This empirical study examines the assessment judgment of Geneva primary school teachers when they are required to grade students’ tests, specially for additive problem-solving exercises. The research questions relate, on the one hand, to the characteristics of the written tests drawn up by the teachers. On the other hand, they refer to the teachers’ judgment as they verbalize their thoughts during assessment. Through the analysis of critical incidents observed during the grading of students’ tests, research findings reveal a concern for teachers to understand students’ mathematical reasoning, specially to handle unexpected and singular responses leading to a specification of the assessment criteria. The analyzes undertaken lead to the conceptualization of different cases between analytical and holistic judgments whose constructive tension can be seen as a major development challenge for the assessment of complex learning activities, such as solving mathematical problems.