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As I see it, yes, context is important but not to show students how they can use math. The context is important to show students how their mathematics is a natural extension of how they think and live in the world. Constance Kamii says it best:

"Most math educators think about verbal problems (word problems) as applications of computational 'skills,' rather than as the beginning point that eventually leads to generalized computation, without content, context, or practical purpose."

*Young children reinvent arithmetic: Implications of Piaget's theory*. New York, NY: Teachers College Press.