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reasoning
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problem solving
作者:
Christina Williamson
6 年以前
99
The Interconnectedness of Mathematical Processes
Understanding mathematical concepts involves multiple interconnected processes that enhance comprehension and problem-solving skills. Representing mathematical ideas in various forms helps students make connections between different concepts.
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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