Over the past two decades, competence-based education has become a dominant trend in vocational and undergraduate education. The term competence-based education covers various conceptual ideas and practices arising from technical thinking in which education is seen as training competency, emphasising the development of complete vocational competence promoting autonomous identity and its continuous improvement. It should reflect how mathematics is taught at all levels of vocational education. As the PISA research has revealed gaps in skills in STEM subjects, our goal is to develop a powerful online learning model to promote access to undergraduate studies and employment for the disadvantaged in Finland. Their mathematical and scientific skills are analysed and trained online according to their self-direction. This facilitates graduating on time and applying for further studies. de Brujin and Leeman’s original model of a powerful learning environment is enhanced, focusing now on online adaptive guidance, and supporting self-regulating skills. The initial state for improving mathematical competence and self-regulating skills is the formation of a vocational identity obtained in previous education. The model is delineated by the idea of cognitive apprenticeship, acquiring knowledge and skills to pursue further studies. Online reflection and constructive learning from authentic situations towards a more abstract construction of knowledge is viewed from sociocultural theory and its perspective on cognition. Understanding the mathematical self-concept of online learners can inform strategies for improving online mathematics education.