The transition between arithmetic and algebraic thinking is challenging for students. One notable difficulty for students is understanding algebraic symbols--pronumerals. Researchers are exploring pedagogical approaches in seeking to address this issue. The current paper is contributing to this body of literature by illustrating how an online card…

I propose that students pay more attention to the approximations that lead to integral formulas when they study applications of the definite integral. The goal is to focus students on the underlying concepts and the definition of the definite integral--and to steer them away from memorizing formulas. To address this goal, I have written some…

Challenging problems can make mathematics more attractive to all learners, including the gifted. Application problems that one still finds in regular textbooks often can be resolved by applying a single mathematical concept, operation, or formula. These problems do not require a higher order of thinking. They are, therefore, less cognitively and…