Robert Siegler - US grants

The basic goal of this project is to advance understanding of change processes in children's thinking. The research incorporates a different conceptualization of change and different methods for studying it than have characterized most research in the field. The overlapping-wave model that underlies the research is based on the view that children typically possess multiple ways of thinking about a given phenomenon; that much of development involves changes in the relative frequencies of these alternative ways of thinking; that children choose adaptively among the alternatives; that they frequently generate new ways of thinking about given phenomena; and that generation of these new ways of thinking is constrained by domain-specific conceptual knowledge. The microgenetic methods that are used frequently within the research are based on densely sampling changing behavior as it is changing, with the goal of identifying the path, rate, breadth, variability, and sources of change. Such dense sampling of changing behavior provides a kind of high resolution microscope for indicating precisely how cognitive changes occur. The particular goals for the next 5 years are to 1) extend microgenetic methods to studying developmental differences in learning, 2) use the methods to compare problem solving in individual and collaborative contexts, 3) examine the impact on children's learning of their efforts to understand the reasoning underlying other people's reasoning, 4) assess how growing conceptual knowledge influences the new problem solving procedures that children generate, and 5) model the mechanisms that produce discovery of new strategies. The work promises to be of educational as well as theoretical importance, due both to the tasks being studied (geometry misconceptions, measurement, arithmetic, scientific reasoning) and many of the variables being investigated (effects of being asked to explain other people's reasoning, effects of calculus experience).

This grant will support a conference to bring together researchers from a variety of backgrounds to consider how children's thinking evolves during development, with a particular focus on the role of experience in causing change. This is a fundamental topic related both to the processes by which children learn and those that make children ready and able to learn from experience. Both behavioral and neural approaches to these issues will be considered. The behavioral approaches will include research on the 'microgenesis' of cognitive change---that is, research that considers development as it occurs over relatively short periods of time (e.g., several hour-long sessions) in specific task situations such as solving arithmetic problems. Research on cognitive change over longer time scales (months and years) will also be considered, as will research that uses computational modeling and dynamical systems approaches to processes by which change in thinking ability occur. Neural approaches will include the study of the way in which neuronal responses, and the connections among neurons, change in response to experience, particularly as these changes are expressed during the actual process of acquiring new thinking skills in children and adults. Other neural approaches include studies of the possible basis of the emergence of cognitive abilities through the progressive maturation of various brain structures, and studies of the effects of experience on the organization of and internal representations in various brain regions. The conference will also consider developmental anomalies such as autism and attention deficit disorder as windows on normal function. The following questions will be examined in the course of the workshop: 1) Why do cognitive abilities emerge when they do during development? 2) What are the sources of developmental and individual differences, and of developmental anomalies in learning? 3) What happens in the brain when people learn? 4) How can experiences be ordered and timed so as to optimize learning? The answers to these questions have strong implications for how we educate children and remediate deficits that impede development of thinking abilities. These implications will be drawn out in discussions among the participants. The proceedings of the symposium will be published as a volume in the Carnegie Symposium series.

This award was provided as part of NSF's Social, Behavioral and Economic Sciences Postdoctoral Research Fellowships (SPRF) program. The goal of the SPRF program is to prepare promising, early career doctoral-level scientists for scientific careers in academia, industry or private sector, and government. SPRF awards involve two years of training under the sponsorship of established scientists and encourage Postdoctoral Fellows to perform independent research. NSF seeks to promote the participation of scientists from all segments of the scientific community, including those from underrepresented groups, in its research programs and activities; the postdoctoral period is considered to be an important level of professional development in attaining this goal. Each Postdoctoral Fellow must address important scientific questions that advance their respective disciplinary fields. Under the sponsorship of Dr. Robert Siegler at Teachers College, Columbia University and Dr. Clarissa Thompson at Kent State University this postdoctoral fellowship award supports an early career scientist investigating children’s understanding of the relations among rational number notations (fractions, decimals, and percentages). Earlier work has shown that rational numbers, particularly fractions, are important for algebra, which in turn, is predictive of life outcomes. Unfortunately, children’s rational number understanding is quite poor. The ultimate goal of the proposed research is to understand children’s conceptions of our number system and to identify methods for improvement. This work may have important implications for curriculum and instruction across elementary and middle school.

The current project builds on Siegler, Thompson, and Schneider’s (2011) Integrated Theory of Numerical Development, which argues that fractions are central to numerical development. Here, we focus on children’s understanding of the relations among fractions, decimals, and percentages, what we call, integrated number sense. Very little is known about children’s cross-notation understandings. Initial findings (Schiller, 2020) suggest that integrated number sense is a critical skill that is largely ignored by curriculum and research. Specifically, integrated number sense, as measured by magnitude comparison across notations, uniquely predicted math achievement beyond fraction magnitude representations. Additionally, integrated number sense predicted fraction arithmetic estimation, whereas fraction magnitude representation did not. However, students demonstrate little cross-notation understanding. For example, students are biased towards perceiving percentages as larger than fractions and decimals (e.g., higher accuracy for comparing 40% vs. 1/4 than 2/5 vs. 25%). The proposed project aims to develop instruction to build integrated number sense by: 1) investigating integrated number sense in much greater detail and the role it plays in other math outcomes, 2) examining use of the mental number line by investigating strategic use of magnitude within and across notations, 3) testing whether it is more effective to use an isolated or integrated approach to build this cross-notation abstraction of the mental number line.

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.