The aim of the study was to determine the effects of a dialogical argumentation instructional model (DAIM) on pre-service teachers' ability to solve conceptual maths-in-physics (MIP) problems. Using a quasi-experimental design the study included two equal groups of pre-service teachers (N = 40) to follow two instructional methods in which the experimental group was engaged in DAIM while the control group was engaged in a traditional teaching method (TTM) for a period of six months. The two groups were assessed to determine the effects of the two instructional methods in enhancing their ability to solve conceptual MIP problems in mechanics using a 48-item questionnaire as a pre- and post-intervention test. Additional data were collected during the intervention through classroom observations (for the DAIM group) and completed worksheets (for the TTM group) in order to gain further insight into the effectiveness or otherwise of the two instructional methods. Both sets of data were analysed for participants' ability to solve conceptual MIP problems by the extent to which they demonstrated the use of analytical skills, critical argumentation skills and reflective skills. The findings indicate that the DAIM intervention was significantly more effective than the TTM intervention in enhancing pre-service teachers' ability to solve conceptual MIP problems and to construct better arguments to support their claims with valid grounds. The implications of the findings for instructional practice are highlighted in the paper.