Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson

Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding.

This study evaluated the effect of instruction on a math concept and procedure within the same lesson relative to a comparable amount of instruction on the concept alone. Direct instruction was provided before or after solving problems to evaluate whether the type of instruction interacted with the timing of instruction within a lesson.

We worked with 180 second-grade children in the United States.

In a randomized experiment, children received a classroom lesson on mathematical equivalence in one of four conditions that varied in instruction type (conceptual or combined conceptual and procedural) and in instruction order (instruction before or after solving problems).

Children who received two iterations of conceptual instruction had better retention of conceptual and procedural knowledge than children who received both conceptual and procedural instruction in the same lesson. Order of instruction did not impact outcomes.

Findings suggest that within a single lesson, spending more time on conceptual instruction may be more beneficial than time spent teaching a procedure when the goal is to promote more robust understanding of target concepts and procedures.