Hilary Barth - US grants

This project will investigate the role of magnitude biases in mathematical cognition, learning, and development. Magnitude bias refers to the idea that psychological magnitudes are often different from their corresponding actual magnitudes. This proposal lays out evidence for these biases in oft-used research paradigms in numerical cognition that are applicable to math education, describes two sets of studies to investigate these further, and sets the stage for a future career that will investigate educational implications by developing partnerships with educational researchers and practitioners.

The first set of experiments investigates the role of abstract magnitude bias in children's learning to integrate their intuitive understanding of quantity with linguistic systems. This work has important theoretical implications for mathematical cognition and learning, and it has demonstrated applications to math education: the developmental changes in question are correlated with changes in school-based math achievement.

The second set investigates the role of perceptual magnitude bias in nonverbal quantitative thinking. This work has important theoretical implications for the nature of the representational foundations of children's math knowledge, and it holds promise for educational applications because perceptual biases affect our thinking about the magnitudes of observed items. To the extent that instructional materials such as manipulatives and visualization tools are meant to convey meaningful magnitude information, these biases are likely to affect math concept learning.

Humans have an innate ability to estimate quantities yet their intuitions often contain biases that interfere with learning new ways to think about quantity. Weaving together strands of psychology, neuroscience, economics, and education, researchers at Wesleyan University and Boston College shed light on the cognitive processes underlying our abilities to estimate 4 kinds of quantities: number, space, time, and probability. By comparing processes across these four distinct areas, the researchers aim to provide a unifying account of how children and adults estimate quantities, which has the potential to transform current understanding of the cognitive bases of how people learn in and across STEM disciplines. Achieving a simple unifying account is important because the ability to think well about quantity in all of these areas is fundamental to STEM learning. Other educational benefits include the establishment of partnerships with local museums that allow the research team to collect data from a diverse population while also supporting the museum's public education efforts. This project also contributes to STEM workforce development by training undergraduate students through a service-learning course offered at Wesleyan, and through a summer research internship exchange across the two universities. These aspects of the project, taken with its robust theoretical grounding, well-formulated research questions and tests of competing models of how people reason about quantity in childhood and adulthood, demonstrate its potential to guide and improve the design of STEM learning environments for all citizens.

This project exemplifies the Education and Human Resources Core Research program's commitment to fundamental research on learning in STEM that combines theory, techniques, and perspectives from a wide range of disciplines and contexts. Specifically, it aims to provide a unifying account of how children and adults estimate quantities across four distinct domains: the development of numerical estimation; spatial categorization (remembering the location of items in space); the theoretical neuroscience of time processing (reproducing temporal durations); and decision making under risk (the processing of probabilities). Through a series of behavioral studies with adults and children, the researchers will test their hypothesis that proportion judgment underlies basic quantity estimation across these domains, across development, and across contexts (varying task constraints). This work is important because -- despite striking similarities in behaviors described across research in these literatures -- each one conceptualizes them quite differently, positing different accounts of the underlying mechanisms that yield quantity judgments. The project will advance and potentially transform our understanding of mental representations and processes involved in quantity judgments while also providing insight into how quantity biases may influence the processing of numerical information in educational contexts and real-life decisions. In this way the project builds a coherent, cumulative knowledge base, focusing on high-leverage topics.

This proposal was submitted in response to EHR Core Research (ECR) program announcement NSF 19-508. The ECR program of fundamental research in STEM education provides funding in critical research areas that are essential, broad and enduring. EHR seeks proposals that will help synthesize, build and/or expand research foundations in the following focal areas: STEM learning, STEM learning environments, STEM workforce development, and broadening participation in STEM. The ECR program is distinguished by its emphasis on the accumulation of robust evidence to inform efforts to (a) understand, (b) build theory to explain, and (c) suggest interventions (and innovations) to address persistent challenges in STEM interest, education, learning, and participation.

This research examines numerical and mathematical cognitive processing, with accompanying correlational work that links study results to formal math skills and complex judgments relevant to mathematics literacy. Estimation tasks predict performance on real-world math outcomes; and are useful as teaching tools. Understanding these tasks, what they conceptually measure, and why these measures predict math outcomes, help us better teach math concepts. The research advances mathematics learning by carefully examining paradigms used in numerical cognition.

The research team will conduct seven experimental studies of estimation tasks using number lines. The research team will examine whether participants' judgements of numeric magnitude are influenced by digit dependence; principally, the left most digit. The work will be conducted with subjects aged 3-11, as well as adults. To support causal claims, participants will be randomly assigned to treatment and control groups. The data will be analyzed causally using analysis of variance techniques. The studies have been appropriately powered to warrant all research claims. The proposed research advances basic knowledge of mathematics learning by carefully examining research paradigms that inform theories of cognition, development, and learning.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.