The argument of this theoretical paper is that the existence and availability of suitable digital curriculum resources, accelerated by the recent pandemic, have required a revision of the pedagogical landscape in terms of ways in which students can be empowered to (co-)design their own curriculum trajectories. For this purpose, I argue, students need to be supported in considering many connections, to arrive at coherent trajectories. Based on complexity thinking and curriculum design with digital resources, I propose the concept of connectivity as a crucial principle for creating coherent curriculum trajectories. If students are to become the co-designers of their own curriculum, they need a frame that raises their awareness about the many connections to be made and that supports their capability for actually realizing them. Drawing strongly on my own work and related work by others, I analyse and illustrate the connections made by students, teachers and curriculum designers in their design of mathematics tasks, lessons and learning trajectories with digital resources. Results show that connections can be made at several levels, namely, at a social level, at a material level, at programme level, and at a didactical level. Leaning on systems thinking, connections can be systematically considered, which is likely to help students to enhance the coherence of their designs. I contend that a student-designed 'connected curriculum trajectory' is likely to become the focus of future research activities in innovative learning environments: this endeavor would connect aspects of curriculum, mathematical content, learning strategies of students, and the use of new technologies.