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The present study focuses on the development of two sub-concepts necessary for a complete mathematical understanding of rational numbers, a) representations of the magnitudes of rational numbers and b) the density of rational numbers. While difficulties with rational number concepts have been seen in students' of all ages, including educated adults, little is known about the developmental trajectories of the separate sub-concepts. We measured 10- to 12-year-old students' conceptual knowledge of rational numbers at three time points over a one-year period and estimated models of their conceptual knowledge using latent variable mixture models. Knowledge of magnitude representations is necessary, but not sufficient, for knowledge of density concepts. A Latent Transition Analysis indicated that few students displayed sustained understanding of rational numbers, particularly concepts of density. Results confirm difficulties with rational number conceptual change and suggest that latent variable mixture models can be useful in documenting these processes. [ABSTRACT FROM AUTHOR]

During collaborative learning, students tend to spontaneously enact different participatory roles that may significantly affect collaborative learning processes. Only few empirical studies to date have investigated groups as systems based on emerging roles and role profiles of the participating students, and how emerging role profile configurations affect achievement. This exploration of students' self-adopted roles investigated the relationship between role profile configurations and achievement. The statistically driven identification of role profiles was based on fine-grained observations of student groups' interactions in two distinct collaborative science-learning settings. While higher achieving groups typically exhibited versatile science-oriented role profile configurations, opinion-based configurations prevailed in lower achieving groups. Although role profiles with a social orientation were rare, a student with a distracting profile can have a significant influence on group work. Consolidated by in-depth case examples, the findings highlight the importance of understanding how collaborating groups' emergent role profiles dynamically interact during collaborative learning and how different role profile configurations relate to achievement. • The study identifies students' self-adopted roles and role profiles. • Identification of role profiles was based on fine-grained coding of interactions. • The study suggests how role profile configurations relate to achievement. • Configurations differ in higher- and lower-achieving groups. • The significance of role profiles for collaborative learning is discussed. [ABSTRACT FROM AUTHOR]

The assessment of reasoning skills is recommended in undergraduate nursing student selection. Reasoning skills are crucial for sound decision-making, improving patient safety and are necessary from the very beginning of studies. Nursing applicants' reasoning skills based on the reasoning process have not been previously measured. To assess undergraduate nursing applicants' reasoning skills and factors related to them. A cross-sectional study. Undergraduate nursing applicants (n = 1056, response rate 55.4%), who consented to the study and performed a joint electronic entrance examination to six Finnish Universities of Applied Sciences in spring 2019, participated in the study. The Reasoning Skills (ReSki) test, based on the steps of the reasoning process, was used, comprising three question sections (collecting information, processing information, and identifying the problem and establishing goals). Background variables were collected through a questionnaire and the Positive System Usability Scale (P-SUS). The data were analysed with descriptive statistics, Pearson correlation coefficients and analysis of covariance with Tukey's test in post-hoc multiple group comparisons. Applicants' total reasoning skills mean scores were above the centre of the range of possible scores (2.72/4.5, SD = 0.80). The applicants scored higher in collecting and processing information than in identifying the problem and establishing goals. Standard deviations demonstrated variance between the applicants' ability. Age, gender, and previous education were statistically significantly related to applicants' reasoning skills. Previous work experience was statistically significantly related to success only in the step of identifying the problem and establishing goals. Nursing applicants' reasoning skills vary in the student selection phase. Applicants are less able to identify the problem and establish goals than to collect and process information. Vocational education does not necessarily develop adequate reasoning skills and thus prepare students for higher education studies. The results have implications for educational institutions and further research. • Nursing applicants' reasoning skills vary in the student selection phase. • Identifying the problem and establishing goals is difficult for the applicants. • Vocational education is not necessarily developing adequate reasoning skills. [ABSTRACT FROM AUTHOR]

Preterm birth is associated with low mathematical skills in children. This study on five-year-old Finnish children investigated whether mathematical skill profiles would differ between prematurely and full-term born children and how such profiles and other cognitive skills would be related. Mathematical skills included digit knowledge, spontaneous focusing on numerosity, arithmetic, counting and geometric skills. The investigated cognitive skills were phonological processing, working memory, instruction comprehension, speeded naming, inhibition and visuomotor skills. The participants were 119 preterm children with birth weight < 1501 g and 100 full-term born children with normal birth weight. The results of latent profile analyses showed that preterm and full-term born children differed in both number and shape of latent mathematical skill profiles, indicating quantitative and qualitative disparities. After controlling for birth weight or gestational age, maternal education, and other cognitive skills phonological processing, visuospatial working memory and speeded naming were uniquely associated with prematurely born children's five mathematical profiles. In full-term born children, only verbal working memory was related to their four mathematical profiles. [ABSTRACT FROM AUTHOR]

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 six. Classes were randomized in two conditions: in the experimental group regular mathematics teaching was enriched with gameplay using the Number Navigation Game (NNG), and in the control group students continued according to their regular math curriculum. An experimental design with pre- and post-test was used to measure students' adaptive number knowledge, arithmetic fluency, and pre-algebra knowledge. Overall, results showed that the experimental group outperformed the control group on adaptive number knowledge and math fluency. Results showed varying effects of the training in different grade levels, with more pronounced improvement of students' adaptive number knowledge in grade five. Game performance was related to the experimental group's post-test scores even after controlling for pre-test scores and grade. Results suggest that the NNG is effective in enhancing different types of arithmetic skills and knowledge in different grades of primary school education and can provide teachers with a practical and flexible tool to extend their regular classroom practice. Highlights • Game-based intervention for training adaptive number knowledge was used. • Results showed a positive impact on adaptive number knowledge. • The intervention had varying effects across different grades. • Game performance was related to the increase of math learning outcomes. • Adaptive number knowledge can be enhanced by the Number Navigation Game. [ABSTRACT FROM AUTHOR]

This study investigated age group differences in Spontaneous Focusing on Numerosity (SFON) tendency and arithmetical skills across age groups with differing starting ages of formal mathematics instruction. Children (N = 685) aged 4–7 years participated from four countries, i.e., Northern Ireland, England, Belgium and Finland, where children start formal school at 4, 5, 6, and 7 years respectively. Children completed measures of SFON tendency, Arabic number naming, verbal arithmetic and written arithmetic. Results revealed strong age group effects for all measures and some developmental differences between SFON tendency and arithmetical skills. Whether children were, or were not, in school had a strong effect on SFON tendency but not on arithmetical skills. In the 5 and 6 years old age group, children already in school had significantly lower SFON tendency compared to those not yet in school. Within each country, when comparing consecutive age groups situated near school starting age, SFON tendency scores were similar in three out of the four countries. Results suggest both informal and formal mathematical skills need to be considered when assessing young children's mathematical competence. • Significant age group differences in SFON and arithmetical skills. • SFON tendency was mostly higher in the groups who were not yet in school. • Results hold if controlling for age, SES and numerical activities at home. • Both informal and formal math skills should be assessed in young children. [ABSTRACT FROM AUTHOR]