On the opposite end of the instructional spectrum from the procedural approach to teaching mathematics is the conceptual approach. Where procedural-based instruction provides mathematics facts, algorithms, and formulas that can be used to solve mathematical problems, conceptual-based instruction seeks to provide the reasons why these algorithms and formulas work. The emphasis is on the students learning important concepts of mathematical connections, relationships, and applications. Rather emphasizing direct-instruction, memorization, drill, and practice, conceptual-based mathematics instruction focuses on student discovery, use of manipulative, problem-solving, and use of technology as teaching methodologies.
The fundamental premise is that students must have a conceptual understanding of mathematics as the scaffold upon which they build their procedural knowledge. Otherwise, they are inflexible in their use of mathematics and unable to effectively transfer their acquired procedural knowledge to new and unique problems and situations. The rise of the conceptual approach to mathematics instruction is consistent with a constructivist approach to education. Typically, students who have been taught math from a conceptual approach tend to have higher scores on the math sections of achievement tests in the areas related to concepts/reasoning than those related to computation.
