Students have great difficulties moving from procedural algebra to structural algebra (Boaler 2013). Procedural algebra can be described as using a letter to represent a single unknown number that students find, such as the value of x when 7x + 4 = 32. In contrast, structural algebra requires using symbols to express generality in a situation and asking such open-ended questions as “Describe how the pattern is growing” or “Can you find the number of squares in case n?” Boaler asserts that analyzing geometric growth patterns using multiple representations (manipulatives, words, pictures, graphs, tables, and symbols) supports the understanding of structural algebra because making connections and seeing different representations lead to deeper learning and can unleash incredible understanding.
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