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]]>As stated in this summary of Cathy Fosnot’s work on trajectories, we can think of “a “hypothetical learning trajectory” from Simon (1995). Learning trajectories are claimed to be “hypothetical” since until students actually attempt a problem, “we can never be sure what they will do or whether and how they will construct new interpretations, ideas and strategies” (Fosnot & Dolk, 2002, p.22).

In this way, Fosnot & Dolk (2002) do not reject the idea of a learning trajectory, but rather emphasize that a linear model does not account for “real” learning since real learning “is messy” (p.23). Instead, they suggest the metaphor of a landscape. In the landscape of learning, “knowledge of models, strategies, and big ideas,” are essential to organizing a coherent hypothetical learning trajectory. In other words, teachers and curriculum developers still need to have a clear and organized idea of what they want their students to know.

I think the landscape model can be closer to the true work. It certainly isn’t linear. But I think the linear model can help us in many ways as long as we remember that is is just a guide to help us think about how ideas build.

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