How can we use mathematics education research to uncover, understand and counteract mathematics specific learning difficulties?

Mathematics education research from the last four decades has helped us to understand more and more about the nature and processes of mathematical learning. This has further helped us to uncover and understand characteristic obstacles that most learners of mathematics - and not only those with general learning difficulties - encounter during their attempts to learn mathematics, some even to a detrimental degree. Mathematics specific learning difficulties seem to be of a rather universal nature across cultures, countries and students. In my lecture I shall highlight some of these difficulties with a focus on recent work and findings. I shall further present a research based in-service education programme for upper secondary school teachers enabling them to detect and diagnose upper secondary students with mathematics specific learning difficulties and eventually to remedy or reduce these difficulties.