Look For and Make Use of Structure
A core feature of doing mathematics is looking for the underlying structure in mathematics. Children often look for and use the structure in the world around them. For example, they notice that things that are alive usually move by themselves and use this to decide if something is alive. Mathematics has a very consistent structure, but often it is taught in a way that does not make the structure apparent. For example, presenting related sets of arithmetic facts in a sequence, such as 3 + 4, 4 + 3, and 7 – 4, helps students learn important mathematical structures – the commutative property of addition and the inverse relation between addition and subtraction. Presenting problems in a random order makes it much harder for students to notice these structures.
Students need to be encouraged to look for structure, not simply to apply a rule or structure given by the teacher. This means encouraging students to notice key features, such as identifying defining characteristics of shapes or noticing whether the order in which you add numbers changes the sum. Patterning activities also support attention to structure when done appropriately. For example, young children can be asked to identify the part of a pattern that repeats over and over and slightly older children can be asked to figure out a rule for predicting a new instance in a growing pattern or function table.
This mathematics practice is key component of Algebraic Thinking, especially in the early grades. Please see the Algebraic Thinking tab under Mathematical Content Areas for more information and ideas.