Problem posing and technology are attracting the attention of mathematics educators because of their potential to affect positively many aspects of students’ learning. Little research has been done on the relationship between technology and mathematical creativity. The present study investigates this issue in the context of problem posing, in the presence and absence of a strategy for problem posing (the “what-if-not” strategy). Participants were pre-service mathematics teachers. The research was conducted during the academic year 2013-2014. Participants were randomly divided into four groups of 19 to 21 participants and who differed in their use of technology and of the what-if-not strategy. The participants who used technology used the Paper Pools applet. The data was collected from the participants’ posing problems on a specific mathematics situation; the Paper Pool situation. The data analysis was done using SPSS 18.0. The research findings indicate that the combination of technology and the what-if-not strategy has a positive and significant effect on the three components of participants’ creativity: fluency, flexibility and originality. Separately, both technology and the what-if-not strategy had a positive and significant effect on participants’ fluency and flexibility related to problem types, but not related to strategy types. The findings also indicate that the originality of participants who worked without technology but with the what-if-not strategy was significantly lower than that of participants who worked with technology, whether with or without the what-if-not strategy. Thus, results indicated that technology is more effective than the what-if-not strategy in encouraging originality in problem posing. We recommend the use of technology together with the what-if-not strategy to enhance pre-service teachers’ mathematical thinking, because this combination makes available for student’s learning multiple agencies required for his/her creative acts.