This paper investigates the transmission of educational attainment from parents to offsprings as a mediator of intergenerational class mobility in Europe. The study covers the last two decades with data drawn from a cross-national large scale sample survey, namely the European Social Survey (ESS), for the years 2002 - 2018. Interest has focused on the question of persistence of inequality of educational opportunities by examining attainment of nominal levels of education and the association between the educational attainment of the parent with the highest level of education and their descendants. The study covers also new trends in social mobility which consider education as a ‘positional good’ and a novel method of incorporating educational expansion into the transition probabilities is proposed, providing answers to whether the rising accessibility of educational qualifications attenuates the association between social origin and educational attainment. Therefore, the concept of positionality is taken into account in the estimation of intergenerational transition probabilities and to complement the analysis mobility measures are provided for both methods, nominal and positional. The proposed positional method is validated through a correlation analysis between the upward mobility scores (nominal and positional) with the Education Expansion Index (EEI) for the respective years. The upward mobility scores estimated via the positional method are higher correlated with the EEI for all years indicating a better alignment with the broader trends in educational participation and achievement.