This study examined how expert and novice (preservice) teachers solved mathematical modelling tasks as well as how they noticed written artifacts of student thinking that were in response to the mathematical modelling tasks. Some teachers in both groups were aware of the openness and underdetermination of the modelling tasks and that these characteristics implied that underlying assumptions needed to be made in order to solve the tasks. Indeed, nearly all of the expert teachers addressed the need to make assumptions for the Seashell Task. When examining student work, both expert and preservice teachers interpreted positive aspects in the students' solutions and provided feedback to students. However, almost all of the expert teachers responded by asking questions, whereas around a third of preservice teachers directly corrected students' mistakes and another third pointed out mistakes without correcting them. This study provides a new angle to study teachers' mathematical competencies, the assessment of modelling competencies, and considerations for the development of teachers' modelling competencies.