Learning From Explanation: The Timing and Source of Explanations for Learning Early Algebra

• In Event: Different Perspectives on the Role of Explanation and Exploration in Learning

Abstract

Theoretical Perspective. Some theories of learning and education focus on how much children learn through exploration and self-discovery of their environment without explicit instruction from a more knowledgeable person (“exploration”; Hirsh-Pasek et al., 2009; Piaget, 1973; Sylva, Bruner & Genova, 1976). Other theories focus on how children learn through guidance and instruction from more knowledgeable others such as parents and teachers (“explicit instruction”; Csibra & Gergely, 2009; Kirschner et al., 2006; Vygotsky, 1978). Both exploration and explicit instruction are thought to benefit learning in numerous ways.

Objective. We have been exploring ways to combine exploration and direct instruction in the context of explanation. Explanation is an important source of knowledge, and explanations can be generated by the learner (i.e., self-explanation) or provided by experts (i.e., instructional explanations). In this talk, I will focus on explanations on mathematical principles, in particular in early algebra.

Research Evidence. In one set of studies, we focused on the source of the explanation – self- vs. instructional-explanations. Four-year-old children learned to abstract repeating patterns (e.g., create the same kind of pattern using new materials), an early pre-cursor to abstraction and generalization in mathematics (Economopoulos, 1998; Papic et al 2011). Across two studies, instructional explanations improved the conceptual quality of children’s self-explanations. However, children learned just as much if they generated explanations on their own than if they received instructional explanations or alternated between self- and instructional explanation. Thus, the source of the explanations was not important.

In a second series of studies, we focused on the timing of instructional explanations on mathematical equivalence, the idea that two sides of an equation represent the same amount. In two studies, we have found that 2nd and 3rd graders learned more if the instructional explanations were delayed until after children attempted to solve related problems, rather than providing the explanations prior to problem solving. One study was in a one-on-one tutoring setting and the other was conducted in classrooms. In a third study, carefully crafted self-explanations prompts during the solve phase reversed this effect, leading to greater learning if instructional explanations were provided immediately, but such a design required a one-on-one tutoring setting. Thus, the timing of instructional explanations impacted learning, but the optimal timing seemed to vary based on whether learners were supported in generating self-explanations that built on the instructional explanations.

Significance. These studies highlight the importance of considering the source and timing of explanations. Overall, these studies suggest that even young children can generate self-explanations that promote learning, that delaying the provision of instructional explanations can increase learning, and that generating self-explanations that incorporate instructional explanations has mixed effects on learning. More generally, they illustrate the benefits of considering both exploration.

Authors

• Bethany Rittle-Johnson, Vanderbilt University

• Emily Ruth Fyfe, Vanderbilt University

• Abbey M. Loehr, Vanderbilt University

• Michael Robert Miller, Vanderbilt University