Activity: Procedural vs. Conceptual Understanding in Solving Equations
Objective: To link procedural and conceptual understanding in solving equations by applying the order of operations and understanding the underlying concepts.
Materials:
Whiteboard or paper and pen/pencil for demonstration
Equations to solve (could include variables, exponents, fractions, etc.)
Directions:
Begin by discussing the importance of both procedural and conceptual understanding in solving equations. Emphasize that while procedural knowledge is necessary for solving equations, conceptual knowledge helps students understand why and how equations work.
Introduce the order of operations, emphasizing the importance of following the correct order to arrive at the correct solution.
Demonstrate solving an equation step-by-step, while explaining the underlying concepts. For example, if solving an equation with variables and exponents, walk through each step of the order of operations and explain why each step is necessary. Emphasize that procedural understanding is demonstrated through following the correct steps in order, while conceptual understanding is demonstrated through understanding why these steps are needed.
Have students work in pairs or small groups to solve equations of varying difficulty, using both procedural and conceptual understanding. Encourage them to check their work for accuracy and explain their steps to each other to reinforce both procedural and conceptual understanding.
As a class, come together to discuss and compare approaches to solving the equations. Encourage students to share their thought processes and ask questions to deepen their understanding.
Conclude the activity by summarizing the importance of both procedural and conceptual understanding in solving equations and how they contribute to a deeper understanding of mathematics.
Assessment: Assess students' understanding through observation during the activity and through individual or group assessments that require both procedural and conceptual understanding. For example, give students an equation to solve and ask them to explain not only the steps they took to solve the equation, but also why those steps were necessary.