7. Look for and make use of Structure.
The mathematically proficient student is capable of making close observations to discern patterns or “structures”. These structures form the basics of mathematics. The ability to discern these structures is vital to problem solving. The structures may be as simplistic as a number line; 2 follows 1 and 3 follows 2, or they may be incredibly complex. Mathematical growth requires building an ever greater awareness of structures and interconnectedness.
Specific instances could include recognizing multiplication is a specific number of sets, or that fractions represent the present parts of a whole. Students start by learning to count in order; 1, 2, 3,…. Later students learn more complex structures such as properties of operation, which can be used to add, subtract, multiply and divide. Recognition of even more complex structures allow for solving difficult algebraic equations, creating geometric proofs and statistical analysis.
Finally, students must be able to describe structures in writing, orally and through visual representations. Critical thinking skills and a true understanding of how the structures are formed is required to process such translations.