The modern difficult epidemiological situation has put forward new requirements for teaching mathematics to school students. Amid the pandemic they have to get their mathematics education remotely or through blended learning. Hence, students – future teachers of mathematics should be ready to organize such learning in this new digital learning environment. Therefore, the purpose of the study was to develop a model for training future teachers of mathematics for distance and blended mathematics education. The model is designed in the format of collaborative learning based on the interaction of five subjects of the educational space: teachers, masters and bachelors (future teachers of mathematics), university teachers and school students. The model was obtained from the analysis of previous studies, practical experience of distance learning, and theoretical analysis of the problem. The study tested the impact of collaborative learning (CL) on the level of readiness of future teachers for distance or blended learning in mathematics. The study used qualitative methods and statistical processing of the experimental results. The experiment showed that the differences in the level of training among the experimental and control groups for blended learning in mathematics turned out to be significant, which confirmed the efficiency of the model developed by the authors.