Investigations with the computer can have different functions in the mathematical learning process, such as to let students explore a subject domain, to guide the process of reinvention, or to give them the opportunity to apply what they have learned. Which function has most effect on mathematical level raising? We investigated that question in the context of developing learning materials for 16-year-old students in the domain of probability theory, consisting of computer simulations based on a gambling game and investigation tasks about these games. We compared the difference in level raising between three versions of the learning materials: investigations with the computer "before", "during" or "after" the learning of a mathematical concept. It was shown that there was no significant difference in the final mathematical level that students attained in the three conditions (the product). However, there were differences in the level on which students approached the investigation tasks (the process). Furthermore, we found evidence of new categories in the students' answers, lying between the perceptual and conceptual levels, which may give important insight into the process of level raising.