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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. – 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: Journal Writing, Numeracy, Mathematics Skills, Mathematical Concepts

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; 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

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.; 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…

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

Peer reviewed

Torbeyns, Joke; Schneider, Michael; Xin, Ziqiang; Siegler, Robert S. – Grantee Submission, 2015

Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…

Descriptors: Mathematical Concepts, Comprehension, Arithmetic, Numeracy

Lortie-Forgues, Hugues; Tian, Jing; Siegler, Robert S. – Grantee Submission, 2015

Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…

Descriptors: Arithmetic, Fractions, Mathematics Instruction, Mathematical Concepts

Schneider, Michael; Siegler, Robert S. – Journal of Experimental Psychology: Human Perception and Performance, 2010

We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However,…

Descriptors: College Students, Community Colleges, Logical Thinking, Student Behavior