About

Robert Stuart Siegler is the Jacob H. Schiff Foundations Professor of Psychology and Education at Teachers College, Columbia University. His scholarly interests focus on how children learn mathematics and how theoretical understanding of mathematical development can be applied to improve that learning. His research has demonstrated that playing certain numerical board games can lead to broad, rapid, and enduring gains in preschoolers' and elementary school children's numerical understanding, especially for children from low-income backgrounds. Siegler has authored over 250 articles, monographs, and book chapters, and has written 13 books and edited 6 others. His contributions to the field have been recognized through numerous honors, including the American Psychological Association's Distinguished Contribution Award in 2005, election to the National Academy of Education in 2010, and the G. Stanley Hall Award for Distinguished Contribution to Developmental Psychology in 2022. He has served on the U.S. National Mathematics Advisory Panel and has led the development of educational practice guides, including one on fractions learning for the U.S. Department of Education. Siegler's work emphasizes the importance of understanding the development of numerical knowledge and strategies in children, and he has played a significant role in advancing research and practice in cognitive development and mathematics education.

Research topics

• Computer Science
• Psychology
• Mathematics education
• Data Mining
• Artificial Intelligence
• Arithmetic
• Epistemology
• Political Science
• Mathematics
• Machine Learning
• Sociology
• Engineering
• Developmental psychology
• Engineering ethics
• Chemistry
• Cognitive psychology
• Cognitive science

Selected publications

• Building integrated number sense in adults and children: Comparing fractions-only training with cross-notation number line training

  Journal of Experimental Child Psychology · 2024-07-26 · 4 citations

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• Learning from errors versus explicit instruction in preparation for a test that counts

  British Journal of Educational Psychology · 2024-01-11 · 15 citations

  articleOpen access

  BACKGROUND: Although the generation of errors has been thought, traditionally, to impair learning, recent studies indicate that, under particular feedback conditions, the commission of errors may have a beneficial effect. AIMS: This study investigates the teaching strategies that facilitate learning from errors. MATERIALS AND METHODS: This 2-year study, involving two cohorts of ~88 students each, contrasted a learning-from-errors (LFE) with an explicit instruction (EI) teaching strategy in a multi-session implementation directed at improving student performance on the high-stakes New York State Algebra 1 Regents examination. In the LFE condition, instead of receiving instruction on 4 sessions, students took mini-tests. Their errors were isolated to become the focus of 4 teacher-guided feedback sessions. In the EI condition, teachers explicitly taught the mathematical material for all 8 sessions. RESULTS: Teacher time-on in the LFE condition produced a higher rate of learning than did teacher time-on in the EI condition. The learning benefit in the LFE condition was, however, inconsistent across teachers. Second-by-second analyses of classroom activities, directed at isolating learning-relevant differences in teaching style revealed that a highly interactive mode of engaging the students in understanding their errors was more conducive to learning than was teaching directed at getting to the correct solution, either by lecturing about corrections or by interaction focused on corrections. CONCLUSION: These results indicate that engaging the students interactively to focus on errors, and the reasons for them, facilitates productive failure and learning from errors.

  PublisherOA PDFDOI

• Connecting learning environments to learning: Two examples from children’s mathematics

  Developmental Review · 2024-06-12 · 7 citations

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• A unified model of arithmetic with whole numbers, fractions, and decimals.

  Psychological Review · 2023-08-17 · 20 citations

  articleOpen accessSenior author

  This article describes UMA (Unified Model of Arithmetic), a theory of children's arithmetic implemented as a computational model. UMA builds on FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite et al., 2017), a model of children's fraction arithmetic. Whereas FARRA-like all previous models of arithmetic-focused on arithmetic with only one type of number, UMA simulates arithmetic with whole numbers, fractions, and decimals. The model was trained on arithmetic problems from the first to sixth grade volumes of a math textbook series; its performance on tests administered at the end of each grade was compared to the performance of children in prior empirical research. In whole number arithmetic (Study 1), fraction arithmetic (Study 2), and decimal arithmetic (Study 3), UMA displayed types of errors, effects of problem features on error rates, and individual differences in strategy use that resembled those documented in the previous studies of children. Further, UMA generated correlations between individual differences in basic and advanced arithmetic skills similar to those observed in longitudinal studies of arithmetic development (Study 4). The results support UMA's main theoretical assumptions regarding arithmetic development: (a) most errors reflect small deviations from standard procedures via two mechanisms, overgeneralization and omission; (b) between-problem variations in error rates reflect effects of intrinsic difficulty and differential amounts of practice; and (c) individual differences in strategy use reflect underlying variation in parameters governing learning and decision making. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

  PublisherDOI

• Integrated knowledge of rational number notations predicts children’s math achievement and understanding of numerical magnitudes

  Cognitive Development · 2023-09-25 · 6 citations

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• Curriculum standards and textbook coverage of fractions in high-achieving East-Asian countries and the United States

  Current Opinion in Behavioral Sciences · 2022-07-22 · 5 citations

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• Comments regarding Numerical Estimation Strategies Are Correlated with Math Ability in School-Age Children

  Cognitive Development · 2022-04-01 · 4 citations

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• Why do we have three rational number notations? The importance of percentages

  Advances in child development and behavior · 2022-01-01 · 7 citations

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• Integrated Knowledge of Rational Number Notations Predicts Children's Math Achievement and Understanding of Numerical Magnitudes

  2022-08-30 · 4 citations

  preprintOpen accessSenior author

  We propose that integrated number sense, the ability to fluidly translate and compare magnitudes within and across notations, is central to understanding of rational numbers. Consistent with this hypothesis, two studies of 6th through 8th grade students (N=264 and N=46) indicated that accuracy comparing magnitudes within and across notations predicted overall math achievement and fraction number line and arithmetic estimation accuracy. Cross-notation magnitude comparison accuracy (i.e., fraction vs. decimal, percentage vs. fraction, and percentage vs. decimal) accounted for variance in math outcomes beyond that explained by magnitude representations of individual notations. The findings also revealed a percentages-are-larger bias, in which percentages are perceived as larger than equivalent fractions and decimals. Theoretical and instructional implications are discussed.

  PublisherOA PDFDOI

• Biased problem distributions in assignments parallel those in textbooks: Evidence from fraction and decimal arithmetic

  Journal of Numerical Cognition · 2022-03-31 · 7 citations

  articleOpen accessSenior author

  Imbalances in problem distributions in math textbooks have been hypothesized to influence students’ performance. This hypothesis, however, rests on the assumption that textbook problems are representative of the problems that students encounter in classroom assignments. This assumption might not be true, because teachers do not present all problems in textbooks and because teachers present problems from sources other than textbooks. To test whether distributions of problems that students encounter parallel distributions of textbook problems, we analyzed fraction and decimal arithmetic problems assigned by 14 teachers over an entire school year. Five of the six documented biases in textbook problem distributions were also present in the classroom assignments. Moreover, the same biases were present in 16 of the 18 combinations of bias and grade level (4 th , 5 th , and 6 th grade) that were examined in assignments and textbooks. Theoretical and educational implications of these findings are discussed.

  PublisherOA PDFDOI

Recent grants

• NIH Grant R01HD019011

  NIH · $3.2M · 2006

Frequent coauthors

• Jenny R. Saffran

  University of Wisconsin–Madison

  61 shared

• Nancy Eisenberg

  Arizona State University

  60 shared

• Elizabeth T. Gershoff

  31 shared

• Judy S. DeLoache

  30 shared

• David W. Braithwaite

  Florida State University

  28 shared

• Tian Jing

  26 shared

• Lisa K. Fazio

  Vanderbilt University

  21 shared

• Lynn S. Fuchs

  American Institutes for Research

  19 shared

Awards & honors

• American Psychological Association's Distinguished Contribut…
• Election to the National Academy of Education (2010)
• Development of a Practice Guide on fractions learning for th…
• Director of the Siegler Center for Innovative Learning at Be…
• Election to the Society of Experimental Psychologists (2015)