Spontaneous Focusing on Numerosity in the Development of Early Mathematical Skills

The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.

Manipulating Greek musical modes and tempo affects perceived musical emotion in musicians and nonmusicians

The combined influence of tempo and mode on emotional responses to music was studied by crossing 7 changes in mode with 3 changes in tempo. Twenty-four musicians aged 19 to 25 years (12 males and 12 females) and 24 nonmusicians aged 17 to 25 years (12 males and 12 females) were required to perform two tasks: 1) listening to different musical excerpts, and 2) associating an emotion to them such as happiness, serenity, fear, anger, or sadness. ANOVA showed that increasing the tempo strongly affected the arousal (F(2,116) = 268.62, mean square error (MSE) = 0.6676, P < 0.001) and, to a lesser extent, the valence of emotional responses (F(6,348) = 8.71, MSE = 0.6196, P < 0.001). Changes in modes modulated the affective valence of the perceived emotions (F(6,348) = 4.24, MSE = 0.6764, P < 0.001). Some interactive effects were found between tempo and mode (F (1,58) = 115.6, MSE = 0.6428, P < 0.001), but, in most cases, the two parameters had additive effects. This finding demonstrates that small changes in the pitch structures of modes modulate the emotions associated with the pieces, confirming the cognitive foundation of emotional responses to music.

Exploring two cases of Piano Teacher Education in Finland and Germany

Research about music instrument teacher education is scattered and fairly recent, especially in the European context. The purpose of this study was to explore two cases of piano teacher education programs at higher music education institutions, one in Finland, and one in Germany, to gain insights into the preparation of piano teachers for their professional working life. The aim was to identify issues for consideration in curriculum development of piano teacher education to enhance the teaching and learning of piano playing, and to ultimately increase musical practice and engagement among young learners. Nine semi-structured interviews with piano teacher educators, heads of program, other lecturers within the program, and student piano teachers in both cases were analyzed using applied thematic analysis. Three main themes with subcategories emerged: (1) the organization of the piano teacher education program, such as the structure, the content, the learning environments provided, and the development mechanisms of the program; (2) the views on the piano teacher profession, the working environment and resulting requirements, including further education during professional life; and (3) the professional skills and teacher identity development of student teachers. While the supposed working environments and requirements of future piano teachers, the student teachers' development characteristics, and the content were found reasonably concurrent in both cases, the structure of the teacher education program, and the organization of learning environments presented notable differences. While the complete teacher qualification in the Finnish case was offered as option in the Bachelor and Master of Music program within the piano department, the German case offered a separate program for music instrument educators. Other main differences concerned the organizations of practical teaching experiences, and the linking of practical with theoretical pedagogy. Conviction and enthusiasm for improving piano and other music instrument teacher education seemed remarkable. These improvements could include the development of a comprehensive teacher education pedagogy for music instrument teacher educators, intensified cross-linking within and of higher music education institutions in local contexts, and the expansion of professional development opportunities.

Schelling e a constituição da estética musical

O presente artigo conta investigar o processo de constituição da estética musical a partir da teoria da arte elaborada por F. W. J. von Schelling. Para tanto, espera-se mostrar a maneira pela qual o filósofo alemão procura redimensionar as bases que davam sustentação à chamada estética sistemática para, a partir de uma ponderação extremamente inovadora, caracterizar a música como um objeto original de saber.

From transcendental to practical intersubjectivity: a social psychological approach to Kant's musical aesthetics

It is well known that Kant’s aesthetics is framed intersubjectively because he upholds the claim of taste to universality. However, the transcendental foundation of this shared universality is a supersensible ground which is taken for granted but which cannot be brought directly into communicative experience. Kant’s reliance on the synthetic a priori structure of aesthetic judgment also removes it from the sphere of observable personal interaction. This argumentative strategy exposes it to skeptical challenge and generates inaccessible references to inner representations (be they intuitions, categories of the understanding or rational ideas). It is not sufficient, as Kant did, to propose a description of aesthetic experience that is subjectively plausible and thereby claim its intersubjective validity. It is indispensable to embody intersubjectivity in behavior and language. In practical intersubjectivity, aesthetic attitudes are dealt with in a concrete and accessible manner without relying on mentalistic assumptions as a foundation. Conceptual terms such as 'agreeable’, 'beauty’, 'sublime’, 'ugly’, 'universality’ acquire new meaning in a conversational context and aesthetic claims are tested in a dialogical game semantics model.

Filosofia, tom e ilusão musical em Kant: da vivificação sonora do ânimo à recepção do tom da razão

O artigo tenciona, primeiramente, enriquecer o estudo da função que o conceito de tom desempenha na ideia kantiana de razão, ao estendê-lo à análise da música como arte dos sons que a Crítica do Juízo contém. Em segundo lugar, propõe-se determinar os motivos pelos quais a matemática se revela incapaz, devido à especificidade do método filosófico e à corporalidade da recepção musical, respectivamente, de expressar o modo de proceder da razão e da arte dos sons. Finalmente, aponta-se para uma semelhança entre música e razão, no que diz respeito à rejeição que compartilham da queda na Schwärmerei, apesar da distância que se estabelece entre ambas enquanto duas maneiras contrárias de exercitar e fomentar a vida e o sentimento dela.

Linguistic skills and trust creation in international business relationships

Today’s international business in highly related to crossing national, cultural and linguistic borders making communication and linguistic skills a vital part of the trade. The purpose of the study is to understand the role of linguistic skills in trust creation in international business relationships. Subobjectives are to discuss the importance of linguistic skills in international business context, to evaluate the strategic value of trust in business relationships and to analyze the extent to which linguistic skills affect trust formation. The scope is restricted to business-to-business markets. The theoretical background consists of different theories and previous studies related to trust and linguistic skills. Based on the theory a new LTS-framework is created to demonstrate a process model of linguistic skills affecting trust creation in international B2B relationships. This study is qualitative using interviews as a data collection method. Altogether eleven interviews were conducted between October 2014 and February 2015. All of the interviewees worked for organizations operating in the field of international business in B2B markets, spoke multiple languages and had a lot of experience in sales and negotiations. This study confirms that linguistic skills are an important part of international business. In many organizations English is used as lingua franca. However, there are several benefits of speaking the mother tongue of the customer. It makes people feel more relaxed and it makes the relationship more intimate and allows to continue developing it at a more personal level. From the strategic point of view trust creates competitive advantage to a company adding strategic value to the business. The data also supported the view that linguistic skills definitely impact the trust formation process. Quickness and easiness could be stated as the main benefits. It was seen that trust forms faster because both parties understand each other better and they become more open about information sharing within a shorter period of time. These findings and the importance of linguistic skills in trust creation should be acknowledged by organizations, especially regarding the human resource management. Boundary spanners are in key positions so special attention should be put into hiring and educating employees which then take care of company’s relationships. Eventually, these benefits are economical and affect to the profitability of the organization

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