approaches to these problems. The results of our study show that the phenomenon of suspension of sense making is more precisely a phenomenon of activation of alternative kinds of sense making: the different kinds of active sense making appear to be strongly affected by the presentation of the word problem.