Developing Mathematical Reasoning: Avoiding the Trap of Algorithms
Chapter 5: Solving Proportions with Proportional Reasoning
This student demonstrates proportional reasoning by scaling two values in tandem for a recipe with a 2:3 ratio of cups of peanut butter to cups of chocolate chips. To figure out the cups of chocolate chips needed to match with 3 cups of PB, she scales to 1 cup of PB to see that 1 more cup of PB would mean 1.5 more cups of chocolate chips. She uses this new unit rate of 1:1.5 to reason that 3 cups of PB would require 3 + 1.5 = 4.5 cups of chocolate chips.
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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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