Digital storytelling (DST) is an innovative narrative practice based on the creation of multimodal stories, which promotes communicative as well as digital competences. This research verifies teachers' perception about the progress in communicative and digital competences in primary education children (N= 201) participating in a collaborative digital storytelling project supported by the Department of Education of the Principality of Asturias (Spain). The descriptive analysis shows teachers' qualitative assessment, related to the change perceived after DST creation. The teachers used an instrument consisting of 15 qualitative indicators and based on an assessment rubric, which was validated by means of the Delphi method. The results reveal that -- according to these instructors' perception -- such a collaborative digital narrative helped to foster both competences in the participating students. They all improve qualitatively, especially students enrolled in the higher stages, through the production of written compositions for DST (thus practicing with vocabulary, spelling and punctuation, as well as verb tenses), the elaboration of scripts with coherent characters and settings, and the expression of the purpose sought with their stories. As for digital competence, the higher stages developed it to a greater extent, due to the greater complexity of the tools used to create DST. In conclusion, teachers see collaborative DST creation as an educational practice which significantly activates schoolchildren's expression and communication skills, since it provides them with suitable environments to acquire story-related competences and abilities, supported by several technological resources and audiovisual techniques.