During the last four decades, we have seen policy makers express an urgency to have all of America’s students proficient and fluent in mathematics. Despite the incredible effort of dedicated mathematics educators, the myths that “only certain people can learn math” and that “it’s OK not to do math” interfere with the potential progress of some, if not many students.
Differentiated instruction is based on fundamental beliefs about differences among learners, how they learn, learning preferences and individual interest, and that instruction should be flexible enough to accommodate individual differences that naturally occur among learners. The key to successful differentiation is to discover how a particular student learns and demonstrates his or her learning. Armed with this knowledge of their students, teachers can take appropriate measures to adjust the three central elements of the curriculum: the content of what is taught, the manner in which it is taught, and how understanding is assessed .
Differentiated instruction, in contrast to the traditional “one-size-fits-all” approach to teaching, responds to classrooms that are increasingly characterized by academic and cultural diversity. However, it is NOT individualized instruction. Differentiated instruction encompasses a versatile collection of strategies that include tiered activities and flexible grouping . Tomlinson summarizes effective teaching in general as responsive teaching where students are highly engaged, contribute actively to the learning, and receive and use quality feedback. More specifically, effective math teaching includes the following key behaviors:
- Focusing content on the essential big ideas of mathematics
- Expecting all students can and will understand mathematics
- Continuously assessing student thinking and understanding
- Planning and structuring lessons based on student needs and important content
- Facilitating high-level conversations with appropriate and timely questions 
The resources below present relevant background information about differentiated instruction and ideas for implementing such practices in the everyday classroom.
Tomlinson, C. A., How to Differentiate in Mixed-Ability Classrooms. Second Ed., 2001, Alexandria, VA: Heinemann.
Tomlinson, C. A., Fulfilling the Promise of the Differentiated Classrooom: Strategies and Tools for Responsive Teachin, 2003, Alexandria, VA: ASCD.
Murray, M., The Differentiated Math Classroom, 2007, Portsmouth, NH: Heinemann.