What This Means for Instruction

Here are some tips to help educators planning instruction in algebra:

• Teach algebra to all students from pre-kindergarten through grade 12. Focus initial instruction on patterns, rules and relationships equivalance and representation. Later, involve variables, structure, representation, patterns, graphing, expressions, equations, rules and functions (Chapin & Johnson, 2000).
• Algebraic Communication: Require students to communicate thinking and justify solutions orally or in writing. This will help students develop understanding, gain familiarity with the language of algebra and make connections between arithmetic and algebra (Greenes & Findell, 1999).
• Algebraic Reasoning: Go beyond asking students to create pictorial (for example, drawings, diagrams or maps), graphic (for example, scatterplots or bar, circle or line graphs) and symbolic (for example, tables, formulas or functions) representations. To develop algebraic reasoning students need to:
• interpret the mathematical relationship in these representations;
• create or use different representations of the same mathematical relationship and make connections among these;
• recognize how a change in one representation affects change in another representation for the same mathematical relationship (Sierpinska, 1992).
• Variables: Help students develop a richer understanding of variables by addressing all ways that variables are used in algebra:
• a specific unknown (such as 4t = 12);
• a varying quantity that depends on another variable (such as x = 4y );
• a generalization that can show relationships (such as a + b = b + a).
• Patterns: Help students learn the importance of patterns in mathematics. Invite them to examine varied types of patterns (repeating, arithmetic, geometric and numeric) to discover that patterns can be generalized with rules and functions and can be represented numerically and geometrically.
• Equality: Teach the concept of equality or balance and share strategies to create equivalent forms. These include strategies such as adding the same amount to both sides, multiplying both sides by the same positive factor and making equal substitutions (Greenes & Findell, 1999).
• Functions: Help students understand the concept of functions. This analogy may be useful: A function is a machine that will take an input and return one output. Once a rule is learned, students can predict outputs or they can use inverse operations to predict inputs from a given output. When students develop skill with a single operation function (such as, f(x) = 3x - 7), students can be given a set of inputs and corresponding outputs and describe the "rule" of that function either in words or symbolically (Greenes & Findell, 1999).