Robert S Siegler
Biographic Data
| ID | 1541573 |
|---|---|
| NAME | Robert S Siegler |
| GIVEN NAMES | Robert S |
| FAMILY NAME | Siegler |
| SIGNATURE | SIEGLER R S |
| AFFILIATIONS | Carnegie Mellon University |
| ORCID | 0000-0001-5457-5158 |
| VERIFIED | Yes |
| TOTAL WORKS | 52 |
| TOTAL CITATIONS | 233 |
| AUTHOR COUNT | 52 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1972 |
| LATEST PUBLICATION YEAR | 2026 |
| H-INDEX | 7 |
The Pictorial–Semantic–Task Framework for Understanding Graph Comprehension
Graphs are used in school, many occupations, and daily life, yet many people struggle to interpret them accurately. To help identify sources of difficulty in graph comprehension, we propose the Pictorial–Semantic–Task Framework. In it, we argue that accurate interpretation of graphs requires integrating pictorial variables (e.g., slope direction, graph format, data points) with semantic variables (e.g., titles, labels, scales, variable types) to …
Learning Variability Network Exchange (Levante): A Global Framework for Measuring Children's Learning Variability Through Collaborative Data Sharing
Despite the ubiquity of variation in child development within individuals, across groups, and across tasks, timescales, and contexts, dominant methods in developmental science and education research still favor group averages, short snapshots of time, and single environments. The Learning Variability Network Exchange (LEVANTE) is a framework designed to enable coordinated data collection by research teams worldwide, with the goal of measuring var…
Learning from errors versus explicit instruction in preparation for a test that counts
BackgroundAlthough 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.AimsThis study investigates the teaching strategies that facilitate learning from errors.Materials and MethodsThis 2-year study, involving two cohorts of ~88 students each, contrasted a learning-from-errors (LFE) with an explicit i…
Connecting learning environments to learning: Two examples from children’s mathematics
Developmental trajectories of numerical magnitude representations of fractions and decimals
We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as fraction and decimal 0-1 and 0-5 number line estimation tasks. Magnitude representations of decimals b…
Predicting adaptive expertise with rational number arithmetic
BACKGROUND: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and procedural knowledge of rational numbers, there are substantial individual differences in adaptive rational…
Putting fractions together
Learning fractions is a critical step in children’s mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions intended to improve understanding of both individual fractions and fraction addition. The framework, Putt…
Distributions of textbook problems predict student learning: Data from decimal arithmetic
This study investigated relations between the distribution of practice problems in textbooks and students’ learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal arithmetic problems were present across the 3 series: Addition and subtraction more often involved 2 …
How do people choose among rational number notations
Manifesto for new directions in developmental science
Although developmental science has always been evolving, these times of fast-paced and profound social and scientific changes easily lead to disorienting fragmentation rather than coherent scientific advances. What directions should developmental science pursue to meaningfully address real-world problems that impact human development throughout the lifespan? What conceptual or policy shifts are needed to steer the field in these directions? The p…
How Children Develop, Canadian Edition
Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade
Development of fraction number line estimation was assessed longitudinally over 5 time points between 4th and 6th grades. Although students showed positive linear growth overall, latent class growth analyses revealed 3 distinct growth trajectory classes: Students who were highly accurate from the start and became even more accurate (n = 154); students who started inaccurate but showed steep growth (n = 121); and students who started inaccurate an…
Entwicklungspsychologie im Kindes- und Jugendalter
Why is learning fraction and decimal arithmetic so difficult
Relations of different types of numerical magnitude representations to each other and to mathematics achievement
Learning from number board games: You learn what you encode
We tested the hypothesis that encoding the numerical-spatial relations in a number board game is a key process in promoting learning from playing such games. Experiment 1 used a microgenetic design to examine the effects on learning of the type of counting procedure that children use. As predicted, having kindergartners count-on from their current number on the board while playing a 0-100 number board game facilitated their encoding of the numeri…
What’s Past Is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement
Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, and few have investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multisite longitudinal data. We find that presc…
Microgenetic Learning Analysis: A Distinction without a Difference
Parnafes and diSessa [this issue] present a useful description of the process of doing microgenetic analysis of qualitative data and report interesting findings about how students’ reasoning changes as they gain relevant experience. We are pleased that microgenetic approaches are being applied to educational issues and agree with the authors that new knowledge can be gained by closely examining changes in students’ thinking over time. Conceptual …
Developmental and individual differences in understanding of fractions
We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross-sectional design. Results indicated that the difference between low achieving and higher achieving children's fraction arithmetic knowledge, already substa…
Early Predictors of High School Mathematics Achievement
Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United Sta…
An integrated theory of whole number and fractions development
How children develop
Commentary
Playing linear number board games—but not circular ones—improves low-income preschoolers’ numerical understanding.
A theoretical analysis of the development of numerical representations indicated that playing linear number board games should enhance preschoolersâ numerical knowledge and ability to acquire new numerical knowledge. The effect on knowledge of numerical magnitudes was predicted to be larger when the game was played with a linear board than with a circular board because of a more direct mapping between the linear board and the desired mental repre…
Recent Trends in the Study of Cognitive Development: Variations on a Task-Analytic Theme
The purpose of this article is to review recent advances in task-analytic techniques for studying cognitive development. Task analysis involves breaking down problems into component operations and then combining the components into models of performance. Two early influential task-analytic techniques were those of Gagné and Simon; each of these is briefly described and evaluated. Next, three recently-developed techniques are explored. Sternberg’s…
What’s Past Is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement
Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, and few have investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multisite longitudinal data. We find that presc…
Developmental and individual differences in pure numerical estimation
The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1, kindergartners and 1st, 2nd, and 3rd graders were presented problems involving the numbers 0-100; in Experimen…
The microgenetic method: A direct means for studying cognitive development
A featural analysis of preschoolers' counting knowledge
Developmental and individual differences in understanding of fractions
We examined developmental and individual differences in 6th and 8th graders' fraction arithmetic and overall mathematics achievement and related them to differences in understanding of fraction magnitudes, whole number division, executive functioning, and metacognitive judgments within a cross-sectional design. Results indicated that the difference between low achieving and higher achieving children's fraction arithmetic knowledge, already substa…
Children's Learning
A new field of children's learning is emerging. This new field differs from the old in recognizing that children's learning includes active as well as passive mechanisms and qualitative as well as quantitative changes. Children's learning involves substantial variability of representations and strategies within individual children as well as across different children. The path of learning involves the introduction of new approaches as well as cha…
Learning from number board games: You learn what you encode
We tested the hypothesis that encoding the numerical-spatial relations in a number board game is a key process in promoting learning from playing such games. Experiment 1 used a microgenetic design to examine the effects on learning of the type of counting procedure that children use. As predicted, having kindergartners count-on from their current number on the board while playing a 0-100 number board game facilitated their encoding of the numeri…
Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade
Development of fraction number line estimation was assessed longitudinally over 5 time points between 4th and 6th grades. Although students showed positive linear growth overall, latent class growth analyses revealed 3 distinct growth trajectory classes: Students who were highly accurate from the start and became even more accurate (n = 154); students who started inaccurate but showed steep growth (n = 121); and students who started inaccurate an…
The other Alfred Binet
Alfred Binet is famous as the author of the IQ test that bears his name. He is almost unkown, however, as the investigator who generated numerous fascinating investigations into developmental, experimental, educational, and social psychology. This «other» Binet generated tasks, findings, and interpretations that foreshadowed current work on children's understanding of number conservation, validity of children's eyewitness testimony, the construct…
Inhelder and Piaget's pendulum problem: Teaching preadolescents to act as scientists
The influence of encoding and strategic knowledge on children's choices among serial recall strategies
This study examined how encoding and strategy knowledge influence 5- to 9-year-olds' choices among serial recall procedures
Development of time, speed, and distance concepts
The rule-assessment approach was used to examine 5-, 8-, 11-, and 20-year-olds' understanding of the concepts of time, speed, and distance. Parallel tasks were developed for the three concepts that allowed specification of whether children were relying on time, speed, distance, end point, end time, beginning point, or beginning time cues in making their judgments. It was found that 5-year-olds understood all three concepts in the same way: Whiche…
Acquisition of formal scientific reasoning by 10- and 13-year-olds: Designing a factorial experiment
A comparison of the geometric reasoning of students attending Israeli ultraorthodox and mainstream schools
Effects of schooling on a geometric misconception were examined by comparing the performance of Israeli students attending ultraorthodox schools with that of peers attending mainstream schools. These groups were of special interest because both value education highly and send essentially all children to school, but I group receives extensive instruction in mathematics and science and the other receives almost none. Despite the ultraorthodox 12- t…
Strategy Diversity and Cognitive Assessment
Is the time ripe to develop technologically based versions of cognitive psychological methods and to apply them to problems of educational assessment? In this article, I point to dangers of using one common cognitive psychological method, chronometric analysis, for purposes of educational assessment. I also argue, though, that progress is being made toward developing more accurate diagnostic techniques, and that this progress promises to allow mo…
Effects of contiguity, regularity, and age on children's causal inferences
Learning from errors versus explicit instruction in preparation for a test that counts
BackgroundAlthough 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.AimsThis study investigates the teaching strategies that facilitate learning from errors.Materials and MethodsThis 2-year study, involving two cohorts of ~88 students each, contrasted a learning-from-errors (LFE) with an explicit i…
Hey, would you like a nice cold cup of lemonade on this hot day: Children's understanding of economic causation
Three experiments were performed to examine development of understanding of functional relations in economics by children between ages 4 and 10 years. Results of Experiment 1 indicated that preschoolers understood the effects of demand, and 2nd graders also understood the effects of supply, but even 4th graders often failed to demonstrate understanding of the effects of motivation and morality. In Experiment 2, 4th but not 2nd graders proved able…
Effects of presenting relevant rules and complete feedback on the conservation of liquid quantity task
Effects of presenting relevant rules and complete feedback on the conservation of liquid quantity task
Inhelder and Piaget's pendulum problem: Teaching preadolescents to act as scientists
Effects of contiguity, regularity, and age on children's causal inferences
Acquisition of formal scientific reasoning by 10- and 13-year-olds: Designing a factorial experiment
Stereotypes of Males' and Females' Speech
Parallel designs were used to test the hypotheses that (a) strongly assertive forms would be attributed relatively more often to males and less assertive forms relatively more often to females, and (b) syntactic forms associated with males would be rated more intelligent and those associated with females less so. The results ( ns = 24) for 4 groups of undergraduates were consistent with each of these predictions, suggesting that recently reported…
Development of time, speed, and distance concepts
The rule-assessment approach was used to examine 5-, 8-, 11-, and 20-year-olds' understanding of the concepts of time, speed, and distance. Parallel tasks were developed for the three concepts that allowed specification of whether children were relying on time, speed, distance, end point, end time, beginning point, or beginning time cues in making their judgments. It was found that 5-year-olds understood all three concepts in the same way: Whiche…
Five generalizations about cognitive development
Five generalizations about cognitive development
A featural analysis of preschoolers' counting knowledge
Strategy Diversity and Cognitive Assessment
Is the time ripe to develop technologically based versions of cognitive psychological methods and to apply them to problems of educational assessment? In this article, I point to dangers of using one common cognitive psychological method, chronometric analysis, for purposes of educational assessment. I also argue, though, that progress is being made toward developing more accurate diagnostic techniques, and that this progress promises to allow mo…
The influence of encoding and strategic knowledge on children's choices among serial recall strategies
This study examined how encoding and strategy knowledge influence 5- to 9-year-olds' choices among serial recall procedures
The microgenetic method: A direct means for studying cognitive development
Microgenetic methods revisited
Microgenetic methods revisited
The other Alfred Binet
Alfred Binet is famous as the author of the IQ test that bears his name. He is almost unkown, however, as the investigator who generated numerous fascinating investigations into developmental, experimental, educational, and social psychology. This «other» Binet generated tasks, findings, and interpretations that foreshadowed current work on children's understanding of number conservation, validity of children's eyewitness testimony, the construct…
Emerging Minds: The Process of Change in Children's Thinking
How do children acquire the vast array of concepts, strategies, and skills that distinguish the thinking of infants and toddlers from that of preschoolers, older children, and adolescents? In this new book, Robert Siegler addresses these and other fundamental questions about children's thinking. Previous theories have tended to depict cognitive development much like a staircase. At an early age, children think in one way; as they get older, they …
Strategy Discovery as a Competitive Negotiation between Metacognitive and Associative Mechanisms
A comparison of the geometric reasoning of students attending Israeli ultraorthodox and mainstream schools
Effects of schooling on a geometric misconception were examined by comparing the performance of Israeli students attending ultraorthodox schools with that of peers attending mainstream schools. These groups were of special interest because both value education highly and send essentially all children to school, but I group receives extensive instruction in mathematics and science and the other receives almost none. Despite the ultraorthodox 12- t…
Hey, would you like a nice cold cup of lemonade on this hot day: Children's understanding of economic causation
Three experiments were performed to examine development of understanding of functional relations in economics by children between ages 4 and 10 years. Results of Experiment 1 indicated that preschoolers understood the effects of demand, and 2nd graders also understood the effects of supply, but even 4th graders often failed to demonstrate understanding of the effects of motivation and morality. In Experiment 2, 4th but not 2nd graders proved able…
Developing conceptual understanding and procedural skill in mathematics: An iterative process.
The authors propose that conceptual and procedural knowledge develop in an iterative fashion and that improved problem representation is 1 mechanism underlying the relations between them. Two experiments were conducted with 5th- and 6th-grade students learning about decimal fractions. In Experiment 1, children's initial conceptual knowledge predicted gains in procedural knowledge, and gains in procedural knowledge predicted improvements in concep…
À chaque âge son mode de pensée
The Development of Numerical Estimation: Evidence for Multiple Representations of Numerical Quantity
We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitu…
Development of Numerical Estimation in Young Children
Two experiments examined kindergartners', first graders', and second graders' numerical estimation, the internal representations that gave rise to the estimates, and the general hypothesis that developmental sequences within a domain tend to repeat themselves in new contexts. Development of estimation in this age range on 0-to-100 number lines followed the pattern observed previously with older children on 0-to-1,000 lines. Between kindergarten a…
Turning memory development inside out
Children's Learning
A new field of children's learning is emerging. This new field differs from the old in recognizing that children's learning includes active as well as passive mechanisms and qualitative as well as quantitative changes. Children's learning involves substantial variability of representations and strategies within individual children as well as across different children. The path of learning involves the introduction of new approaches as well as cha…
Psychology (45 works) · Developmental psychology (30 works) · Cognitive psychology (27 works) · Cognitive and developmental aspects of mathematical skills (25 works) · Mathematics education (24 works) · Cognition (22 works) · Mathematics Education and Teaching Techniques (21 works) · Mathematics (17 works) · Education Methods and Practices (13 works) · Computer Science (12 works)