In the MTI course I took, they recommended using Contexts For Learning Mathematics by Catherine Twomey Fosnot to let students learn math by experimenting, making decisions, and exploring math. The methods used help students know and understand math instead of memorizing facts. It shows them through discovery how to decompose and compose numbers to add and subtract. It is a very hands-on, self discovery way to teach numbers and their functions. Each child proceeds at their own rate so it encourages differentiation. I feel last years students left second grade as mathematicians ready for the Common Core because of the deeper understandings this program encourages.