Jake McMullen

University of Turku

Fraction (mathematics)Developmental psychologyMathematics educationPsychologyNumerosity adaptation effectCognitionCognitive psychologyNatural numberControl (management)FluencyLearning environmentAdaptive expertiseContext (language use)Mathematical developmentMathematicsRational numberLatent variableMixture modelSocial psychologyArithmetic

44Publications

13H-index

431Citations

Publications 44

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

#2Jake McMullen (UTU: University of Turku)H-Index: 13

Last. Michelle Hurst (U of C: University of Chicago)H-Index: 5

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Understanding fractions and decimals requires not only understanding each notation separately, or within-notation knowledge, but also understanding relations between notations, or cross-notation knowledge. Multiple notations pose a challenge for learners but could also present an opportunity, in that cross-notation knowledge could help learners to achieve a better understanding of rational numbers than could easily be achieved from within-notation knowledge alone. This hypothesis was tested by r...

#1Antero LindstedtH-Index: 4

#2Antti KoskinenH-Index: 1

Last. Kristian KiiliH-Index: 19

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The purpose of this study was to investigate flow experience and situational interest in a math learning game that included adaptive scaffolding Fifty-two Finnish 5th graders played the game about fractions at home during COVID-19 enforced distance learning The results showed that flow experience correlated positively with situational interest Importantly, a deeper analysis of the Flow Short Scale (FSS) subscales revealed that only absorption by activity but not fluency of performance explained ...

#1Jake McMullen (UTU: University of Turku)H-Index: 13

#2Ryan Lewis (UCI: University of California, Irvine)H-Index: 3

Last. Drew H. Bailey (UCI: University of California, Irvine)H-Index: 25

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Abstract Latent variable mixture models are commonly used to examine patterns of students' knowledge. These models, including Latent Class Analysis (LCA), have proven valuable for uncovering qualitative variation in students' knowledge that is hidden by traditional variable-centered approaches, particularly when testing a particular cognitive or developmental theory. However, it is far less clear that these models, when applied to broader measures of student knowledge, have practical application...

#1Jake McMullen (UTU: University of Turku)H-Index: 13

#2Lieven Verschaffel (Katholieke Universiteit Leuven)H-Index: 71

Last. Minna M. Hannula-Sormunen (UTU: University of Turku)H-Index: 15

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Children’s own spontaneous mathematical activities are crucial for their mathematical development. Mathematical thinking and learning does not only occur in explicitly mathematical situations, such...

#1Jake McMullen (UTU: University of Turku)H-Index: 13

#2Robert S. Siegler (Columbia University)H-Index: 100

To test the hypothesis that a higher tendency to spontaneously focus on multiplicative relations (SFOR) leads to improvements in rational number knowledge via more exact estimation of fractional qu...

#1Jake McMullen (UTU: University of Turku)H-Index: 13

#2Minna M. Hannula-Sormunen (UTU: University of Turku)H-Index: 15

Last. Robert S. Siegler (ATC: Advanced Technology Center)H-Index: 100

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Abstract Adaptive expertise is a valued, but under-examined, feature of students' mathematical development (e.g. Hatano & Oura, 2012). The present study investigates the nature of adaptive expertise with rational number arithmetic. We therefore examined 394 7th and 8th graders’ rational number knowledge using both variable-centered and person-centered approaches. Performance on a measure of adaptive expertise with rational number arithmetic, the arithmetic sentence production task, appeared to b...

#1Jake McMullen (UTU: University of Turku)H-Index: 13

#2Jo Van Hoof (Katholieke Universiteit Leuven)H-Index: 9

Abstract Many students still have not developed a robust understanding of rational number concepts at the end of primary school, despite several years of instruction on the topic. The present study aims to examine the patterns, predictors, and outcomes of the development of rational number knowledge in lower secondary school. Latent transition analysis revealed that rational number development from primary to lower secondary school (N = 362) appears to follow similar patterns as in younger stude...

#1Jake McMullen (UTU: University of Turku)H-Index: 13

#2Kaisa Kanerva (UH: University of Helsinki)H-Index: 4

Last. Noona Kiuru (University of Jyväskylä)H-Index: 34

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The present study aims to examine inter-individual differences in adaptive number knowledge in secondary school students. Adaptive number knowledge is defined as a well-connected network of knowledge of numerical characteristics and arithmetic relations. Substantial and relevant qualitative differences in the strategies and expression of adaptive number knowledge have been found in primary school students still in the process of learning arithmetic. We present a study involving 879 seventh-grade...

#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...

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Minna M. Hannula-Sormunen

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Erno Lehtinen

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Eero Laakkonen

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Robert S. Siegler

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Gabriela Rodríguez-Aflecht

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Nonmanut Pongsakdi

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Manuel Ninaus

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Boglárka Brezovszky

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