How Children Discover Mathematical Structure through Relational Mapping
A core question in human development is how we bring meaning to conventional symbols. This question is deeply connected to understanding how children learn mathematics—a symbol system with unique vocabularies, syntaxes, and written forms. In this talk, I will present findings from a program of research focused on children’s acquisition of place value symbols (i.e., multidigit number meanings). The base-10 symbol system presents a variety of obstacles to children, particularly in English. Children who cannot overcome these obstacles face years of struggle as they progress through the mathematics curriculum of the upper elementary and middle school grades. Through a combination of longitudinal, cross-sectional, and pretest-training-posttest approaches, I aim to illuminate relational learning mechanisms by which children sometimes succeed in mastering the place value system, as well as instructional techniques we might use to help those who do not.
Consciousness and implicit learning
Can we learn without conscious awareness? Numerous evidences in the research of implicit learning have indicated that people can learn the statistical structure of the stimuli but seemingly without any awareness of its underlying rules. However, it remains unclear what types of knowledge can be learned in implicit learning, what is the relationship between conscious and unconscious knowledge, and what are the neural substrates for the acquisition of conscious and unconscious knowledge. In this talk, I will discuss with you about these ongoing questions.