Rubrics are assessment tools that help students gain complex competencies. Our quasi-experimental study aimed to evaluate whether rubrics help teachers teach and assess mathematical reasoning in primary school and whether such an instrument might support student learning. In two Swiss cantons, 762 students in 44 5th- and 6th-grade primary classes worked on their reasoning competencies, and half of them additionally employed our standards-based rubric. All of the teachers received a 1-day training and participated in the final project evaluation. To standardise and support the teachers during the implementation phase, they received a detailed curriculum. An achievement test and questionnaires for students and teachers were administered before and at the end of the intervention. The results of our quantitative longitudinal analyses indicate that the rubric fosters the teachers' perceived diagnostic skills but only indirectly impacts their use of formative feedback. Based on the students' perceptions, however, we observed a direct effect of the rubric on formative feedback and student self-assessment. Effects on students' outcomes could not be observed, but there are indications of effects mediated by self-regulation and self-efficacy.