Readiness for the study of patterns, functions, and algebra should begin in the PreK-K years of school. A strong foundation should be carefully constructed and expand gradually as the years of schooling progress. All students should be comfortable with basic algebraic concepts and the meaning of function by the end of eighth grade. The treatment of algebra and functions should accelerate and continue to grow throughout the secondary years. All students should be aware of the mathematics in patterns and use mathematical representations to describe patterns.
Young students identify, translate, and extend repeating rhythmic, verbal, and visual patterns.
They learn to recognize patterns and relationships among objects, and to sort and classify them, observing similarities and differences. Young students then probe more deeply into the study of patterns as they explore the properties of the operations of addition and multiplication. Through numerous explorations, elementary grade students deepen their own understanding of pattern and work informally with the concept of function. In middle and high school, students build on prior experiences and formalize recursive thinking as they compare sequences and functions represented in recursive and in closed forms. Algebra emerged through the analysis of solutions to equations while the concept of a function developed as the roots of calculus began to spread.