This report summarises the existing analysis, and adds new analysis, on historical trends with respect to learning outcomes in schooling systems around the world, with a view to informing projections for Sustainable Development Goal (SDG) indicator 4.1.1, which deals with the percentage of children who are proficient in reading or mathematics. Trends with regard to two statistics receive attention: mean scores of countries, and the percentage of students reaching specific levels of proficiency. Though SDG 4.1.1 concentrates on the latter, both statistics are important for gauging and modelling qualitative change. The report concludes that the findings presented here constitute a good basis for determining realistic and empirically informed, though not necessarily politically palatable, SDG 4.1.1 targets. The analysis could be replicated, using further data sources. However, there are other, more serious, research gaps. In particular, there is very little multi-disciplinary research aimed at understanding what policy and socio-economic factors explain how certain countries, such as Indonesia and Trinidad and Tobago, have achieved exceptional educational improvements over time.