a child-centered approach

One thing that I have noticed through the readings of the different theorists is this over-arching theme that education should be child-centered. Students should learn through real world experiences and by “doing,” and that the teacher’s role should not be just transmitting the information. I can see doing that in things like art, science and reading but, I have questions on how you can do that in math. How do you make math hands-on? How do you take a concept like long division and not just make it worksheets and repeated practice of the steps? Is it considered hands on if the student is working it out on paper? Or, would it be hands on if it was applied in real-world situations, which are still solved with paper and pencil? Just some questions…maybe the math class will have the solution I seek.