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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; 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
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
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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
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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
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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
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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
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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
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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
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Bailey, Drew H.; Siegler, Robert S.; Geary, David C. – Developmental Science, 2014
Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic…
Descriptors: Predictor Variables, Middle School Students, Mathematical Concepts, Mathematics Instruction
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Ramani, Geetha B.; Siegler, Robert S. – Journal of Applied Developmental Psychology, 2011
We compared the learning from playing a linear number board game of preschoolers from middle-income backgrounds to the learning of preschoolers from low-income backgrounds. Playing this game produced greater learning by both groups than engaging in other numerical activities for the same amount of time. The benefits were present on number line…
Descriptors: Low Income, Preschool Children, Comparative Analysis, Numeracy
Siegler, Robert S.; Ramani, Geetha – Society for Research on Educational Effectiveness, 2009
The present study focused on two main goals. One was to test the "representational mapping hypothesis": The greater the transparency of the mapping between physical materials and desired internal representations, the greater the learning of the desired internal representation. The implication of the representational mapping hypothesis in the…
Descriptors: Feedback (Response), Disadvantaged Youth, Learning Strategies, Pretests Posttests
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Flynn, Emma; Siegler, Robert – Infant and Child Development, 2007
This special issue is dedicated to research that adopts the microgenetic method in order to investigate change as it is happening. In this commentary we reflect on the diversity of the articles included in this special issue, and examine how the findings from these articles relate to five critical features of change: path, rate, breadth,…
Descriptors: Cognitive Development, Case Studies, Change, Developmental Psychology
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