The starting point of our article is to identify integrative phenomena, that are suitable for both visual arts and mathematics and, moreover, for teaching that preserves the nature of each of these subjects and their specific methods of acquiring and processing information. The article consists of two separate, yet interconnected studies: a teaching experiment, implemented in a Finnish 7^th grade lower secondary school, and a survey aimed at preservice mathematics teachers with the question: `What are mathematical phenomena?'. The teaching experiment revealed that integrative phenomena suitable for use in school must be sufficiently open, to enable pupils and teachers to have a genuine joint investigative learning experience. Following this finding, we looked for more general principles and, from the survey, we found that the phenomena could either be related to concepts that are shared by each of the integrating disciplines, such as ratio and representation, or they could be more dynamic, typical processes of knowledge- acquisition and construction, such as sorting and classification.