Funded Grants

Understanding the development of early mathematics knowledge

One of the goals of science is to predict human behavior. For example, who will complete their college degree and who will drop out? Who will develop mental or physical ailments and who will remain healthy? It turns out that mathematics achievement is a robust predictor of many human behaviors, including those related to academic success, economic status, and healthful living (e.g., Adelman, 2006; Ritchie & Bates, 2013). On average, individuals with higher mathematics knowledge and achievement tend to have more positive outcomes in life.

But what is mathematics knowledge and how does it develop? What kind of learning experiences cause improvements in mathematics knowledge? My research program focuses on these questions and others surrounding the development of mathematics knowledge in early childhood. My goals are to characterize changes in children’s knowledge over time and to evaluate the effects of early learning experiences on those changes. I employ an interdisciplinary, multi- method approach that capitalizes on perspectives from cognitive science and educational psychology. Using behavioral experiments and longitudinal designs, I seek to understand the mechanisms of change that promote mathematics knowledge.

In a newer line of research, I have studied the emergence of a particular type of early mathematics knowledge – children’s patterning skills. Picture a child creating a necklace that alternates between green and orange beads or a child reproducing a parent’s rhythm of stomp- stomp-clap-stomp-stomp-clap. This ability to notice and generate predictable sequences may play a pivotal role in the development of mathematics knowledge. For example, we have established that knowledge of basic repeating patterns at age five predicts formal mathematics achievement seven years later, even after controlling for general math and language skills, socioeconomic status, and other individual characteristics (Fyfe, Rittle-Johnson, & Farran, 2018). However, it remains unclear what is unique about “patterning skills,” whether they are malleable, and whether changes in those skills lead to changes in math achievement.

Moving forward, my independent research will help address these questions in two main ways. First, I aim to use both cross-sectional and longitudinal data to explore the relations between different types of patterning skills and different types of formal mathematics knowledge. In this work, I will consider the complexity of different pattern types and tasks as well as developmental differences in children’s strategies and errors. Second, I aim to experimentally compare different techniques for enhancing children’s patterning skills at different ages. In this work, I will consider the language used by teachers to describe patterns and the types of materials used to create patterns and the social interactions they inspire. Ultimately, this program of research will provide novel insights into the development of mathematics knowledge as well as early childhood experiences that promote mathematics learning.