Typical of experimental thinking is primarily the generation and testing of hypotheses. It forms the foundation for scientific as well as mathematical work. Exploring relationships and formulating and testing hypotheses based on examples are important elements in the process of gaining mathematical knowledge. Kathleen Philipp describes and structures these activities based on epistemological models under the concept of experimental thinking. Through two empirical studies, she investigates and categorizes cognitive processes of experimental thinking in relation to intra-mathematical explorations. She demonstrates that experimental competencies can be captured as different dimensions of ability and can be enhanced through appropriate training.