This chart doesn't seem accurate to me. I always think of Montessori as being in the progressive vein, at least as compared to traditional education. However, Montessori's theories and methods are very different from those of Piaget and Dewey, upon which Progressive education (capital P to distinguish), is based. In fact, Dewey was a major critic of Montessori. Montessori seems far more structured than Progressive. While both are project based, Progressive education stresses social participation, creativity and more thinking outside the box, at least for younger kids, than Montessori seems to.
This is a better link to the various theorists:
http://everydaylife.globalpost.com/comparison-early-childhood-development-theorists-6320.html