Algebraic reasoning is the cognitive and mathematical ability to identify patterns, generalize relationships, and manipulate symbols to solve problems. It entails using symbols, variables, and mathematical operations to represent and analyze quantitative relationships abstractly. Key aspects of algebraic reasoning include:

• Recognizing and generalizing patterns and regularities.
• Formulating equations and inequalities to represent real-world situations.
• Applying logical reasoning to solve these equations and inequalities.
• Making connections between different mathematical concepts and developing logical arguments.

Algebraic reasoning is fundamental for understanding algebra because it introduces abstraction and symbolic thinking, allowing students to move beyond specific calculations to grasp underlying structures and relationships. It supports analytical and problem-solving skills by breaking down complex problems into manageable parts. Besides math, algebraic reasoning is involved in everyday decision-making and many careers, such as architecture, software development, banking, and science. In summary, algebraic reasoning is about understanding patterns, generalizing from these patterns, and expressing these generalizations mathematically to solve problems both in math and real life. It plays a foundational role for developing critical thinking and problem- solving skills in mathematics education and beyond.