Robyn Jackson has written a lot on differentiated instruction and her first book, Never Work Harder Than Your Students, suggested many ways in which the students can take ownership of their own learning. Recently, she posted a blog about common mistakes when trying to differentiate lessons and highlighted four common areas. These are: Creating multiple assignments rather than multiple pathways; Differentiating by learning style versus learning needs; Differentiating by achievement level rather than by students’ current learning level; and Differentiating up rather than down. click here for more info
These four common mistakes really deal with the concept of differentiation: knowing your students and creating multiple pathways for each learner to achieve the learning outcomes. By posing purposeful questions and problems in mathematics, students at any level can enter into the problem (multiple entry points), delve deeper into the mathematics (multiple pathways) and reach the conceptual understanding of the mathematics.
Just some ideas and thoughts. Please let me know what you think.