David W. Braithwaite

Florida State University

Fraction (mathematics)StatisticsCombinatoricsCognitive developmentMathematics educationMultiplicationPsychologyCognitionCognitive psychologyCognitive scienceWhole NumberMathematical developmentMathematicsSequenceComputer scienceConcept learningDivision (mathematics)DecimalSubtractionTheoretical computer scienceNumber lineStatistical hypothesis testingArithmetic

32Publications

7H-index

160Citations

Publications 28

#1David W. BraithwaiteH-Index: 7

#2Robert S. SieglerH-Index: 100

#1Jing TianH-Index: 5

#2David W. BraithwaiteH-Index: 7

Last. Robert S. SieglerH-Index: 100

view all 3 authors...

#1Robert S. Siegler (BNU: Beijing Normal University)H-Index: 100

#2Soo-hyun Im (Hanyang University)H-Index: 5

Last. David W. Braithwaite (FSU: Florida State University)H-Index: 7

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Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by ...

#1Jing Tian (TU: Temple University)H-Index: 5

#2David W. Braithwaite (FSU: Florida State University)H-Index: 7

Last. Robert S. Siegler (Columbia University)H-Index: 100

view all 3 authors...

Abstract Three rational number notations -- fractions, decimals, and percentages -- have existed in their modern forms for over 300 years, suggesting that each notation serves a distinct function. However, it is unclear what these functions are and how people choose which notation to use in a given situation. In the present article, we propose quantification process theory to account for people’s preferences among fractions, decimals, and percentages. According to this theory, the preferred nota...

Understanding development requires assessing the relevant environment: Examples from mathematics learning.

#1Robert S. Siegler (BNU: Beijing Normal University)H-Index: 100

#2Soo-hyun Im (Hanyang University)H-Index: 5

Last. David W. Braithwaite (FSU: Florida State University)H-Index: 7

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Although almost everyone agrees that the environment shapes children's learning, surprisingly few studies assess in detail the specific environments that shape children's learning of specific content. The present article briefly reviews examples of how such environmental assessments have improved understanding of child development in diverse areas, and examines in depth the contributions of analyses of one type of environment to one type of learning: how biased distributions of problems in mathe...

#1David W. Braithwaite (FSU: Florida State University)H-Index: 7

#2Elena R. Leib (University of California, Berkeley)H-Index: 2

Last. Jake McMullen (UTU: University of Turku)H-Index: 13

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Abstract Understanding fractions is critical to mathematical development, yet many children struggle with fractions even after years of instruction. Fraction arithmetic is particularly challenging. The present study employed a computational model of fraction arithmetic learning, FARRA ( F raction A rithmetic R eflects R ules and A ssociations; Braithwaite, Pyke, and Siegler, 2017), to investigate individual differences in children’s fraction arithmetic. FARRA predicted four qualitatively distinc...

#1David W. Braithwaite (CMU: Carnegie Mellon University)H-Index: 7

#2Jing Tian (CMU: Carnegie Mellon University)H-Index: 5

Last. Robert S. Siegler (CMU: Carnegie Mellon University)H-Index: 100

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Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining fourth to eighth graders' estimates of fraction sums. We found that roughly half of estimates of sums were smaller than the same child's estimate of one of t...

#1David W. Braithwaite (CMU: Carnegie Mellon University)H-Index: 7

#2Robert S. Siegler (CMU: Carnegie Mellon University)H-Index: 100

: Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge-rather than understanding of mathematical concepts and procedures-to guide choices of solution strategies. They further proposed that this associative knowledge reflects distributional characteristics of the fraction ar...

#1David W. Braithwaite (CMU: Carnegie Mellon University)H-Index: 7

#2Robert S. Siegler (CMU: Carnegie Mellon University)H-Index: 100

Many students’ knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under speeded conditions persists into adulthood, even among mathematicians, little is known about its development. Performance with equivalent fractions indic...

#1David W. Braithwaite (CMU: Carnegie Mellon University)H-Index: 7

#2Aryn Pyke (CMU: Carnegie Mellon University)H-Index: 6

Last. Robert S. Siegler (CMU: Carnegie Mellon University)H-Index: 100

view all 3 authors...

: Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it with the problems from a widely used textbook series. The simulation generated many phenomena of children's fraction arithmetic performance through a ...