This is an area of education where the practice that happens in schools is far from the research evidence that exists. International analysts conclude that the most successful countries are those that group by ability the latest and the least. Mixed achievement teaching is associated with higher overall achievement for students of all levels and when schools move from tracking to giving all students high-level math classes, achievement increases significantly (see Evidence – Research Papers). But teaching children in mixed achievement groups requires a different form of teaching than the more typical lecture and short question repetition that prevails in US math classrooms. If schools and classrooms de-track without adjusting their teaching, high results are unlikely to be the outcome. Over the years I have been fortunate to work with many incredible teachers, committed to equity, who teach mixed achievement groups. On this page are two papers detailing the successful use of mixed achievement grouping, one in a high school setting (How a detracked mathematics approach ..) and one describing what happened when a district took away advanced classes in middle schools (Raising Expectations and Achievement). Our Group Work page also details ways to teach students heterogeneously. My book: Mathematical Mindsets details ways to teach mixed achievement groups successfully. Other cases of successful mixed achieving grouping include our summer camp teaching, which is shown under Evidence – Our Teaching Approach.
This paper by Jo Boaler and David Foster reviews an intervention in which student learning of mathematics increased dramatically.