Employer complaints of engineering graduate inability to 'apply knowledge' call for a better understanding of the theory-practice relationship in technology-driven twenty-first century industries. A novel systems-based model was developed to analyse how mechatronics engineering practitioners apply mathematics, physics and logic-based knowledge to practical problems in different industrial systems contexts. Theoretically and methodologically, the research draws on the work of Herbert Simon, Basil Bernstein and Legitimation Code Theory. The graphic analysis of the relationship between the problem solver and problem structure in different industrial contexts demonstrates that different ways of thinking are required in considering the 'what' and the 'how' of the problem under different conditions. Current curricula not only need to explicitly enable the shifting between different engineering thinking 'codes', but also need to promote a more conceptual grasp of contextual factors. This paper offers a research-informed perspective on what 'apply knowledge' really means in twenty-first century engineering contexts. (149)