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US Department of Education, 2008

For students to compete in the 21st-century global economy, knowledge of and proficiency in mathematics are critical. Whether headed to college or to the workforce, today's high school graduates need solid mathematics skill. The National Mathematics Advisory Panel was created in 2006 and charged with reviewing the best available scientific…

Descriptors: Mathematics Education, High School Graduates, Learning Processes, Mathematics Skills

Siegler, Robert S. – Grantee Submission, 2016

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

Descriptors: Numbers, Theories, Individual Development, Symbols (Mathematics)

Siegler, Robert S. – Developmental Science, 2016

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

Descriptors: Numbers, Theories, Individual Development, Symbols (Mathematics)

Tian, Jing; Siegler, Robert S. – Grantee Submission, 2016

Learning of fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind TA peers in…

Descriptors: Fractions, Mathematics Education, Mathematical Aptitude, Individual Differences

Siegler, Robert; Lortie-Forgues, Hugues – Grantee Submission, 2014

Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…

Descriptors: Numbers, Theories, Individual Development, Cognitive Development

Peer reviewed

Siegler, Robert S.; Braithwaite, David W. – Grantee Submission, 2016

In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

Descriptors: Numeracy, Numbers, Arithmetic, Fractions

Lortie-Forgues, Hugues; Siegler, Robert S. – Grantee Submission, 2016

In two studies (N's = 55 and 54), we examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or…

Descriptors: Arithmetic, Mathematical Concepts, Knowledge Level, Middle School Students

Chen, Zhe; Siegler, Robert S. – Grantee Submission, 2013

This study examined how toddlers gain insights from source video displays and use the insights to solve analogous problems. Two- to 2.5-year-olds viewed a source video illustrating a problem-solving strategy and then attempted to solve analogous problems. Older but not younger toddlers extracted the problem-solving strategy depicted in the video…

Descriptors: Problem Solving, Young Children, Logical Thinking, Toddlers

Siegler, Robert S.; Lortie-Forgues, Hugues – Journal of Educational Psychology, 2015

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

Descriptors: Arithmetic, Mathematics Education, Knowledge Level, Hypothesis Testing

Fazio, Lisa; Siegler, Robert – UNESCO International Bureau of Education, 2011

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Descriptors: Class Activities, Learning Activities, Teaching Methods, Numbers

Laski, Elida V.; Siegler, Robert S. – Developmental Psychology, 2014

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…

Descriptors: Games, Numbers, Learning, Cognitive Processes

Fazio, Lisa K.; Kennedy, Casey A.; Siegler, Robert S. – Grantee Submission, 2016

We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards' suggestions for teaching fractions, would improve children's fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played "Catch…

Descriptors: Educational Games, Computer Games, Fractions, Mathematics Instruction

Fazio, Lisa K.; DeWolf, Melissa; Siegler, Robert S. – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2016

We examined, on a trial-by-trial basis, fraction magnitude comparison strategies of adults with more and less mathematical knowledge. College students with high mathematical proficiency used a large variety of strategies that were well tailored to the characteristics of the problems and that were guaranteed to yield correct performance if executed…

Descriptors: Undergraduate Students, College Mathematics, Mathematics Skills, Learning Strategies

Siegler, Robert S.; Pyke, Aryn A. – Grantee Submission, 2013

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 crosssectional design. Results indicated that the difference…

Descriptors: Age Differences, Individual Development, Individual Differences, Mathematics

Siegler, Robert S.; Pyke, Aryn A. – Developmental Psychology, 2013

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…

Descriptors: Grade 6, Arithmetic, Mathematics Skills, Mathematics Instruction