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 be distinct from more routine features of performance. Even among the top 45% of students, all of whom had strong routine procedural and conceptual knowledge, students varied greatly in their performance the arithmetic sentence production task. Strong performance on this measure also predicted later algebra knowledge. The findings suggest that it is possible to distinguish adaptive expertise from routine expertise with rational numbers and that this distinction is important to consider in research on mathematical development.

: Recent research suggests that fraction understanding is predictive of algebra ability; however, the relative contributions of various aspects of rational number knowledge are unclear. Furthermore, whether this relationship is notation-dependent or rather relies upon a general understanding of rational numbers (independent of notation) is an open question. In this study, college students completed a rational number magnitude task, procedural arithmetic tasks in fraction and decimal notation, an...

Last. Wim Van Dooren(Katholieke Universiteit Leuven)H-Index: 27

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Abstract In this study we longitudinally followed 201 upper elementary school learners in the crucial years of acquiring rational number understanding. Using latent transition analysis we investigated their conceptual change from an initial natural number based concept of a rational number towards a mathematically more correct one by characterizing the various intermediate states learners go through. Results showed that learners first develop an understanding of decimal numbers before they have ...

Last. Kelly Trezise(University of Melbourne)H-Index: 5

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This article gives an introduction to latent class, latent profile, and latent transition models for researchers interested in investigating individual differences in learning and development. The models allow analyzing how the observed heterogeneity in a group (e.g., individual differences in conceptual knowledge) can be traced back to underlying homogeneous subgroups (e.g., learners differing systematically in their developmental phases). The estimated parameters include a characteristic respo...

Many videos on the Web about international events are maintained in different countries, and some come with text descriptions from different cultural points of view. We introduce a new task-detecting culture-specific tags for news videos: given video keyframes and culture information, assign the most relevant tags with cultural preferences. We approach this problem by mapping visual and multilingual textual features into a joint latent space by reliable visual cues, by our proposed two-view pair...

Last. Erno Lehtinen(UTU: University of Turku)H-Index: 33

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Abstract Traditionally measured skills with arithmetic are not related to later algebra success at levels that would be expected given the close conceptual relation between arithmetic and algebra. However, adaptivity with arithmetic may be one aspect of arithmetic competences that can account for additional variation in algebra attainment. With this in mind, the present study aims to present evidence for the existence and relevance of a newly acknowledged component of adaptivity with arithmetic,...

The importance of fraction knowledge to later mathematics achievement, along with U.S. students’ poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants’ (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed over 4 time points between 4th and 6th grades. Latent state-trait modeling was used to examine codevelopment of these 2 areas of fraction knowledge. F...

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what mathematical proficiency means in today’s world and what shifts need to be made in both content and pedagogy to prepare students for 21st Century Skill...

Last. Hans Gruber(University of Regensburg)H-Index: 29

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Contemporary theories of expertise development highlight the crucial role of deliberate practice in the development of high level performance. Deliberate practice is practice that intentionally aims at improving one’s skills and competencies. It is not a mechanical or repetitive process of making performance more fluid. Instead, it involves a great deal of thinking, problem solving, and reflection for analyzing, conceptualizing, and cultivating developing performance. This includes directing and...

The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1701 primary and secondary school students. Eight components, which all involve representational transformations, were encompassed under the construct of representati...

#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...

Last. Erno Lehtinen(VMU: Vytautas Magnus University)H-Index: 33

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The number of available educational games has enormously grown and it is difficult for users to identify which games are pedagogically effective among the multitude of options in app marketplaces. Recent studies on math games have highlighted the importance of (1) linking learning attributes and gameplay and (2) game design that supports students' deliberate practise. Using these as a measure for pedagogical quality, we investigated 109 math games found on Google Play Store (n=61) and iOS App St...