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 45
Newest
#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...
6 CitationsSource
Spontaneous focusing on quantitative relations (SFOR) has been shown to be a strong predictor of rational number conceptual development in late primary school. The present study outlines an intervention program that examines the possibilities to enhance late primary school students' SFOR tendency. The intervention program harnessed mobile technology in order to allow students to explore and identify quantitative relations in their everyday environment, including situations outside of the classro...
8 CitationsSource
#1Minna M. Hannula-Sormunen (UTU: University of Turku)H-Index: 15
#2Jake McMullen (UTU: University of Turku)H-Index: 13
Last. Erno Lehtinen (UTU: University of Turku)H-Index: 33
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This chapter summarizes classical studies on numeracy development and highlights the impact of children’s own, self-initiated numerical activities in informal everyday situations on the learning trajectories toward an advanced number sense. Theories and empirical evidence of the role early exact and approximate magnitude processing, relational reasoning, counting, number sequence, and arithmetical skills play in the development of natural and rational number knowledge are described. Furthermore,...
Source
#1Boglárka Brezovszky (UTU: University of Turku)H-Index: 6
#2Jake McMullen (UTU: University of Turku)H-Index: 13
Last. Erno Lehtinen (UTU: University of Turku)H-Index: 33
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Abstract Developing adaptive expertise with arithmetic problem solving is a much desired aim of primary school mathematics education. However, there are very few practical tools for teachers that would aid reaching this complex mathematical learning goal. The aim of the present study was to test the effects of a game-based learning environment in supporting primary school students' adaptive number knowledge and related arithmetic skills. Participants were 1168 students in grades four, five, and ...
27 CitationsSource
#1Jake McMullenH-Index: 13
#2Kaisa KanervaH-Index: 4
Last. Noona KiuruH-Index: 34
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Source
#1Jake McMullen (UTU: University of Turku)H-Index: 13
#2Jenny Yun Chen Chan (UMN: University of Minnesota)H-Index: 4
Last. Minna M. Hannula-Sormunen (UTU: University of Turku)H-Index: 15
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A growing body of evidence reveals the need for research on, and consideration for, children’s and students’ own—self-guided—spontaneous use of mathematical reasoning and knowledge in action. Spontaneous focusing on numerosity (SFON) and quantitative relations (SFOR) have been implicated as key components of mathematical development. In this chapter, we review existing research on SFON and SFOR tendencies in the broader context of the development of mathematical skills and knowledge and examine ...
9 CitationsSource
#1Erno Lehtinen (UTU: University of Turku)H-Index: 33
#2Jake McMullen (UTU: University of Turku)H-Index: 13
Last. Hans Gruber (University of Regensburg)H-Index: 29
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The focus of expertise research is on exceptionally advanced performance in professions that require long academic—and at least partly scientific—education before entering into work. Surprisingly, only a few studies have systematically examined the role of scientific thinking in expertise development. Many studies have shown that initial scientific knowledge seems to disappear during the course of expertise development. This conclusion was challenged by the theory of encapsulation, which describ...
1 CitationsSource
#1Jake McMullen (UTU: University of Turku)H-Index: 13
#2Jo Van Hoof (Katholieke Universiteit Leuven)H-Index: 9
Last. Wim Van Dooren (Katholieke Universiteit Leuven)H-Index: 27
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Abstract Students have a great deal of difficulties learning about rational number concepts, as they are confounded by misapplying reasoning about natural numbers to fractions and decimals, referred to as a natural number bias. For example, students often think that the number of digits of a decimal, or the size of the component numbers of fractions, is enough information to determine the magnitude of rational numbers. As well, students have trouble understanding that there is an infinite number...
7 CitationsSource
#1Jake McMullen (UTU: University of Turku)H-Index: 13
#2Marian Hickendorff (LEI: Leiden University)H-Index: 10
Herein, we provide an introduction to the special issue "Latent variable mixture models in research on learning and individual differences". Latent variable mixture models are argued to be a powerful tool for capturing non-linear and qualitative individual differences in learners' knowledge, characteristics, and development. The current special issue provides an overview of the use of these analytical tools in investigations of learning and individual differences by presenting a wide-range of em...
1 CitationsSource
#1Cristina E. Nanu (UTU: University of Turku)H-Index: 2
#2Jake McMullen (UTU: University of Turku)H-Index: 13
Last. Minna M. Hannula-Sormunen (UTU: University of Turku)H-Index: 15
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Abstract Previous studies in a variety of countries have shown that there are substantial individual differences in children’s spontaneous focusing on numerosity (SFON), and these differences are positively related to the development of early numerical skills in preschool and primary school. A total of 74 5-year-olds participated in a 7-year follow-up study, in which we explored whether SFON measured with very small numerosities at 5 years of age predicts mathematical skills and knowledge, math ...
18 CitationsSource