Recent research has studied teachers’ individual mathematical and didactical knowledge through multiple choice items. This method is especially convenient for a large-scale study, but it does not cover teachers’ collective mathematical and didactical knowledge, including knowledge they may develop together and share with others. To examine this question in a concrete case, we use a method known as hypothetical teacher tasks (HTTs) to study pre-service elementary teachers’ (PsETs) mathematical and didactical knowledge of rational numbers. This method is based on the anthropological theory of the didactic, specifically praxeological reference models. It is applied to study thirty-two Indonesian PsETs’ mathematical and didactical knowledge of rational numbers. Through this method, we found that the PsETs tend to propose a direct instruction of mathematical techniques to teach pupils about rational numbers, and they often struggle to construct appropriate didactical techniques due to a lack of mathematical knowledge. In addition, we see how HTTs can be used to study collective components of teachers’ mathematical and didactical knowledge.