Easy to digest research on Mathematics education from Cambridge Mathematics, see their Espresso page where in their words, “Each month we bring you an Espresso – a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind. Each Espresso considers one particular issue in mathematics education, and how the latest good-quality research can provide helpful guidance or further reading.”
These Espressos are I believe an excellent example of clear communication of research as described by Harvard Graduate School of Education, see Communicating Research with readings, tips and strategies for clear expression.
Note Harvard’s ‘Find by topic’ for a menu of Usable Topics’; try Teaching for example for a further menu including the chance to ‘Ask a researcher’. The series, Ask a Researcher, offers evidence-based guidance for the classroom in the areas of literacy, mathematics, and English language learning. Try Math Problems? Ask a Researcher for example.
Craig Barton has an excellent selection of research papers he recommends for teachers. Craig has structured this really clearly as you can see from his Contents.
Craig states that his page contains the academic research he has read that has influenced the way he plans and teaches mathematics.
See also Research – Learning & Teaching. relevant for teachers of any subject.