Developing Mathematical Reasoning: Avoiding the Trap of Algorithms
Chapter 6: Not Functional Reasoning 1
T-shirts: A function represents a relationship between x and y as well as a relationship between symbolic and graphical representations. Functional reasoning in this context of purchasing t-shirts involves a simultaneous coordination of story, equation, and graph. In this video, the student successfully represents the situation with an equation. However, when he guesses a range for y rather than reasoning about one, he shows he doesnโt yet have a sense of how the relationship between x and y shows up in the graph.
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This Book:
Developing Mathematical Reasoning: Avoiding the Trap of Algorithms emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. This book illuminates a hierarchy of mathematical reasoning to help teachers guide students through various domains of math development, from basic counting and adding to more complex proportional and functional reasoning.
Everyone is capable of understanding and doing real math.
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