A Case Based Methodology for Problem Solving aiming at Knee Osteoarthritis Detection

Knee osteoarthritis is the most common type of arthritis and a major cause of impaired mobility and disability for the ageing populations. Therefore, due to the increasing prevalence of the malady, it is expected that clinical and scientific practices had to be set in order to detect the problem in its early stages. Thus, this work will be focused on the improvement of methodologies for problem solving aiming at the development of Artificial Intelligence based decision support system to detect knee osteoarthritis. The framework is built on top of a Logic Programming approach to Knowledge Representation and Reasoning, complemented with a Case Based approach to computing that caters for the handling of incomplete, unknown, or even self-contradictory information.

Age Prediction through Pelvis X-Ray Images - A Case Based approach to Problem Solving

It is well known that the dimensions of the pelvic bones depend on the gender and vary with the age of the individual. Indeed, and as a matter of fact, this work will focus on the development of an intelligent decision support system to predict individual’s age based on pelvis’ dimensions criteria. On the one hand, some basic image processing technics were applied in order to extract the relevant features from pelvic X-rays. On the other hand, the computational framework presented here was built on top of a Logic Programming approach to knowledge representation and reasoning, that caters for the handling of incomplete, unknown, or even self-contradictory information, complemented with a Case Base approach to computing.

Prática de ensino supervisionado no 1.º e 2.º ciclo do ensino básico: a discussão no ensino exploratório da matemática

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

Pensar, testar, opinar e construir: a resolução de problemas no jardim de infância e primeiro ciclo

Relatório de estágio de mestrado em Educação Pré-Escolar e Ensino do 1.º Ciclo do Ensino Básico

Proceso de transformación de las concepciones del profesorado sobre la resolución de problemas matemáticos

The aim of this study is to analyze the transformation of Primary School teachers’ conceptions about mathematical problem solving. We performed a study with 18 teachers from three public schools: in each class (from 1º to 6º) there were two interventions, and we were interviewed teachers before and after them. The results have show identified changes in: 1) teacher’s expectations about students’ abilities; classroom management; perception of diversity; mathematical strategies used by students; communication in the classroom; causes of the problems encountered; and relevance process of problem solving in mathematics teaching. The transformation of teachers’ conceptions is due to the following factors: a) awareness of the practice; b) systematic reflection; c) the contrast between different ways to work solving problems in math class

Socially shared metacognitive regulation during collaborative learning processes in student dyads and small groups

Traditionally metacognition has been theorised, methodologically studied and empirically tested from the standpoint mainly of individuals and their learning contexts. In this dissertation the emergence of metacognition is analysed more broadly. The aim of the dissertation was to explore socially shared metacognitive regulation (SSMR) as part of collaborative learning processes taking place in student dyads and small learning groups. The specific aims were to extend the concept of individual metacognition to SSMR, to develop methods to capture and analyse SSMR and to validate the usefulness of the concept of SSMR in two different learning contexts; in face-to-face student dyads solving mathematical word problems and also in small groups taking part in inquiry-based science learning in an asynchronous computer-supported collaborative learning (CSCL) environment. This dissertation is comprised of four studies. In Study I, the main aim was to explore if and how metacognition emerges during problem solving in student dyads and then to develop a method for analysing the social level of awareness, monitoring, and regulatory processes emerging during the problem solving. Two dyads comprised of 10-year-old students who were high-achieving especially in mathematical word problem solving and reading comprehension were involved in the study. An in-depth case analysis was conducted. Data consisted of over 16 (30–45 minutes) videotaped and transcribed face-to-face sessions. The dyads solved altogether 151 mathematical word problems of different difficulty levels in a game-format learning environment. The interaction flowchart was used in the analysis to uncover socially shared metacognition. Interviews (also stimulated recall interviews) were conducted in order to obtain further information about socially shared metacognition. The findings showed the emergence of metacognition in a collaborative learning context in a way that cannot solely be explained by individual conception. The concept of socially-shared metacognition (SSMR) was proposed. The results highlighted the emergence of socially shared metacognition specifically in problems where dyads encountered challenges. Small verbal and nonverbal signals between students also triggered the emergence of socially shared metacognition. Additionally, one dyad implemented a system whereby they shared metacognitive regulation based on their strengths in learning. Overall, the findings suggested that in order to discover patterns of socially shared metacognition, it is important to investigate metacognition over time. However, it was concluded that more research on socially shared metacognition, from larger data sets, is needed. These findings formed the basis of the second study. In Study II, the specific aim was to investigate whether socially shared metacognition can be reliably identified from a large dataset of collaborative face-to-face mathematical word problem solving sessions by student dyads. We specifically examined different difficulty levels of tasks as well as the function and focus of socially shared metacognition. Furthermore, the presence of observable metacognitive experiences at the beginning of socially shared metacognition was explored. Four dyads participated in the study. Each dyad was comprised of high-achieving 10-year-old students, ranked in the top 11% of their fourth grade peers (n=393). Dyads were from the same data set as in Study I. The dyads worked face-to-face in a computer-supported, game-format learning environment. Problem-solving processes for 251 tasks at three difficulty levels taking place during 56 (30–45 minutes) lessons were video-taped and analysed. Baseline data for this study were 14 675 turns of transcribed verbal and nonverbal behaviours observed in four study dyads. The micro-level analysis illustrated how participants moved between different channels of communication (individual and interpersonal). The unit of analysis was a set of turns, referred to as an ‘episode’. The results indicated that socially shared metacognition and its function and focus, as well as the appearance of metacognitive experiences can be defined in a reliable way from a larger data set by independent coders. A comparison of the different difficulty levels of the problems suggested that in order to trigger socially shared metacognition in small groups, the problems should be more difficult, as opposed to moderately difficult or easy. Although socially shared metacognition was found in collaborative face-to-face problem solving among high-achieving student dyads, more research is needed in different contexts. This consideration created the basis of the research on socially shared metacognition in Studies III and IV. In Study III, the aim was to expand the research on SSMR from face-to-face mathematical problem solving in student dyads to inquiry-based science learning among small groups in an asynchronous computer-supported collaborative learning (CSCL) environment. The specific aims were to investigate SSMR’s evolvement and functions in a CSCL environment and to explore how SSMR emerges at different phases of the inquiry process. Finally, individual student participation in SSMR during the process was studied. An in-depth explanatory case study of one small group of four girls aged 12 years was carried out. The girls attended a class that has an entrance examination and conducts a language-enriched curriculum. The small group solved complex science problems in an asynchronous CSCL environment, participating in research-like processes of inquiry during 22 lessons (á 45–minute). Students’ network discussion were recorded in written notes (N=640) which were used as study data. A set of notes, referred to here as a ‘thread’, was used as the unit of analysis. The inter-coder agreement was regarded as substantial. The results indicated that SSMR emerges in a small group’s asynchronous CSCL inquiry process in the science domain. Hence, the results of Study III were in line with the previous Study I and Study II and revealed that metacognition cannot be reduced to the individual level alone. The findings also confirm that SSMR should be examined as a process, since SSMR can evolve during different phases and that different SSMR threads overlapped and intertwined. Although the classification of SSMR’s functions was applicable in the context of CSCL in a small group, the dominant function was different in the asynchronous CSCL inquiry in the small group in a science activity than in mathematical word problem solving among student dyads (Study II). Further, the use of different analytical methods provided complementary findings about students’ participation in SSMR. The findings suggest that it is not enough to code just a single written note or simply to examine who has the largest number of notes in the SSMR thread but also to examine the connections between the notes. As the findings of the present study are based on an in-depth analysis of a single small group, further cases were examined in Study IV, as well as looking at the SSMR’s focus, which was also studied in a face-to-face context. In Study IV, the general aim was to investigate the emergence of SSMR with a larger data set from an asynchronous CSCL inquiry process in small student groups carrying out science activities. The specific aims were to study the emergence of SSMR in the different phases of the process, students’ participation in SSMR, and the relation of SSMR’s focus to the quality of outcomes, which was not explored in previous studies. The participants were 12-year-old students from the same class as in Study III. Five small groups consisting of four students and one of five students (N=25) were involved in the study. The small groups solved ill-defined science problems in an asynchronous CSCL environment, participating in research-like processes of inquiry over a total period of 22 hours. Written notes (N=4088) detailed the network discussions of the small groups and these constituted the study data. With these notes, SSMR threads were explored. As in Study III, the thread was used as the unit of analysis. In total, 332 notes were classified as forming 41 SSMR threads. Inter-coder agreement was assessed by three coders in the different phases of the analysis and found to be reliable. Multiple methods of analysis were used. Results showed that SSMR emerged in all the asynchronous CSCL inquiry processes in the small groups. However, the findings did not reveal any significantly changing trend in the emergence of SSMR during the process. As a main trend, the number of notes included in SSMR threads differed significantly in different phases of the process and small groups differed from each other. Although student participation was seen as highly dispersed between the students, there were differences between students and small groups. Furthermore, the findings indicated that the amount of SSMR during the process or participation structure did not explain the differences in the quality of outcomes for the groups. Rather, when SSMRs were focused on understanding and procedural matters, it was associated with achieving high quality learning outcomes. In turn, when SSMRs were focused on incidental and procedural matters, it was associated with low level learning outcomes. Hence, the findings imply that the focus of any emerging SSMR is crucial to the quality of the learning outcomes. Moreover, the findings encourage the use of multiple research methods for studying SSMR. In total, the four studies convincingly indicate that a phenomenon of socially shared metacognitive regulation also exists. This means that it was possible to define the concept of SSMR theoretically, to investigate it methodologically and to validate it empirically in two different learning contexts across dyads and small groups. In-depth micro-level case analysis in Studies I and III showed the possibility to capture and analyse in detail SSMR during the collaborative process, while in Studies II and IV, the analysis validated the emergence of SSMR in larger data sets. Hence, validation was tested both between two environments and within the same environments with further cases. As a part of this dissertation, SSMR’s detailed functions and foci were revealed. Moreover, the findings showed the important role of observable metacognitive experiences as the starting point of SSMRs. It was apparent that problems dealt with by the groups should be rather difficult if SSMR is to be made clearly visible. Further, individual students’ participation was found to differ between students and groups. The multiple research methods employed revealed supplementary findings regarding SSMR. Finally, when SSMR was focused on understanding and procedural matters, this was seen to lead to higher quality learning outcomes. Socially shared metacognition regulation should therefore be taken into consideration in students’ collaborative learning at school similarly to how an individual’s metacognition is taken into account in individual learning.

Utilisation des TIC dans l’enseignement secondaire et développement des compétences des élèves en résolution de problèmes mathématiques au Burkina Faso

La présente étude intitulée « utilisation des technologies de l’information et de la communication dans l’enseignement secondaire et développement des compétences des élèves en résolution de problèmes mathématiques au Burkina Faso » est une recherche descriptive de type mixte examinant à la fois des données qualitatives et quantitatives. Elle examine les compétences en résolution de problèmes mathématiques d’élèves du Burkina Faso pour révéler d’éventuelles relations entre celles-ci et l’utilisation des TIC par les élèves ou leur enseignant de mathématiques. L’intérêt de cette recherche est de fournir des informations aussi bien sur la réalité des TIC dans l’enseignement secondaire au Burkina que sur les effets de leur présence dans l’enseignement et l’apprentissage des mathématiques. Les éléments théoriques ayant servi à l’analyse des données sont présentés suivant trois directions : la résolution des problèmes, le développement des compétences, et les relations entre les TIC, le développement de compétences et la résolution de problèmes. Du croisement de ces éléments émergent trois axes pour le développement de la réponse apportée à la préoccupation de l’étude : 1) décrire l’utilisation de l’ordinateur par les élèves du Burkina Faso pour améliorer leur apprentissage des mathématiques ; 2) identifier des rapports éventuels entre l’utilisation de l’ordinateur par les élèves et leurs compétences en résolution de problèmes mathématiques ; 3) identifier des rapports entre les compétences TIC de l’enseignant de mathématiques et les compétences de ses élèves en résolution de problèmes. Les processus de la résolution de problèmes sont présentés selon l’approche gestaltiste qui les fait passer par une illumination et selon l’approche de la théorie de la communication qui les lie au type de problème. La résolution de problèmes mathématiques passe par des étapes caractéristiques qui déterminent la compétence du sujet. Le concept de compétence est présenté selon l’approche de Le Boterf. Les données révèlent que les élèves du Burkina Faso utilisent l’ordinateur selon une logique transmissive en le considérant comme un répétiteur suppléant de l’enseignant. Par la suite, il n’y a pas de différence significative dans les compétences en résolution de problèmes mathématiques entre les élèves utilisant l’ordinateur et ceux qui ne l’utilisent pas. De même, l’étude révèle que les enseignants présentant des compétences TIC n’ont pas des élèves plus compétents en résolution de problèmes mathématiques que ceux de leurs collègues qui n’ont pas de compétences TIC.

Förlorad i övergången från aritmetik till algebra : Hur gymnasieelever översätter aritmetik till algebra

The aim of this thesis is to look for signs of students’ understanding of algebra by studying how they make the transition from arithmetic to algebra. Students in an Upper Secondary class on the Natural Science program and Science and Technology program were given a questionnaire with a number of algebraic problems of different levels of difficulty. Especially important for the study was that students leave comments and explanations of how they solved the problems. According to earlier research, transitions are the most critical steps in problem solving. The Algebraic Cycle is a theoretical tool that can be used to make different phases in problem solving visible. To formulate and communicate how the solution was made may lead to students becoming more aware of their thought processes. This may contribute to students gaining more understanding of the different phases involved in mathematical problem solving, and to students becoming more successful in mathematics in general.The study showed that the students could solve mathematical problems correctly, but that they in just over 50% of the cases, did not give any explanations to their solutions.

Fundamentos teóricos do método de resolução de problemas ampliados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

PARFOR e a formação inicial dos professores: um estudo sobre a confiança, as atitudes e as estratégias em relação à resolução de problemas

The mathematical problem solving is very important in the student's school career, leading him to develop his creativity and self-confidence. The way the teacher explains specific content may interfere in the student learning. Some researches show that the teacher trust and his problem solving rapport lead to a more satisfying job. This research focused on students of the course PARFOR at UNESP Bauru. This work was performed in order to investigate the affinity, trust and attitudes toward mathematical problem solving, the performance from who have positive and negative attitudes and the results that may be generated during class

Multivariate genetic analysis of academic skills of the Queensland Core Skills Test and IQ highlight the importance of genetic g

This study examined the genetic and environmental relationships among 5 academic achievement skills of a standardized test of academic achievement, the Queensland Core Skills Test (QCST; Queensland Studies Authority, 2003a). QCST participants included 182 monozygotic pairs and 208 dizygotic pairs (mean 17 years +/- 0.4 standard deviation). IQ data were included in the analysis to correct for ascertainment bias. A genetic general factor explained virtually all genetic variance in the component academic skills scores, and accounted for 32% to 73% of their phenotypic variances. It also explained 56% and 42% of variation in Verbal IQ and Performance IQ respectively, suggesting that this factor is genetic g. Modest specific genetic effects were evident for achievement in mathematical problem solving and written expression. A single common factor adequately explained common environmental effects, which were also modest, and possibly due to assortative mating. The results suggest that general academic ability, derived from genetic influences and to a lesser extent common environmental influences, is the primary source of variation in component skills of the QCST.

Systemological Bases of Management Consulting

The problem of management consulting for sustainable development organization support is discussed. The problem is formally described by means of systemological terms. The mathematical problem solving is considered. Practical use of the obtained results is outlined.

O papel das representações na resolução de problemas de Matemática: um estudo no 1º ano de escolaridade

Este estudo tem como objectivo investigar o papel que as representações, construídas por alunos do 1.o ano de escolaridade, desempenham na resolução de problemas de Matemática. Mais concretamente, a presente investigação procura responder às seguintes questões: Que representações preferenciais utilizam os alunos para resolver problemas? De que forma é que as diferentes representações são influenciadas pelas estratégias de resolução de problemas utilizadas pelos alunos? Que papéis têm os diferentes tipos de representação na resolução dos problemas? Nesta investigação assume-se que a resolução de problemas constitui uma actividade muito importante na aprendizagem da Matemática no 1.o Ciclo do Ensino Básico. Os problemas devem ser variados, apelar a estratégias diversificadas de resolução e permitir diferentes representações por parte dos alunos. As representações cativas, icónicas e simbólicas constituem importantes ferramentas para os alunos organizarem, registarem e comunicarem as suas ideias matemáticas, nomeadamente no âmbito da resolução de problemas, servindo igualmente de apoio à compreensão de conceitos e relações matemáticas. A metodologia de investigação segue uma abordagem interpretativa tomando por design o estudo de caso. Trata-se simultaneamente de uma investigação sobre a própria prática, correspondendo os quatro estudos de caso a quatro alunos da turma de 1.0 ano de escolaridade da investigadora. A recolha de dados teve lugar durante o ano lectivo 2007/2008 e recorreu à observação, à análise de documentos, a diários, a registos áudio/vídeo e ainda a conversas com os alunos. A análise de dados que, numa primeira fase, acompanhou a recolha de dados, teve como base o problema e as questões da investigação bem como o referencial teórico que serviu de suporte à investigação. Com base no referencial teórico e durante o início do processo de análise, foram definidas as categorias de análise principais, sujeitas posteriormente a um processo de adequação e refinamento no decorrer da análise e tratamento dos dados recolhidos -com vista à construção dos casos em estudo. Os resultados desta investigação apontam as representações do tipo icónico e as do tipo simbólico como as representações preferenciais dos alunos, embora sejam utilizadas de formas diferentes, com funções distintas e em contextos diversos. Os elementos simbólicos apoiam-se frequentemente em elementos icónicos, sendo estes últimos que ajudam os alunos a descompactar o problema e a interpretá-lo. Nas representações icónicas enfatiza-se o papel do diagrama, o qual constitui uma preciosa ferramenta de apoio ao raciocínio matemático. Conclui-se ainda que enquanto as representações activas dão mais apoio a estratégias de resolução que envolvem simulação, as representações icónicas e simbólicas são utilizadas com estratégias diversificadas. As representações construídas, com papéis e funções diferentes entre si, e que desempenham um papel crucial na correcta interpretação e resolução dos problemas, parecem estar directamente relacionadas com as caraterísticas da tarefa proposta no que diz respeito às estruturas matemáticas envolvidas. ABSTRACT; The objective of the present study is to investigate the role of the representations constructed by 1st grade students in mathematical problem solving. More specifically, this research is oriented by the following questions: Which representations are preferably used by students to solve problems? ln which way the strategies adopted by the students in problem solving influence those distinct representations? What is the role of the distinct types of representation in the problems solving process? ln this research it is assumed that the resolution of problems is a very important activity in the Mathematics learning at the first cycle of basic education. The problems must be varied, appealing to diverse strategies of resolution and allow students to construct distinct representations. The active, iconic and symbolic representations are important tools for students to organize, to record and to communicate their mathematical ideas, particularly in problem solving context, as well as supporting the understanding of mathematical concepts and relationships. The adopted research methodology follows an interpretative approach, and was developed in the context of the researcher classroom, originating four case studies corresponding to four 1 st grade students of the researcher's class. Data collection was carried out during the academic year of 2007/2008 and was based on observation, analysis of documents, diaries, audio and video records and informal conversations with students. The initial data analysis was based on the problems and issues of research, as well in the theoretical framework that supports it. The main categories of analysis were defined based on the theoretical framework, and were subjected to a process of adaptation and refining during data processing and analysis aiming the -case studies construction. The results show that student's preferential representations are the iconic and the symbolic, although these types of representations are used in different ways, with different functions and in different contexts. The symbolic elements are often supported by iconic elements, the latter helping students to unpack the problem and interpret it. ln the iconic representations the role of the diagrams is emphasized, consisting in a valuable tool to support the mathematical reasoning. One can also conclude that while the active representations give more support to the resolution strategies involving simulation, the iconic and symbolic representations are preferably used with different strategies. The representations constructed with distinct roles and functions, are crucial in the proper interpretation and resolution of problems, and seem to be directly related to the characteristics of the proposed task with regard to the mathematical structures involved.

Trabalhar com a matemática em educação de infância

Este estudo tem como principal objetivo compreender e analisar o modo como crianças de creche e jardim-de-infância resolvem problemas matemáticos e o que pode constranger a resolução. Em particular, procurei analisar a atividade matemática que as crianças desenvolvem quando se confrontam com problemas matemáticos e os desafios com que se deparam. Do ponto de vista metodológico, o estudo enquadra-se numa abordagem qualitativa de investigação e num paradigma interpretativo. Além disso, trata-se de uma investigação-ação orientada pela questão “como otimizar a atividade de resolver problemas matemáticos em contextos de educação de infância?”. Neste âmbito, propus a quatro crianças de creche e a 21 de jardim-de-infância um conjunto de tarefas selecionadas para, potencialmente, terem, para si, algum grau de desafio. Os principais métodos de recolha de dados foram a observação participante, a análise documental e um inquérito por questionário realizado às educadoras cooperantes. O estudo ilustra que é possível envolver crianças de creche e de jardim-de-infância numa atividade de resolução de problemas matemáticos e que esta atividade é favorecida se o contexto dos problemas estiver próximo do que fazem no dia-a-dia da sala. Durante o processo de resolução das tarefas propostas, foram mobilizadas e trabalhadas diversas noções matemáticas. Na creche, todas as crianças evidenciaram possuir conhecimentos acerca da noção topológica “dentro de” e “fora de” e algumas foram bem-sucedidas no uso do processo de classificação, tendo em conta um critério. Neste âmbito, recorreram a representações ativas. No jardim-de-infância, todas as crianças conseguiram fazer a contagem sincronizada das letras do seu nome, de indicar a quantidade de letras, o que indicia o conhecimento da noção de cardinal, e de representar esta quantidade recorrendo tanto a numerais como a representações icónicas. Além disso, foram capazes de interpretar uma tabela de modo a construir um gráfico com barras e de elaborar um pictograma, o que revela possuírem conhecimentos ao nível da literacia estatística. Por último, algumas crianças foram bem-sucedidas na descoberta de estratégias de resolução de problemas que lhes permitiram inventariar exaustivamente todas as possibilidades de resolução e contar, organizadamente, estas possibilidades. No decurso desta atividade surgiram tentativas de generalização, embora nem sempre corretas, sobressaindo o recurso a representações ativas nomeadamente à dramatização de situações. Quanto aos desafios com que se depararam destacam-se, no caso da creche, o uso correto do processo de classificação. No caso do jardim-de-infância, as crianças demonstraram dificuldades em distinguir a legenda do pictograma dos dados, em resolver um problema em que estava em jogo o sentido combinatório da multiplicação e em encontrar estratégias de generalização. O estudo indicia, ainda, que é essencial que o educador proponha tarefas diversificadas e desafiantes que, partindo sempre da curiosidade e interesse das crianças, lhes permitam trabalhar com ideias matemáticas importantes e representar adequadamente o conhecimento com que lidam.

Strategies to Promote Research and Logical Reasoning in the Teaching of Mathematics in the Schools

The purpose of this paper is to raise a debate on the urgent need for teachers to generate innovative situations in the teaching-learning process, in the field of Mathematics, as a way for students to develop logical reasoning and research skills applicable to everyday situations. It includes some statistical data and possible reasons for the poor performance and dissatisfaction of students towards Mathematics. Since teachers are called to offer meaningful and functional learning experiences to students, in order to promote the pleasure of learning, teacher training should include experiences that can be put into practice by teachers in the education centers. This paper includes a work proposal for Mathematics Teaching to generate discussion, curiosity and logical reasoning in students, together with the Mathematical problem solving study.