Algebra is an important branch of mathematics, both historically and presently.

“… algebra has been too often misunderstood and misrepresented as an abstract and difficult subject to be taught only to a subset of … students who aspire to study advanced mathematics; in truth, algebra and algebraic thinking are fundamental to the basic education of all students… Algebra is frequently described as ‘generalized arithmetic’, and indeed, algebraic thinking is a natural extension of arithmetical thinking.

To think algebraically, one must be able to understand patterns, relations and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various contexts.

In high schools, students create and use tables, symbols, graphs and verbal representations to generalize and analyze patterns, relations and functions with increasing sophistication and they flexibly convert among these various representations. They compare and contrast situations modeled by different types of functions and they develop an understanding of classes of functions, both linear and non- linear, and of their properties.

High school students continue to develop fluency with mathematical symbols and become proficient in operating on algebraic expressions in solving problems. Their facility with representations expands to include equations, inequalities, systems of equations, graphs, matrices and functions, and they recognize and describe the advantages and disadvantages of various representations for each particular situation. Such facility with symbols and alternative representations enables them to analyze a mathematical situation, choose an appropriate model, select an appropriate solution method and evaluate the plausibility of their solutions.

High school students develop skill in identifying essential quantitative relationships in a situation and in determining the type of function with which to model the relationship. They use symbolic expressions to represent relationships arising from various contexts, including situations in which they generate and use data. Using their models, students conjecture about relationships and formulae, test hypotheses and draw conclusions about the situations being modeled." (Greenes, et. al., 2001, pp. 1-4)