ABSTRACT
A theoretical framework, like any abstraction, must simplify from the chaos of life, must ignore parts of the data in order to be truly useful. In education, the almost inevitable danger is oversimplification. Educational theory is therefore a tricky thing. When we are being teachers, theory does guide us some, but not completely. Sawyer (1964), in Vision in Elementary Mathematics, explains: It is a defect of most algebra books that they begin by developing a lot of machinery, and it is a long time before the learner sees what he can do with all this machinery. Life, of course, is a bit more nuanced than we've just portrayed it, especially when one is quite near the frontier of a child's thinking. The Math Workshop approach certainly did not avoid questions that pushed at the edges of children's thinking. Judd (1928) explicitly questioned the assumptions being made about so-called real-world contextualization.
