Crystallization characteristics of bioactive glasses

Bioactive glasses are excellent candidates for implant materials, because they can form a chemical bond to bone or guide bone growth, depending on the glass composition. Some compositions have even shown soft tissue attachment and antimicrobial effects. So far, most clinical applications are based on monoliths, plates and particulates of different grain sizes. There is a growing interest in special products such as porous implants sintered from microspheres and fibers drawn from preforms or glass melts. The viscosity range at which these are formed coincides with the crystallization temperature range for most bioactive glasses, thus complicating the manufacturing process. In this work, the crystallization tendency and its kinetics for a series of glasses with their compositions within the range of bioactivity were investigated. The factors affecting crystallization and how it is related to composition were studied by means of thermal analysis and hot stage microscopy. The crystal compositions formed during isothermal and non-isothermal heat treatments were analyzed with SEM-EDXA and X-ray diffraction analysis. The temperatures at which sintering and fiber drawing can take place without interfering with crystallization were determined and glass compositions which are suitable for these purposes were established. The bioactivity of glass fibers and partly crystallized glass plates was studied by soaking them in simulated body fluid (SBF). The thickness of silica, calcium and phosphate rich reaction layers on the glass surface after soaking was used as an indication of the bioactivity. The results indicated that the crystallization tendencies of the experimental glasses are strongly dependent on composition. The main factor affecting the crystallization was found to be the alkali oxide content: the higher the alkali oxide content the lower the crystallization temperature. The primary crystalline phase formed at low temperatures in these glasses was sodium calcium silicate. The crystals were found to form through internal nucleation, leading to bulk crystallization. These glasses had high bioactivity in vitro. Even when partially crystalline, they formed typical reaction layers, indicating bioactivity. In fact, sodium calcium silicate crystals were shown to transform in vitro into hydroxyapatite during soaking. However, crystallization should be avoided because it was shown to retard dissolution, bioactivity reactions and complicate fiber drawing process. Glass compositions having low alkali oxide content showed formation of wollastonite crystals on the surface, at about 300°C above the glass transition temperature. The wide range between glass transition and crystallization allowed viscous flow sintering of these compositions. These glasses also withstood the thermal treatments required for fiber drawing processing. Precipitation of calcium and phosphate on fibers of these glasses in SBF suggested that they were osteoconductive. Glasses showing bioactivity crystallize easily, making their hot working challenging. Undesired crystallization can be avoided by choosing suitable compositions and heat treatment parameters, allowing desired product forms to be attained. Small changes in the oxide composition of the glass can have large effects and therefore a thorough understanding of glass crystallization behavior is a necessity for a successful outcome, when designing and manufacturing implants containing bioactive glasses.

Christina Rossetti's "Goblin market" : Milton revised or revived?

The present study examines Christina Rossetti's (1830-94) best-known poem "Goblin Market" (1859) as a response to John Milton's (1608-74) Paradise Lost (1667) and Paradise Regained (1674). Rossetti's poem relates to Milton's twin epics with a surprising degree of complexity, something that the thesis demonstrates through a large number of hitherto unexplored textual parallels. In its recontextualisation of Rossetti's poetry, this study balances interpretative strategies evolved by feminism with more historicist readings. SinceGilbert and Gubar's landmark feminist work of 1979, it has become something of a critical commonplace that Milton was a figure of patriarchal oppression whom women writers have challenged through revision. As a consequence, intertextual Rossetti studies have tended to emphasise such a revisionist element in her achievement. But if we place "Goblin Market" within the larger context of Rossetti's thoughts on religion and poetry throughout her writing, and if we de-emphasise the dichotomy between Rossetti and her male precursor, alternative patterns of reading begin to emerge. This thesis argues that Rossetti's aim was not only to revise Milton but also to revive him. It develops this point in several ways: first, by introducing the subject and theoretically arguing that literary allusiveness is not necessarily a matter of oedipal or feminist envy only (Chapter One); second, by determining the nature and extent of Rossetti's Miltonic allusions in terms of theme, imagery and language (Chapter Two);and third, by examining their function in terms of argument (Chapters Three andFour). I n an age of increasing religious doubt, Rossetti's poetry provided a subtle challenge not so much to Milton as to the emerging scepticism and aestheticism in Victorian society and its art-world, and not least to the secular tendencies of the second generation of Pre-Raphaelites, including Dante Gabriel Rossetti. Christina Rossetti was ahead of her time (and perhaps ours) in seeing the feminist potential in both John Milton and the Christian message. In the soul's relation to Christ, gender does not matter. What matters is the individual's quest for salvation, a quest in which poetry is a sacramental act, with a transformative, unifying function. Rossetti's poems both depict and constitute such a quest for union with God, on the assumption that God's word offers a pathway that is open to men as well as women.

På spaning efter den goda läroboken : om pedagogiska texters lärande potential

By interpreting research results about textbooks this study tries to answer the question: how should texts be formulated to optimize the learning of the reading pupil? Seven perspectives structure the research: History. The amount of information available in a society influences the learning offered by textbooks. A compressed description indicates that memorizing activities have turned to tendencies for critical reading. Curriculum. The decentralization of curriculum development accentuates the importance of the textbook authors as interpreters of significant information. Because of the authority of textbooks, the way that information is presented can function as an unintended curriculum. Use. In the use of textbooks different functions can be identified. Thus the textbooks have, for instance, an authoritarian, a cohesive and a disciplinary function. Level of difficulty. A text that optimally matches the skills of the readers ina class should both provide facilitating scaffolds for the learning and at the same time challenge especially capable students by not being too obvious. Changing of preconceptions. The only possible starting point for teaching is the knowledge developed earlier by the student. In certain areas misconceptions are usual, which motivates the use of conceptual change texts that enhance the transformation of earlier obtained knowledge. Coherence. Well structured texts can usually be considered beneficial for learning. The same applies to the use of meta-discourse guiding the reader through the text. If the structuring is too obvious, the content may not, at least by capable students, be processed on a deep level. Content. The analysis underlines the need for deep approaches in textbooks. Though this is a relative statement, textbooks from a learning perspective seem to have been too superficial in their presentations. Ten principles were developed as a concluding interpretation of the good textbook. Though these principles capture important tendencies for developing a good textbook, textbook writing has to be considered as an art that cannot be captured in a short formula. The paradoxes identified indicate that the results should be seen as a starting point for further research.

Dialogue in the crisis of representation : realism and antirealism in the context of the conversation between theologians and quantum physicists in Göttingen 1949-1961

The aim of this study is to analyse the content of the interdisciplinary conversations in Göttingen between 1949 and 1961. The task is to compare models for describing reality presented by quantum physicists and theologians. Descriptions of reality indifferent disciplines are conditioned by the development of the concept of reality in philosophy, physics and theology. Our basic problem is stated in the question: How is it possible for the intramental image to match the external object?Cartesian knowledge presupposes clear and distinct ideas in the mind prior to observation resulting in a true correspondence between the observed object and the cogitative observing subject. The Kantian synthesis between rationalism and empiricism emphasises an extended character of representation. The human mind is not a passive receiver of external information, but is actively construing intramental representations of external reality in the epistemological process. Heidegger's aim was to reach a more primordial mode of understanding reality than what is possible in the Cartesian Subject-Object distinction. In Heidegger's philosophy, ontology as being-in-the-world is prior to knowledge concerning being. Ontology can be grasped only in the totality of being (Dasein), not only as an object of reflection and perception. According to Bohr, quantum mechanics introduces an irreducible loss in representation, which classically understood is a deficiency in knowledge. The conflicting aspects (particle and wave pictures) in our comprehension of physical reality, cannot be completely accommodated into an entire and coherent model of reality. What Bohr rejects is not realism, but the classical Einsteinian version of it. By the use of complementary descriptions, Bohr tries to save a fundamentally realistic position. The fundamental question in Barthian theology is the problem of God as an object of theological discourse. Dialectics is Barth¿s way to express knowledge of God avoiding a speculative theology and a human-centred religious self-consciousness. In Barthian theology, the human capacity for knowledge, independently of revelation, is insufficient to comprehend the being of God. Our knowledge of God is real knowledge in revelation and our words are made to correspond with the divine reality in an analogy of faith. The point of the Bultmannian demythologising programme was to claim the real existence of God beyond our faculties. We cannot simply define God as a human ideal of existence or a focus of values. The theological programme of Bultmann emphasised the notion that we can talk meaningfully of God only insofar as we have existential experience of his intervention. Common to all these twentieth century philosophical, physical and theological positions, is a form of anti-Cartesianism. Consequently, in regard to their epistemology, they can be labelled antirealist. This common insight also made it possible to find a common meeting point between the different disciplines. In this study, the different standpoints from all three areas and the conversations in Göttingen are analysed in the frameworkof realism/antirealism. One of the first tasks in the Göttingen conversations was to analyse the nature of the likeness between the complementary structures inquantum physics introduced by Niels Bohr and the dialectical forms in the Barthian doctrine of God. The reaction against epistemological Cartesianism, metaphysics of substance and deterministic description of reality was the common point of departure for theologians and physicists in the Göttingen discussions. In his complementarity, Bohr anticipated the crossing of traditional epistemic boundaries and the generalisation of epistemological strategies by introducing interpretative procedures across various disciplines.

Hvordan øve hellige handlinger? : en profesjonsdidaktisk studie av øving av muntlige ferdigheter innenfor en norsk presteutdanning

How can the holy craft of liturgy be trained? A study of approaches to instruction in training oral skills within education of the Norwegian clergy The theme of this study is the competence of expression of clerics performing liturgies as part of their duties in the Norwegian Lutheran Church. The aim of the study is to find a teaching practice which can raise the competence in oral expression characteristic of the clergy profession. The teaching practice is explored and discussed within the context of the basic education of the clergy. The main thesis is formulated as a question: How can the holy craft of liturgy be trained? An underpinning of the study is that liturgical acts are holy, which gives these performances an aspect of otherness. This otherness constitutes a clear agreement between the students and the teacher, and between the professional and the employer. The pre-understanding of the researcher is that these liturgical oral acts are trainable, and that there is a need and a necessity to train in these skills. Three research questions are elaborated on in the explorative section of the study: • What is characteristic of a competence of expression connected to the profession? • How can this competence of expression connected to liturgical performance be developed? • What is the importance of this competence in the holy craft of liturgy for the development of a cohesive professional self-understanding? The study is based on a research and development project where the researcher as the teacher and students from one specific clergy education in Norway (MF) were the source of the empirical material. The empirical data came from practice with two external observers› logs on the coaching, video observations, of the teacher and the students› texts on the practice under study, which is liturgical performance. The researcher›s log and field notes also provide material for the analysis. This is a qualitative project and an arts education project carried out within an interpretative framework. The theoretical framework has three perspectives: a structural approach based on the system theory of Niklas Luhmann, an epistemological approach discussing forms of knowledge in practice or informing practice and an arts education approach. The results indicate that the competence in oral liturgical performance can be considered a trainable skill, and that this training can be understood as an arts education method of instruction based on meaningful communication, dramaturgical thinking and the development of authenticity. The main result from this study can be considered as articulating and sketching the contours of the field of knowledge where the students embody the meaning of the clergy profession ‒ and this articulation has an innovative potential as knowledge combining experience and theoretical understanding.

Hybrid warfare – just a twist of compound warfare? : views on warfare from the United States Armed Forces perspective

The wars the Western armies are involved with today are different from those that were fought in the end of 20th century. To explain this change, the Western military thinkers have come up with various different types of definitions of warfare over the last 30 years, each describing the tendencies involved in the conflicts of the time. The changing nature of conflicts surfaced a new term – hybrid warfare. The term was to describe and explain the multi-modality and complexity of modern day conflict. This thesis seeks the answer for the question: what is the development of thought behind hybrid warfare? In this thesis the Vietnam War (1965-1975) is used as an example of compound warfare focusing on the American involvement in the war. The Second Lebanon War (2006) serves as an example of hybrid warfare. Both case studies include an irregular opposing force, namely National Liberation Front in Vietnam War and Hezbollah in the Second Lebanon War. These two case studies are compared with the term full spectrum operations introduced in the current U.S. Department of Army Field Manual No. 3-0 Operations to see the differences and similarities of each term. The perspective of this thesis is the American point of view. This thesis concludes that hybrid warfare, compound warfare and full spectrum operations are very similar. The first two terms are included in the last one. Although hybrid warfare is not officially defined, it will most likely remain to be used in the discussion in the future, since hybrid wars and hybrid threats are officially accepted terms.

Corporate responsibility guaranteed by dialogue? Examining the relationship between nongovernmental organizations and business

The main objective of this doctoral dissertation is to examine the relationship between non-governmental organizations and business in the context of academic discourse, corporate responsibility discourse, and stakeholder dialogue. More specifically, motivated by the increasing emphasis on stakeholder dialogue as a tool for corporate responsibility and accountability, the aim is to critically assess the role of stakeholder dialogue as a self-regulatory mechanism, in particular from the perspective of foreign direct investments. The study comprises two parts; an introductory essay containing the research objectives, theoretical foundations and methodological choices, and four research articles that address one sub-objective: 1) to review the literature on NGO-business relations in business and society, management, and international business journals from 1998–2007; 2) to critically analyze the academic discourse on NGO-business relations; 3) to analyze the problematic aspects of sustainable foreign direct investments as a conceptual construct; and 4) to analyze the problematic aspects of stakeholder dialogue in connection with a foreign direct investment. The ontological and epistemological foundations of this dissertation build on the social constructionist view of reality. The dialogue in this study is viewed as a legitimacy bargaining process that is actively shaped by societal parties in discourse. Similarly, articulations of ‘partnership’ and ‘adversarial’ in NGO-business relations in academic business and society discourse are viewed as competing hegemonic interventions in the field. More specifically, the methods applied in the articles are literature review (Article 1), discourse theory (Article 2), conceptual analysis (Article 3), and case study with document analysis (Article 4). This dissertation has three main arguments and contributions. First, it is argued that the potential of stakeholder dialogue as a tool for corporate responsibility and accountability is inherently limited in both contexts. Second, the study shows the power implications of privileging partnership oriented NGO-business relations over adversarial ones, and of placing business at the centre of governance discourse. The third contribution is methodological: a new way to analyze academic discourse is presented by focusing on the problem setting of an article.

Ultrafiltration of pulp mill bleaching effluents

Main objective of this research was to find suitable polymeric ultrafiltration membranes with high retentions, good capacities and low fouling tendencies for the E2- and EP-effluent ultrafiltration. Purpose was to treat alkaline bleaching effluents with ultrafiltration in a way that permeates of the filtrations could be recycled back to process and the consumption of fresh water in the pulp mill could be reduced significantly. In the theoretical part of this work the challenges set by the pulp and paper indus-try processes for membranes were examined. An overview of the membrane tech-nology in the pulp industry was also provided. In addition process conditions in the chemical pulp bleaching and properties of bleaching effluents were discussed in literature study. In experimental part the E2- and EP-stage bleaching effluents from Stora Enso Imatra kraft pulp mill were ultrafiltered with CR250- and CR200-filters. Suitable membranes for ultrafiltration were chosen after screening experiments. Concentra-tion experiment was made for the E2-effluent in order to estimate water saving potential. The E2-effluent was finally ultrafiltered in the pulp mill in order to test the feasibility of ultrafiltration in a real industrial environment. Good membrane for the EP-effluent ultrafiltration based on the EP-screening ex-periments was polyethersulfone membrane UP020 with cut-off value of 20 000 Da. Polysulfone membrane UFX05 with cut-off value of 5 000 Da was promising membrane for the ultrafiltration of the E2-effluent. Based on the concentration filtration of the E2-effluent with UFX05 membrane the water saving potential could be 2.2 m3/Adt for the industrial scale ultrafiltration process. Retention re-sults, such as average COD retention of 60 %, from the trial filtration at the pulp mill with UFX05 membrane were modest compared to the screening experiments, where average COD retention was 75 %. Therefore tighter ultrafiltration mem-branes should be tested for the ultrafiltration of the E2-effluent. The UP020 mem-brane seemed to be suitable for the ultrafiltration of the EP-effluent however con-centration and pilot scale ultrafiltration experiments are needed to verify this.

The Impact of National Innovation System on Entrepreneurial Venture Creation Process

The important role of entrepreneurship in countries’ economic development and overall society well-being is widely recognized by researchers, experts as well as policy makers. Every phase of the process of starting a new business is related to the interaction with at least one player of country innovation system and therefore the efficiency of this interaction may have an influence on the success of whole entrepreneurial process and consequently on the willingness of potential entrepreneurs to engage into this process. The study proposes a System Dynamics model for studying the impact of National Innovation System (NIS) on the entrepreneurial venture creation process. The developed model also takes country population aspect into account and provides results for estimation the effect various demographic tendencies on the process performance. The special impact is made on possible ways to facilitate the development of entrepreneurial framework conditions. Business incubators are seen as one of the effective tool for accomplishing such task. The study also provides the result for estimation of possible impact arising from properly functioned Business Incubators.

Extremfall, stjärnelever och verktygsskramlare : en diskursanalytisk studie av lärares tal om studerande som behöver särskilt stöd

The groups within Finnish vocational upper secondary education and training (VET) are often heterogeneous with respect to the student's need for support in their studies. According to the national core curricula, Special Education Needs (SEN) students should in the first place, get their education in the same group as everyone else. This dissertation aims to clarify and create an understanding about how the ideals and intention of equality in education is constructed in communication among teachers in VET in the Swedish-speaking parts of Finland. Through this understanding it should be possible to highlight a potential which could ultimately contribute to a positive development of a more inclusive education within VET. The epistemological platform of the study is to be found within the post structuralist philosophy of language that is considered as subsumed in a social constructionist thinking. The data has been collected through focus group discussions in groups of 3–6 participants (teachers) in seven schools in Finnish-Swedish VET. The analyses are based on a discursive psychological analysis combined with an analysis based on Michel Foucault's concepts with an emphasis on the subject, government and power. Four discourser where identified in the analysis of teachers' constructions of the educational assignment in relation to SEN students. The most dominant was discussing the educational assignment as a pragmatic project i.e. as a matter of transmission of knowledge. The discourse included both interpretative repertoires where the heterogeneous group was constructed as self-evident and possible to manage as well as a constructed as an impossible project. The educational assignment was also constructed as a holistic project, as part of a democratic project, and as a labor market project. Each discourse contains both including as well as excluding features in relation to SEN students. The development of an inclusive practice can and should therefore include elements from all of them. Three discourses were identified in the analysis concerning teachers' versions of SEN students: students with difficulties and problems; students who do not use or do not have ability and students who are irresponsible and lack the will to study. Within the various discourses and interpretative repertoires were both constructs when teachers described a concern and kindness in relation to the individual SEN student and constructions where teachers mainly expressed fears that other students in the group would be negatively affected by students in need of special support. Results from the third research question conclude the results from the two others, the analysis is done out of a government perspective. In the material use of different government techniques are identified: disciplinary power through direct reprimands; pastoral power by a desire of insight in order to promote the opportunities for consultation and the use of bio-power that primarily focuses on what is best for the population and whose tool racism results in a legitimation of the exclusion of SEN students. The conclusion is that teachers in VET need to pay attention to inclusive and exclusive elements identified in various discourses.

GIS assessing traditional and modern agricultural land use/land cover change. A case study 1959-2005: Rekijoki, Somero, SW-Finland

Finland’s rural landscape has gone through remarkable changes from the 1950’s, due to agricultural developments. Changed farming practices have influenced especially traditional landscape management, and modifications in the arable land structure and grasslands transitions are notable. The review of the previous studies reveal the importance of the rural landscape composition and structure to species and landscape diversity, whereas including the relevance in presence of the open ditches, size of the field and meadow patches, topology of the natural and agricultural landscape. This land-change study includes applying remote sensed data from two time series and empirical geospatial analysis in Geographic Information Systems (GIS). The aims of this retrospective research is to detect agricultural landscape use and land cover change (LULCC) dynamics and discuss the consequences of agricultural intensification to landscape structure covering from the aspects of landscape ecology. Measurements of LULC are derived directly from pre-processed aerial images by a variety of analytical procedures, including statistical methods and image interpretation. The methodological challenges are confronted in the process of landscape classification and combining change detection approaches with landscape indices. Particular importance is paid on detecting agricultural landscape features at a small scale, demanding comprehensive understanding of such agroecosystems. Topological properties of the classified arable land and valley are determined in order to provide insight and emphasize the aspect the field edges in the agricultural landscape as important habitat. Change detection dynamics are presented with change matrix and additional calculations of gain, loss, swap, net change, change rate and tendencies are made. Transition’s possibility is computed following Markov’s probability model and presented with matrix, as well. Thesis’s spatial aspect is revealed with illustrative maps providing knowledge of location of the classified landscape categories and location of the dynamics of the changes occurred. It was assured that in Rekijoki valley’s landscape, remarkable changes in landscape has occurred. Landscape diversity has been strongly influenced by modern agricultural landscape change, as NP of open ditches has decreased and the MPS of the arable plot has decreased. Overall change in the diversity of the landscape is determined with the decrease of SHDI. Valley landscape considered as traditional land use area has experienced major transitional changes, as meadows class has lost almost one third of the area due to afforestation. Also, remarkable transitions have occurred from forest to meadow and arable land to built area. Boundaries measurement between modern and traditional landscape has indicated noticeable proportional increase in arable land-forest edge type and decrease in arable land-meadow edge type. Probability calculations predict higher future changes for traditional landscape, but also for arable land turning into built area.

Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge

The aim of the present set of studies was to explore primary school children’s Spontaneous Focusing On quantitative Relations (SFOR) and its role in the development of rational number conceptual knowledge. The specific goals were to determine if it was possible to identify a spontaneous quantitative focusing tendency that indexes children’s tendency to recognize and utilize quantitative relations in non-explicitly mathematical situations and to determine if this tendency has an impact on the development of rational number conceptual knowledge in late primary school. To this end, we report on six original empirical studies that measure SFOR in children ages five to thirteen years and the development of rational number conceptual knowledge in ten- to thirteen-year-olds. SFOR measures were developed to determine if there are substantial differences in SFOR that are not explained by the ability to use quantitative relations. A measure of children’s conceptual knowledge of the magnitude representations of rational numbers and the density of rational numbers is utilized to capture the process of conceptual change with rational numbers in late primary school students. Finally, SFOR tendency was examined in relation to the development of rational number conceptual knowledge in these students. Study I concerned the first attempts to measure individual differences in children’s spontaneous recognition and use of quantitative relations in 86 Finnish children from the ages of five to seven years. Results revealed that there were substantial inter-individual differences in the spontaneous recognition and use of quantitative relations in these tasks. This was particularly true for the oldest group of participants, who were in grade one (roughly seven years old). However, the study did not control for ability to solve the tasks using quantitative relations, so it was not clear if these differences were due to ability or SFOR. Study II more deeply investigated the nature of the two tasks reported in Study I, through the use of a stimulated-recall procedure examining children’s verbalizations of how they interpreted the tasks. Results reveal that participants were able to verbalize reasoning about their quantitative relational responses, but not their responses based on exact number. Furthermore, participants’ non-mathematical responses revealed a variety of other aspects, beyond quantitative relations and exact number, which participants focused on in completing the tasks. These results suggest that exact number may be more easily perceived than quantitative relations. As well, these tasks were revealed to contain both mathematical and non-mathematical aspects which were interpreted by the participants as relevant. Study III investigated individual differences in SFOR 84 children, ages five to nine, from the US and is the first to report on the connection between SFOR and other mathematical abilities. The cross-sectional data revealed that there were individual differences in SFOR. Importantly, these differences were not entirely explained by the ability to solve the tasks using quantitative relations, suggesting that SFOR is partially independent from the ability to use quantitative relations. In other words, the lack of use of quantitative relations on the SFOR tasks was not solely due to participants being unable to solve the tasks using quantitative relations, but due to a lack of the spontaneous attention to the quantitative relations in the tasks. Furthermore, SFOR tendency was found to be related to arithmetic fluency among these participants. This is the first evidence to suggest that SFOR may be a partially distinct aspect of children’s existing mathematical competences. Study IV presented a follow-up study of the first graders who participated in Studies I and II, examining SFOR tendency as a predictor of their conceptual knowledge of fraction magnitudes in fourth grade. Results revealed that first graders’ SFOR tendency was a unique predictor of fraction conceptual knowledge in fourth grade, even after controlling for general mathematical skills. These results are the first to suggest that SFOR tendency may play a role in the development of rational number conceptual knowledge. Study V presents a longitudinal study of the development of 263 Finnish students’ rational number conceptual knowledge over a one year period. During this time participants completed a measure of conceptual knowledge of the magnitude representations and the density of rational numbers at three time points. First, a Latent Profile Analysis indicated that a four-class model, differentiating between those participants with high magnitude comparison and density knowledge, was the most appropriate. A Latent Transition Analysis reveal that few students display sustained conceptual change with density concepts, though conceptual change with magnitude representations is present in this group. Overall, this study indicated that there were severe deficiencies in conceptual knowledge of rational numbers, especially concepts of density. The longitudinal Study VI presented a synthesis of the previous studies in order to specifically detail the role of SFOR tendency in the development of rational number conceptual knowledge. Thus, the same participants from Study V completed a measure of SFOR, along with the rational number test, including a fourth time point. Results reveal that SFOR tendency was a predictor of rational number conceptual knowledge after two school years, even after taking into consideration prior rational number knowledge (through the use of residualized SFOR scores), arithmetic fluency, and non-verbal intelligence. Furthermore, those participants with higher-than-expected SFOR scores improved significantly more on magnitude representation and density concepts over the four time points. These results indicate that SFOR tendency is a strong predictor of rational number conceptual development in late primary school children. The results of the six studies reveal that within children’s existing mathematical competences there can be identified a spontaneous quantitative focusing tendency named spontaneous focusing on quantitative relations. Furthermore, this tendency is found to play a role in the development of rational number conceptual knowledge in primary school children. Results suggest that conceptual change with the magnitude representations and density of rational numbers is rare among this group of students. However, those children who are more likely to notice and use quantitative relations in situations that are not explicitly mathematical seem to have an advantage in the development of rational number conceptual knowledge. It may be that these students gain quantitative more and qualitatively better self-initiated deliberate practice with quantitative relations in everyday situations due to an increased SFOR tendency. This suggests that it may be important to promote this type of mathematical activity in teaching rational numbers. Furthermore, these results suggest that there may be a series of spontaneous quantitative focusing tendencies that have an impact on mathematical development throughout the learning trajectory.

Defining the art of grammar: Ancient perceptions of γραμματική and grammatical

The subject of this dissertation, which belongs to the field of Classical Philology, are the definitions of the art of grammar found in Greek and Latin sources from the Classical era to the second century CE. Definitions survive from grammarians, philosophers, and general scholars. I have examined these definitions from two main points of view: how they are formed, and how they reflect the development of the art itself. Defining formed part of dialectic, in practice also of rhetoric, and was perceived as important from the Classical era onwards. Definitions of grammar seem to have become established as part of preliminary discussions, located at the beginning of grammatical manuals (tékhnai, artes). These discussions included certain principal notions of the art; in addition to the definition, a list of the parts of the art was also typically included. These lists were formed by two different methods: division (diaíresis, divisio) and partition (merismós, partitio). Many of the grammarians may actually have been unfamiliar with these methods, unlike the two most important scholars of the Late Republic, Varro and Cicero. Significant attention was devoted to the question whether the art of grammar is based on lógos or empeiría. This epistemological question had its roots in medical theories, which were prominent in Alexandria. In the history of the concept of grammatiké or grammatica, three stages become evident. In the Classical era, the Greek term is used to refer to a very concrete art of letters (grámmata); from the Hellenistic era onwards it refers to the art developed by the Alexandrian scholars, a matter of textual and literary criticism. Towards the end of the Hellenistic era, the grammarian also becomes involved with the question of correct language, which gradually begins to appear in the definitions as well.