Early numerical knowledge lays the foundation for later mathematics achievement, career advancement, and daily functioning. Therefore, it is troubling that mathematics achievement in the United States is especially poor. For this reason, it is crucial that ways to improve learning outcomes in young children, particularly in the area of mathematical development are explored. Mathematics is a complex process, which requires flexible thinking, exploration and analysis of novel, complicated, and real world problems. Guided discovery is a pedagogical context, which is adult-initiated and child-directed and promotes flexible thinking, analysis of complex problems- the same skills required for early mathematical learning. The goal of this study was to examine the effectiveness of one element of guided discovery- dialogic inquiry- for improving children’s numerical knowledge when used in a guided discovery setting. Dialogic inquiry is the practice of asking questions that lead children to think differently about the mathematical concepts at hand or act differently on the objects in their environments.

Ninety-four preschoolers played a life-sized linear number board game under three conditions and were randomly assigned to one of three conditions: math-related dialogic inquiry, math statements, and positive encouragement. Children’s learning from pretest to posttest was compared on four numerical knowledge outcomes: number line estimation, magnitude comparison, arithmetic, and ordinality. Additionally, children’s mathematical talk and behavior during board game play were compared across conditions.

Children in the dialogic inquiry condition improved more than children in the math statements and positive encouragement conditions on arithmetic performance. Children in the math statements condition declined in performance on magnitude comparison significantly more than children in the dialogic inquiry and positive encouragement conditions. Lastly, children in both the dialogic inquiry and math statements conditions outperformed children in the positive encouragement condition on ordinality. There were no significant differences between conditions for mathematical talk and behavior. Understanding the specific mechanisms, such as dialogic inquiry, which contribute to the effectiveness of guided discovery will improve the implementation of guided discovery pedagogies aimed at improving numerical knowledge.