Engineering students in technical universities in Sweden, as probably in many other countries, tend to treat mathematics as a mechanical subject in which you do calculations and manipulations and there is very little explanation. In order to create deeper understanding, verbal or written explanations by students can be beneficial. In our study we show a possible way of teaching students to reflect about their mechanical solutions to mathematical problems. The method is based on the supplementary written explanations that students may provide in their written examination in what would be a second stage of the examination, a so-called "home exam". In our project students were forced to rethink their answers, attending to comments and questions posed by the teacher who marked the scripts and supplying further explanation of his/her work. Judging from the results of the research, this facet of the project was successful. The additional opportunity to reflect on their responses assisted students in developing a deeper understanding of the mathematical concepts and also exposed weaknesses and gaps in their knowledge. (Contains 1 table.)