Often, algebra has not been treated explicitly in the school curriculum until the traditional algebra course offered in middle school or high school. By promoting algebra as a strand that is begun in the early grades, Principles and Standards supports other possibilities for configuring programs in the middle grades and secondary schools. Understand patterns, relations, and functions Early experiences with classifying and ordering objects are natural and interesting for young children. By the end of secondary school, they should be comfortable using the notation of functions to describe relationships. This is the beginning of recursive thinking.
Recursive sequences appear naturally in many contexts and can be studied using technology.
As they progress from preschool through high school, students should develop a repertoire of many types of functions. In the middle grades, students should focus on understanding linear relationships. In high school, they should enlarge their repertoire of functions and learn about the characteristics of classes of functions. By the middle grades, students should be able to understand the relationships among tables, graphs, and symbols and to judge the advantages and disadvantages of each way of representing relationships for particular purposes. Students' understanding of properties of numbers develops gradually from preschool through high school.