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.

Conceptual knowledge discovery with frequent concept lattices

Knowledge discovery support environments include beside classical data analysis tools also data mining tools. For supporting both kinds of tools, a unified knowledge representation is needed. We show that concept lattices which are used as knowledge representation in Conceptual Information Systems can also be used for structuring the results of mining association rules. Vice versa, we use ideas of association rules for reducing the complexity of the visualization of Conceptual Information Systems.

Conceptual knowledge discovery and data analysis

In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a theory of conceptual information systems which has been applied by using the management system TOSCANA in a wide range of domains. In this paper, we use such an application in database marketing to demonstrate how methods and procedures of CKDD can be applied in Data Analysis. In particular, we show the interplay and integration of data mining and data analysis techniques based on Formal Concept Analysis. The main concern of this paper is to explain how the transition from data to knowledge can be supported by a TOSCANA system. To clarify the transition steps we discuss their correspondence to the five levels of knowledge representation established by R. Brachman and to the steps of empirically grounded theory building proposed by A. Strauss and J. Corbin.

Conceptual knowledge processing with formal concept analysis and ontologies

Among many other knowledge representations formalisms, Ontologies and Formal Concept Analysis (FCA) aim at modeling ‘concepts’. We discuss how these two formalisms may complement another from an application point of view. In particular, we will see how FCA can be used to support Ontology Engineering, and how ontologies can be exploited in FCA applications. The interplay of FCA and ontologies is studied along the life cycle of an ontology: (i) FCA can support the building of the ontology as a learning technique. (ii) The established ontology can be analyzed and navigated by using techniques of FCA. (iii) Last but not least, the ontology may be used to improve an FCA application.

Autobiographical memory and amnesia: using conceptual knowledge to ground the self

A case of retrograde amnesia, PJM, elucidated the relationship between self, episodic memory and autobiographical knowledge. Results from a variety of measures including the I Am Memory Task (IAM Task), where memories are cued by self-generated self concepts, demonstrate that PJM has a coherent, continuous sense of self, despite having lost episodic memories for an 18-month period. Her use of conceptual autobiographical knowledge, in episodic tasks and to support aspects of identity, shows how autobiographical knowledge can support the self when episodic memories are inaccessible. These results are discussed with relation to current neuropsychological models of self and memory.

Programa estruturado de enriquecimento conceptual e lexical

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ciências da Educação - Especialidade Educação Especial

Propuesta de un test para determinar el conocimiento conceptual de estudiantes universitarios sobre la constante de equilibrio químico y su aplicación en estudiantes españoles

This article outlines a procedure that was used to develop a written test for evaluating the conceptual knowledge of chemical equilibrium constant among university students. The concepts in the subject matter were carefully defined through propositional statements. Students' understanding of the topic was determined through interviews. These data were used to produce nine multiple choice questions. Each question was designed to identify misconceptions related to the chemical equilibrium constant. The test was evaluated by foure associate professors and was administred to a total of 196 spanish university students. This test has a Cronbach's alpha reliability of 0.63 and its content validity values ranged from 3.7 to 5.

Knowledge Building in Landscape Architecture

The objective of this study was to develop an internet-based seminar framework applicable for landscape architecture education. This process was accompanied by various aims. The basic expectation was to keep the main characteristics of landscape architecture education also in the online format. On top of that, four further objectives were anticipated: (1) training of competences for virtual team work, (2) fostering intercultural competence, (3) creation of equal opportunities for education through internet-based open access and (4) synergy effects and learning processes across institutional boundaries. This work started with the hypothesis that these four expected advantages would compensate for additional organisational efforts caused by the online delivery of the seminars and thus lead to a sustainable integration of this new learning mode into landscape architecture curricula. This rationale was followed by a presentation of four areas of knowledge to which the seminar development was directly related (1) landscape architecture as a subject and its pedagogy, (2) general learning theories, (3) developments in the ICT sector and (4) wider societal driving forces such as global citizenship and the increase of open educational resources. The research design took the shape of a pedagogical action research cycle. This approach was constructive: The author herself is teaching international landscape architecture students so that the model could directly be applied in practice. Seven online seminars were implemented in the period from 2008 to 2013 and this experience represents the core of this study. The seminars were conducted with varying themes while its pedagogy, organisation and the technological tools remained widely identical. The research design is further based on three levels of observation: (1) the seminar design on the basis of theory and methods from the learning sciences, in particular educational constructivism, (2) the seminar evaluation and (3) the evaluation of the seminars’ long term impact. The seminar model itself basically consists of four elements: (1) the taxonomy of learning objectives, (2) ICT tools and their application and pedagogy, (3) process models and (4) the case study framework. The seminar framework was followed by the presentation of the evaluation findings. The major findings of this study can be summed up as follows: Implementing online seminars across educational and national boundaries was possible both in term of organisation and technology. In particular, a high level of cultural diversity among the seminar participants has definitively been achieved. However, there were also obvious obstacles. These were primarily competing study commitments and incompatible schedules among the students attending from different academic programmes, partly even in different time zones. Both factors had negative impact on the individual and working group performances. With respect to the technical framework it can be concluded that the majority of the participants were able to use the tools either directly without any problem or after overcoming some smaller problems. Also the seminar wiki was intensively used for completing the seminar assignments. However, too less truly collaborative text production was observed which could be improved by changing the requirements for the collaborative task. Two different process models have been applied for guiding the collaboration of the small groups and both were in general successful. However, it needs to be said that even if the students were able to follow the collaborative task and to co-construct and compare case studies, most of them were not able to synthesize the knowledge they had compiled. This means that the area of consideration often remained on the level of the case and further reflections, generalisations and critique were largely missing. This shows that the seminar model needs to find better ways for triggering knowledge building and critical reflection. It was also suggested to have a more differentiated group building strategy in future seminars. A comparison of pre- and post seminar concept maps showed that an increase of factual and conceptual knowledge on the individual level was widely recognizable. Also the evaluation of the case studies (the major seminar output) revealed that the students have undergone developments of both the factual and the conceptual knowledge domain. Also their self-assessment with respect to individual learning development showed that the highest consensus was achieved in the field of subject-specific knowledge. The participants were much more doubtful with regard to the progress of generic competences such as analysis, communication and organisation. However, 50% of the participants confirmed that they perceived individual development on all competence areas the survey had asked for. Have the additional four targets been met? Concerning the competences for working in a virtual team it can be concluded that the vast majority was able to use the internet-based tools and to work with them in a target-oriented way. However, there were obvious differences regarding the intensity and activity of participation, both because of external and personal factors. A very positive aspect is the achievement of a high cultural diversity supporting the participants’ intercultural competence. Learning from group members was obviously a success factor for the working groups. Regarding the possibilities for better accessibility of educational opportunities it became clear that a significant number of participants were not able to go abroad during their studies because of financial or personal reasons. They confirmed that the online seminar was to some extent a compensation for not having been abroad for studying. Inter-institutional learning and synergy was achieved in so far that many teachers from different countries contributed with individual lectures. However, those teachers hardly ever followed more than one session. Therefore, the learning effect remained largely within the seminar learning group. Looking back at the research design it can be said that the pedagogical action research cycle was an appropriate and valuable approach allowing for strong interaction between theory and practice. However, some more external evaluation from peers in particular regarding the participants’ products would have been valuable.

Patterns of regional brain hypometabolism associated with knowledge of semantic features and categories in Alzheimer's disease

The study of semantic memory in patients with Alzheimer's disease (AD) has raised important questions about the representation of conceptual knowledge in the human brain. It is still unknown whether semantic memory impairments are caused by localized damage to specialized regions or by diffuse damage to distributed representations within nonspecialized brain areas. To our knowledge, there have been no direct correlations of neuroimaging of in vivo brain function in AD with performance on tasks differentially addressing visual and functional knowledge of living and nonliving concepts. We used a semantic verification task and resting 18-fluorodeoxyglucose positron emission tomography in a group of mild to moderate AD patients to investigate this issue. The four task conditions required semantic knowledge of (1) visual, (2) functional properties of living objects, and (3) visual or (4) functional properties of nonliving objects. Visual property verification of living objects was significantly correlated with left posterior fusiform gyrus metabolism (Brodmann's area [BA] 37/19). Effects of visual and functional property verification for non-living objects largely overlapped in the left anterior temporal (BA 38/20) and bilateral premotor areas (BA 6), with the visual condition extending more into left lateral precentral areas. There were no associations with functional property verification for living concepts. Our results provide strong support for anatomically separable representations of living and nonliving concepts, as well as visual feature knowledge of living objects, and against distributed accounts of semantic memory that view visual and functional features of living and nonliving objects as distributed across a common set of brain areas.

A Knowledge-Oriented Technology of System-Objective Analysis and Modelling of Business-Systems

A new original method and CASE-tool of system analysis and modelling are represented. They are for the first time consistent with the requirements of object-oriented technology of informational systems design. They essentially facilitate the construction of organisational systems models and increase the quality of the organisational designing and basic technological processes of object application developing.

Multilingualism and conceptual modelling

One of the leading motivations behind the multilingual semantic web is to make resources accessible digitally in an online global multilingual context. Consequently, it is fundamental for knowledge bases to find a way to manage multilingualism and thus be equipped with those procedures for its conceptual modelling. In this context, the goal of this paper is to discuss how common-sense knowledge and cultural knowledge are modelled in a multilingual framework. More particularly, multilingualism and conceptual modelling are dealt with from the perspective of FunGramKB, a lexico-conceptual knowledge base for natural language understanding. This project argues for a clear division between the lexical and the conceptual dimensions of knowledge. Moreover, the conceptual layer is organized into three modules, which result from a strong commitment towards capturing semantic knowledge (Ontology), procedural knowledge (Cognicon) and episodic knowledge (Onomasticon). Cultural mismatches are discussed and formally represented at the three conceptual levels of FunGramKB.

Relaciones entre el conocimiento conceptual y el procedimental en el aprendizaje de las fracciones

El objetivo de este trabajo fue analizar las relaciones entre el conocimiento conceptual y el procedimental de las fracciones durante su aprendizaje. Para esto se efectuó una búsqueda bibliográfica en las bases de datos ERIC, PsycInfo, Scielo y Redalyc, con los siguientes términos en español y sus equivalentes en inglés: fracciones (fractions), conocimiento conceptual (conceptual knowledge), conocimiento procedimental (procedural knowledge) y niños (children), combinados de diferente forma con el operador booleano AND (Y). Los resultados de esta búsqueda permitieron hallar quince artículos empíricos que pueden clasificarse en cuatro grupos de investigaciones: las que indican una relación bidireccional, las que sugieren una relación unidireccional, las que muestran cierta independencia o restricciones en su vinculación y, por último, las que señalan que las relaciones varían según los sujetos. Esta falta de acuerdo podría explicarse por ciertas diferencias metodológicas de los estudios, por ejemplo, diferencias en el grado de consolidación del conocimiento de las fracciones de los participantes, el sentido conceptual o la habilidad procedimental estudiada, el tipo de enseñanza matemática recibida, etc. Por ello se sugiere que, para profundizar la comprensión de las relaciones entre el conocimiento conceptual y procedimental de las fracciones, estos aspectos metodológicos deben ser controlados.

A aprendizagem baseada na resolução de problemas na aprendizagem da Geologia: uma intervenção centrada no tópico "Ocupação antrópica e problemas de ordenamento"

Dissertação de mestrado em Ensino de Biologia e Geologia no 3º Ciclo do Ensino Básico e no Ensino Secundário