Philosophiae Doctor - PhD (Education) / This study chronicles a teacher training education programme. The findings emerged from the observation of argumentation skills employed by students in a physical science education classroom for pre-service high school teachers. Their task was to use the nature of arguments to solve mathematical problems of mechanics in a physics classroom. Forty first-year students were examined on how they used a dialogical argumentation instructional model (DAIM) based on Toulmin's (1958/2003) Argument Pattern (TAP), Downing's (2007) Analytical Model (DAM) and Ogunniyi's (2007a & b) Contiguity Argumentation Theory (CAT) to solve mathematical problems in physics. Thus efforts to judge the pre-service teachers' capability to solve mathematical problems in physics with respect to mechanics were compounded by the demand for the inclusion of a self-efficacy framework. According to Bandura (2006) self-efficacy is the judgment of capability. Selfefficacy plays a key role in human functioning in that it affects not only people's behaviour but other issues such as goals and aspirations, outcome expectations, affective proclivities and perception of impediments and opportunities in the social environment (Bandura, 1995, 1997 & 2006).