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Posted: November 28, 2013 in The root of the matter

Complicated thinking assumes that math is a collection of pieces that can be assembled or disassembled in order to understand a concept. I thought of this as a big jigsaw puzzle: each time you put together the puzzle, the outcome is the same; you are not creating anything different.

Complex understanding acknowledges that mathematics is more than a collection of parts and how they work together. “Complex thinking involves understanding the role that is played by the whole is necessarily embedded in social and natural environments.” Each time the pieces are put together, something new is created. This also means that it cannot be easily taken apart, such as when you bake a cake. You cannot simply go backwards in your procedure and end up with your original ingredients. They are now apart of this new thing, called cake.

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Jennifer then postulates that a complex view of curriculum is needed. Okay, so instead of looking at curriculum as separate, distinct parts we need to consider viewing curriculum as dynamic, flexible, and co-evolving based on interactions between teacher-student-environment. I understand this concept, and I feel that this is the direction learning is headed toward. I am interested in what this curriculum would look like: Would subjects be taught by guided questioning, problem solving and exploration? Instead of distinct subjects (mathematics, art, science) would we view learning as embedding these elements in every learning experience? At the end of the chapter Jennifer likens mathematics to residue, explaining that it “resides seamlessly and all at once with past, present, and future contexts of students’ knowing.” I will admit I feel overwhelmed by this chapter, as you have to completely disregard all previous notions of curriculum and learning. However, the ideas in the chapter ring true for me, and I will work on examining these concepts further.

 

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