Introduction. In the context of the proliferation of digital educational environments and artificial intelligence systems, the problem of transmitting mathematical meanings in teaching becomes particularly relevant. The availability of ready-made solutions does not guarantee that students will develop their own reasoning methods, which is especially significant in teaching combinatorics, where constructing a model, choosing an enumeration method, and justifying the solution are required. Aim. To identify the conditions under which the Wise Tasks Combinatorics system can act as a boundary object in teaching combinatorics. Materials and Methods. The study is based on analyzing students’ work with a digital environment that supports solving, constructing, and verifying combinatorial problems. A comparison was made between independent work, work with mandatory protocoling of the solution process, and work with pedagogical support. Solution protocols, errors, number of attempts, and reasoning patterns were analyzed. Results. It was found that during independent work, students primarily focus on obtaining an answer. Mandatory protocoling makes the solution process more detailed but does not in itself provide meaningful deepening. It is shown that only in combination with pedagogical support does the digital environment begin to support exploratory research activity and the transmission of basic combinatorial ideas. It is substantiated that the boundary object is not the system itself, but the system embedded in a specially organized interaction. Conclusion.  It is not the Wise Tasks Combinatorics system itself that acts as a boundary object, but rather the same system embedded in a specially organized interaction that includes pedagogical support and reflection on the solution process – which alone ensures the transfer of combinatorial meanings.