DescriptionIn a traditional math curriculum, the solving of quadratic equations is a topic for a first year algebra course, usually in the eighth or ninth grade. Solving quadratic equations typically follows other topics such as solving linear equations and factoring polynomials. Traditionally, the concept of solving quadratic equations is introduced through combining these two topics to find the solution(s).
The purpose of this analytic is to illustrate a different approach to solving quadratic equations that is introduced at a much younger age. The researcher in the analytic, Robert B. Davis, introduces these complex algebraic topics to sixth graders, using their arithmetic skills and natural curiosity to guide them in discovering some patterns about quadratic equations and their solutions. The students eventually develop their own understanding of how the product of the two solutions equals the constant term of the equation and the sum of the two solutions equals the coefficient of the linear term (note that all of their equations have a negative sign in front of their linear term and have "1" for a coefficient of the quadratic term).
Researcher Davis’ carefully structured problems follow an order that increases in difficulty and engage students to notice patterns in their solutions. He intermittently challenges their understanding with additional problems that reveal the underlying structure. Throughout the lesson, Researcher Davis listens carefully to the children, providing guidance and encouragement through probing questions without explaining the heuristics. His inquiry-based lesson invites students to explore advanced algebraic concepts with quadratic equations and discover patterns between the components of the problems and their solutions on their own.
For more information about the lessons in this analytic, see Spang, Kathleen E. (2009). Teaching algebra ideas to elementary school children: Robert B. Davis’ introduction to Early Algebra. (Doctoral dissertation).
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