The Interconnectedness of Mathematical Processes

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Ontological argument

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The Interconnectedness of the Mathematical Processes

Selecting Tools and Computational Strategies

is used to prove one's solution

will affect how the solution is represented

calls for making connections to similar problems solved in the past and reflection in order to choose what is most efficient

enables problem solving

Communicating

is a part of each step in the problem-solving model

is required for reasoning / proving or justifying one's answer

can be seen through representing

Reflecting

is a characteristic of a good problem-solver

helps students make connections and internalize a deeper understanding

will lead to more efficient ways of selecting tools and computational strategies

Reasoning and Proving

requires a form of representing and communicating one's work/solution

is done using a selected tool or computational strategy

calls for communication to help justify thinking

Representing

is a way of proving one's solution

is part of problem solving

is a form of communicating one's thinking/solution

in various forms helps students to understand the connections among related representations and mathematical concepts

Connecting

occurs through problem solving

goes hand and hand with reflection

Problem Solving

calls for a form of representing their solution

will lead to connecting mathematical ideas and deepen conceptual understanding

calls for reflection of their own thinking and/or the thinking of others to refine their thinking

requires communication to articulate their thinking

encourages reasoning/proving a solution

requires one to select a tool or computational strategy in order to solve the problem