Sara J. Cordes, Ph.D. - US grants

Infants are sensitive to numerical information in the world around them, and evidence suggests that the ease with which they discriminate the number of items in a set may be correlated with later achievements in mathematics in the classroom setting. While much work has been dedicated to identifying simple and effective means for targeting math skills in school-aged children, no work has identified similar interventions for enhancing numerical abilities in infancy. Can infants be taught to attend to number? If so, does this training have lasting effects? The first goal of this project is to validate simple and inexpensive methods for facilitating numerical discriminations in preverbal infants, long before mathematics difficulties may be encountered in the classroom.

The second goal of the project is to clarify how it is infants and young children make the connection between these preverbal representations of number and verbal count words. Many studies have focused on examining the acquisition of verbal counting in preschoolers, however few, if any have examined the receptive language end of this question -- namely, at what point do infants understand that words can refer to numbers? What factors facilitate and/or hinder their ability to form the mapping between words and numerosities? By exploring the relationship between language and number in preverbal infants, this project will provide a foundational understanding of exactly what conceptual knowledge young children bring to the table when learning to count.

The educational and research integration plan of the project involves a three-pronged approach of (1) graduate and undergraduate training in developmental research, including the initiation of a summer internship program for students at undergraduate institutions with limited research opportunities, (2) the development of a new undergraduate research-based course on infancy, and (3) the creation of a free annual lecture series for parents in the greater Boston area interested in learning about infant cognition, with the goal of helping parents become better consumers of scientific information and of infant-oriented marketed products. Combined, this project has the potential to impact education both at Boston College and throughout the Boston community, to inform our understanding of the mapping between preverbal with verbal representations of number, and to identify effective interventions to enhance the preverbal foundations of mathematics that can be implemented at a much earlier age and across the socioeconomic spectrum.

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.

The learning of mathematical concepts, such as proportions and negative numbers, is frequently fraught with difficulty because often these concepts do not structurally align with whole number concepts acquired during the preschool years. This proposed work investigates how to promote reasoning about such concepts by capitalizing on recent findings demonstrating young children's relative competence in social domains that recruit similar mathematical knowledge. This proposal aims to identify how the acquisition of difficult mathematical concepts may be readily transferred from informal social contexts in which they may be first encountered (e.g., sharing) to more formal contexts in which children are typically asked to apply them (e.g., formal arithmetic).

Through behavioral experiments with over 1000 4-9-year-old children, this work will explore how social contexts may promote math learning. In Series 1, studies investigate how social framing impacts children's learning of two traditionally counter-intuitive concepts: negative numbers and proportions. Series 2 will investigates factors that facilitate transfer of knowledge between math concepts learned in contextualized, informal scenarios such as those encountered in one's daily life (e.g., sharing) to more formal, symbolic-based contexts (e.g., division). Finally, Series 3 will investigate how socio-contextual influences may, in turn, serve to promote or hinder children?s learning. These studies investigate how preferences for competition versus collaboration, and gender stereotypes about academic domains impact children's decisions to opt in and out of learning opportunities affect their math learning. The culmination of this work should paint a broader understanding of social influences on math learning, pointing to new directions for math education practices. This project will provide deeper insight into how social contexts may promote or hinder the learning of counter-intuitive math concepts. The project is supported by the EHR Core Research (ECR) program that emphasizes fundamental research in STEM.

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.

There is currently a gender gap in STEM fields, such that females participate at lower rates and have lower career attainment than their male counterparts. While much research has focused on gender differences in math attitudes, little work has explored how attitudes in a closely related STEM domain, spatial reasoning, may also contribute to the observed gender gap. The proposed research will characterize the acquisition of gender stereotypes in childhood in two key domains critical to success and participation in STEM fields: math and spatial skills. Recent evidence suggests that children acquire math gender stereotypes (i.e., the belief that "math is for boys") as early as 1st - 2nd grades, but less is known about children's attitudes about spatial abilities. This project will be one of the first to investigate the development and emergence of spatial gender stereotypes (and their relation to math gender stereotypes) in elementary school-aged children, and their impact on parent-child interactions in the pre-school period. This project is funded by the EHR Core Research program, which emphasizes STEM education research that will generate foundational knowledge in the field.

Eight behavioral studies involving 1290 children (Pre-K - 4th graders), 240 caregivers, and 180 adults will participate in studies that evaluate an integrated theoretical model of the relations between gender, gender stereotypes, attitudes, and abilities in the domains of math and space. In Series 1, studies will characterize the emergence of and assumptions behind spatial- and math- gender stereotypes in 1st - 4th graders, while determining how they may be acquired. In Series 2, studies will explore the real-world impacts of spatial-gender stereotypes on STEM participation and achievement in childhood. Lastly, Series 3 studies will explore the malleability of these stereotypes in the hopes of identifying ways to ameliorate their impact early in development. The project will provide training for doctoral graduate and undergraduate students. Moreover, this project will support new and ongoing collaborations with local children's museums, which facilitate interactions and communication with families, educators, and the public about the research findings. By being some of the first work to uncover the developmental origins and consequences of math and spatial stereotypes, this work may inform possible future interventions to reduce and/or eliminate the perpetuation of these stereotypes in children, long before they can have greater lifelong impacts.

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.

Preschool numeracy is a crucial foundation for STEM learning and long-term academic success. Previous research suggests that the development of strong numeracy skills depends on a combination of perceptual, cognitive, and language skills. However, most past studies have focused on a relatively small and homogeneous groups of children in US urban areas. As a result, current understanding of early numeracy may not<br/>generalize to diverse groups of learners. It is likely that home language background, socio-economic status, and geographic and cross-cultural differences could also influence numeracy development. To address this, and to probe what factors drive early numeracy in a representative sample, this first-of-its-kind project investigates how toddlers and preschool-aged children perceive, reason, and talk about numbers in a massive multi-lab collaboration involving over 130 research sites worldwide.<br/><br/>To investigate early numeracy, this collaborative project includes two foundational studies. The first study focuses on how 2- to 5-year-old children perceive quantity, learn number words, and how to accurately count groups of objects. The study examines variability in how children learn about number and quantity while exploring the underlying perceptual, cognitive and linguistic mechanisms that drive their learning. The second foundational study focuses on toddler’s abilities to keep track of small groups of objects, which researchers have argued may play an especially important role in early numerical learning. This study examines variability across larger and more diverse groups of participants than previously studied. The study also asks whether limits to children’s object tracking abilities change when they begin to learn number words. In addition to these foundational studies, the project supports the creation of multiple exploratory studies, allowing for novel, ground-breaking collaborations between researchers worldwide. These exploratory studies examine how numerical abilities are related to diverse phenomena including but not limited to social cognition, linguistic diversity, cognitive abilities like executive function, and cross-cultural differences in mathematics education and attitudes. Collectively, these studies will test over 3000 children in 28 US states and 27 countries, using a combination of cross-sectional and longitudinal behavioral assessments. Final data will be shared with the broader scientific community, and will be presented on a website in simplified form to make findings accessible to the broader public.<br/><br/>This project is funded by the EHR Core Research (ECR) program, which supports work that advances fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.<br/><br/>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.