845 resultados para How Finns learn mathematics and science


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This report shares my efforts in developing a solid unit of instruction that has a clear focus on student outcomes. I have been a teacher for 20 years and have been writing and revising curricula for much of that time. However, most has been developed without the benefit of current research on how students learn and did not focus on what and how students are learning. My journey as a teacher has involved a lot of trial and error. My traditional method of teaching is to look at the benchmarks (now content expectations) to see what needs to be covered. My unit consists of having students read the appropriate sections in the textbook, complete work sheets, watch a video, and take some notes. I try to include at least one hands-on activity, one or more quizzes, and the traditional end-of-unit test consisting mostly of multiple choice questions I find in the textbook. I try to be engaging, make the lessons fun, and hope that at the end of the unit my students get whatever concepts I‘ve presented so that we can move on to the next topic. I want to increase students‘ understanding of science concepts and their ability to connect understanding to the real-world. However, sometimes I feel that my lessons are missing something. For a long time I have wanted to develop a unit of instruction that I know is an effective tool for the teaching and learning of science. In this report, I describe my efforts to reform my curricula using the “Understanding by Design” process. I want to see if this style of curriculum design will help me be a more effective teacher and if it will lead to an increase in student learning. My hypothesis is that this new (for me) approach to teaching will lead to increased understanding of science concepts among students because it is based on purposefully thinking about learning targets based on “big ideas” in science. For my reformed curricula I incorporate lessons from several outstanding programs I‘ve been involved with including EpiCenter (Purdue University), Incorporated Research Institutions for Seismology (IRIS), the Master of Science Program in Applied Science Education at Michigan Technological University, and the Michigan Association for Computer Users in Learning (MACUL). In this report, I present the methodology on how I developed a new unit of instruction based on the Understanding by Design process. I present several lessons and learning plans I‘ve developed for the unit that follow the 5E Learning Cycle as appendices at the end of this report. I also include the results of pilot testing of one of lessons. Although the lesson I pilot-tested was not as successful in increasing student learning outcomes as I had anticipated, the development process I followed was helpful in that it required me to focus on important concepts. Conducting the pilot test was also helpful to me because it led me to identify ways in which I could improve upon the lesson in the future.

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Published: Chicago : School Science and Mathematics, 1905- ; Chicago : Smith & Turton, <1907- >; Mount Morris, Ill. : Central Association of Science and Mathematics Teachers, Oct. 1928-1970; Bloomington, Ind. : School Science and Mathematics Association, 1971-May/June 1981; Bowling Green, Ohio : The Association, Oct. 1981-; Hoboken, NJ : Wiley Subscription Services, Inc., .

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The 2008 National Student Survey revealed that: 44% of full-time students in England did not think that the feedback on their work had been prompt nor did they agree that the feedback on their work helped them clarify things that they did not understand (HEFCE, 2008). Computer Science and Engineering & Technology have been amongst the poorest performers in this aspect as they ranked in the lower quartile (Surridge, 2007, p.32). Five years since the first NSS survey, assessment and feedback remains the biggest concern. Dissatisfaction in any aspect of studies demotivates students and can lead to disengagement and attrition. As the student number grows, the situation can only get worse if nothing is done about it. We have conducted a survey to investigate views on assessment and feedback from Engineering, Mathematics and Computing students. The survey aims at investigating the core issues of dissatisfaction in assessment and feedback and ways in which UK Engineering students can learn better through helpful feedback. The study focuses on collecting students' experiences with feedback received in their coursework, assignments and quizzes in Computing Science modules. The survey reveals the role of feedback in their learning. The results of the survey help to identify the forms of feedback that are considered to be helpful in learning and the time frame for timely feedback. We report on the findings of the survey. We also explore ways to improve assessment and feedback in a bid to better engage engineering students in their studies.

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Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

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This study deals with the problem of how to collect genuine and useful data about science classroom practices, and preserving the complex and holistic nature of teaching and learning. Additionally, we were looking for an instrument that would allow comparability and verifiability for teaching and research purposes. Given the multimodality of teaching and learning processes, we developed the multimodal narrative (MN), which describes what happens during a task and incorporates data such as examples of students’ work.

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Dissertação para obtencão do grau de Mestrado em Arte e Ciência do Vidro

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Dissertação apresentada para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Estudos Ingleses e Norte Americanos

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The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

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Machine learning provides tools for automated construction of predictive models in data intensive areas of engineering and science. The family of regularized kernel methods have in the recent years become one of the mainstream approaches to machine learning, due to a number of advantages the methods share. The approach provides theoretically well-founded solutions to the problems of under- and overfitting, allows learning from structured data, and has been empirically demonstrated to yield high predictive performance on a wide range of application domains. Historically, the problems of classification and regression have gained the majority of attention in the field. In this thesis we focus on another type of learning problem, that of learning to rank. In learning to rank, the aim is from a set of past observations to learn a ranking function that can order new objects according to how well they match some underlying criterion of goodness. As an important special case of the setting, we can recover the bipartite ranking problem, corresponding to maximizing the area under the ROC curve (AUC) in binary classification. Ranking applications appear in a large variety of settings, examples encountered in this thesis include document retrieval in web search, recommender systems, information extraction and automated parsing of natural language. We consider the pairwise approach to learning to rank, where ranking models are learned by minimizing the expected probability of ranking any two randomly drawn test examples incorrectly. The development of computationally efficient kernel methods, based on this approach, has in the past proven to be challenging. Moreover, it is not clear what techniques for estimating the predictive performance of learned models are the most reliable in the ranking setting, and how the techniques can be implemented efficiently. The contributions of this thesis are as follows. First, we develop RankRLS, a computationally efficient kernel method for learning to rank, that is based on minimizing a regularized pairwise least-squares loss. In addition to training methods, we introduce a variety of algorithms for tasks such as model selection, multi-output learning, and cross-validation, based on computational shortcuts from matrix algebra. Second, we improve the fastest known training method for the linear version of the RankSVM algorithm, which is one of the most well established methods for learning to rank. Third, we study the combination of the empirical kernel map and reduced set approximation, which allows the large-scale training of kernel machines using linear solvers, and propose computationally efficient solutions to cross-validation when using the approach. Next, we explore the problem of reliable cross-validation when using AUC as a performance criterion, through an extensive simulation study. We demonstrate that the proposed leave-pair-out cross-validation approach leads to more reliable performance estimation than commonly used alternative approaches. Finally, we present a case study on applying machine learning to information extraction from biomedical literature, which combines several of the approaches considered in the thesis. The thesis is divided into two parts. Part I provides the background for the research work and summarizes the most central results, Part II consists of the five original research articles that are the main contribution of this thesis.

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The focus of the present work was on 10- to 12-year-old elementary school students’ conceptual learning outcomes in science in two specific inquiry-learning environments, laboratory and simulation. The main aim was to examine if it would be more beneficial to combine than contrast simulation and laboratory activities in science teaching. It was argued that the status quo where laboratories and simulations are seen as alternative or competing methods in science teaching is hardly an optimal solution to promote students’ learning and understanding in various science domains. It was hypothesized that it would make more sense and be more productive to combine laboratories and simulations. Several explanations and examples were provided to back up the hypothesis. In order to test whether learning with the combination of laboratory and simulation activities can result in better conceptual understanding in science than learning with laboratory or simulation activities alone, two experiments were conducted in the domain of electricity. In these experiments students constructed and studied electrical circuits in three different learning environments: laboratory (real circuits), simulation (virtual circuits), and simulation-laboratory combination (real and virtual circuits were used simultaneously). In order to measure and compare how these environments affected students’ conceptual understanding of circuits, a subject knowledge assessment questionnaire was administered before and after the experimentation. The results of the experiments were presented in four empirical studies. Three of the studies focused on learning outcomes between the conditions and one on learning processes. Study I analyzed learning outcomes from experiment I. The aim of the study was to investigate if it would be more beneficial to combine simulation and laboratory activities than to use them separately in teaching the concepts of simple electricity. Matched-trios were created based on the pre-test results of 66 elementary school students and divided randomly into a laboratory (real circuits), simulation (virtual circuits) and simulation-laboratory combination (real and virtual circuits simultaneously) conditions. In each condition students had 90 minutes to construct and study various circuits. The results showed that studying electrical circuits in the simulation–laboratory combination environment improved students’ conceptual understanding more than studying circuits in simulation and laboratory environments alone. Although there were no statistical differences between simulation and laboratory environments, the learning effect was more pronounced in the simulation condition where the students made clear progress during the intervention, whereas in the laboratory condition students’ conceptual understanding remained at an elementary level after the intervention. Study II analyzed learning outcomes from experiment II. The aim of the study was to investigate if and how learning outcomes in simulation and simulation-laboratory combination environments are mediated by implicit (only procedural guidance) and explicit (more structure and guidance for the discovery process) instruction in the context of simple DC circuits. Matched-quartets were created based on the pre-test results of 50 elementary school students and divided randomly into a simulation implicit (SI), simulation explicit (SE), combination implicit (CI) and combination explicit (CE) conditions. The results showed that when the students were working with the simulation alone, they were able to gain significantly greater amount of subject knowledge when they received metacognitive support (explicit instruction; SE) for the discovery process than when they received only procedural guidance (implicit instruction: SI). However, this additional scaffolding was not enough to reach the level of the students in the combination environment (CI and CE). A surprising finding in Study II was that instructional support had a different effect in the combination environment than in the simulation environment. In the combination environment explicit instruction (CE) did not seem to elicit much additional gain for students’ understanding of electric circuits compared to implicit instruction (CI). Instead, explicit instruction slowed down the inquiry process substantially in the combination environment. Study III analyzed from video data learning processes of those 50 students that participated in experiment II (cf. Study II above). The focus was on three specific learning processes: cognitive conflicts, self-explanations, and analogical encodings. The aim of the study was to find out possible explanations for the success of the combination condition in Experiments I and II. The video data provided clear evidence about the benefits of studying with the real and virtual circuits simultaneously (the combination conditions). Mostly the representations complemented each other, that is, one representation helped students to interpret and understand the outcomes they received from the other representation. However, there were also instances in which analogical encoding took place, that is, situations in which the slightly discrepant results between the representations ‘forced’ students to focus on those features that could be generalised across the two representations. No statistical differences were found in the amount of experienced cognitive conflicts and self-explanations between simulation and combination conditions, though in self-explanations there was a nascent trend in favour of the combination. There was also a clear tendency suggesting that explicit guidance increased the amount of self-explanations. Overall, the amount of cognitive conflicts and self-explanations was very low. The aim of the Study IV was twofold: the main aim was to provide an aggregated overview of the learning outcomes of experiments I and II; the secondary aim was to explore the relationship between the learning environments and students’ prior domain knowledge (low and high) in the experiments. Aggregated results of experiments I & II showed that on average, 91% of the students in the combination environment scored above the average of the laboratory environment, and 76% of them scored also above the average of the simulation environment. Seventy percent of the students in the simulation environment scored above the average of the laboratory environment. The results further showed that overall students seemed to benefit from combining simulations and laboratories regardless of their level of prior knowledge, that is, students with either low or high prior knowledge who studied circuits in the combination environment outperformed their counterparts who studied in the laboratory or simulation environment alone. The effect seemed to be slightly bigger among the students with low prior knowledge. However, more detailed inspection of the results showed that there were considerable differences between the experiments regarding how students with low and high prior knowledge benefitted from the combination: in Experiment I, especially students with low prior knowledge benefitted from the combination as compared to those students that used only the simulation, whereas in Experiment II, only students with high prior knowledge seemed to benefit from the combination relative to the simulation group. Regarding the differences between simulation and laboratory groups, the benefits of using a simulation seemed to be slightly higher among students with high prior knowledge. The results of the four empirical studies support the hypothesis concerning the benefits of using simulation along with laboratory activities to promote students’ conceptual understanding of electricity. It can be concluded that when teaching students about electricity, the students can gain better understanding when they have an opportunity to use the simulation and the real circuits in parallel than if they have only the real circuits or only a computer simulation available, even when the use of the simulation is supported with the explicit instruction. The outcomes of the empirical studies can be considered as the first unambiguous evidence on the (additional) benefits of combining laboratory and simulation activities in science education as compared to learning with laboratories and simulations alone.

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This is a study of the implementation and impact of formative assessment strategies on the motivation and self-efficacy of secondary school mathematics students. An explanatory sequential mixed methods design was implemented where quantitative and qualitative data were collected and analyzed sequentially in 2 different phases. The first phase involved quantitative data from student questionnaires and the second phase involved qualitative data from individual student and teacher interviews. The findings of the study suggest that formative assessment is implemented in practice in diverse ways and is a process where the strategies are interconnected. Teachers experience difficulty in incorporating peer and self-assessment and perceive a need for exemplars. Key factors described as influencing implementation include teaching philosophies, interpretation of ministry documents, teachers’ experiences, leadership in administration and department, teacher collaboration, misconceptions of teachers, and student understanding of formative assessment. Findings suggest that overall, formative assessment positively impacts student motivation and self-efficacy, because feedback is provided which offers encouragement and recognition by highlighting the progress that has been made and what steps need to be taken to improve. However, students are impacted differently with some considerations including how students perceive mistakes and if they fear judgement. Additionally, the impact of formative assessment is influenced by the connection between self-efficacy and motivation, namely how well a student is doing is a source of both concepts.

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La thèse examine les liens entre la vision pluraliste de la science et l’éthique de la médecine tibétaine et les nouvelles pratiques en médecine occidentale, soit la longévité et la recherche sur la génétique amélioratrice. Elle cherche à cerner l’apport que la médecine tibétaine peut apporter aux recherches occidentales sur la longévité et la génétique humaine amélioratrice. Elle traite donc d’un enjeu social clé et du débat qui s’y rattache. La découverte et la description sont centrales à la méthodologie et informent l’analyse. Nous avons examiné dans un premier temps, les travaux de recherche sur la longévité reliée à la génétique amélioratrice (mémoire et muscles). Nous nous sommes penchés également sur les fondements de la médecine tibétaine en tant que système intégré. Pour ce faire, nous avons traité des notions telles que la santé, l’identité, la perfection et l’immortalité. Notre cadre conceptuel repose sur la théorie bouddhiste de l’interdépendance qui se caractérise par la formulation de catégories qui ensuite sont synthétisées dans l’essence; les deux niveaux d’interprétation de la théorie sont décrits en détail avant de passer à une comparaison avec la notion de complexité occidentale. La médecine tibétaine de fait présente un système où l’éthique et la science sont intégrées et se prête bien à une comparaison avec la vision pluraliste de la science à partir d’une perspective éthique/bioéthique. Les commentaires recueillis auprès des experts nous ont permis de cerner comment la science, l’éthique et l’amélioration de la longévité sont définies au sein des deux paradigmes de l’Est et de l’Ouest. Nos résultats montrent six points qui se dégagent au terme de cette recherche permettent de jeter un pont sur la vision pluraliste de ces paradigmes. Ceux-ci transcendent les points de vue doctrinaux individuels de religions ainsi que du monde scientifique occidental. Plus que tout, ils laissent entrevoir un cadre de références novatrices qui contribuera à la prise de décision à l’égard de questionnements bioéthiques.

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This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

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El auténtico protagonismo de los centros educativos tiene que dirigirse a ayudar a pensar a sus alumnos y a enseñarlos a aprender, es decir, el docente tiene que enseñar estrategias de aprendizaje y debe promover el esfuerzo del estudiante para facilitar la construcción de esquemas y el aprendizaje permanente. El profesor debe utilizar cualquier situación de aprendizaje para enseñar dichas estrategias de aprendizaje, incluso en las situaciones de evaluación; por lo tanto, en este trabajo se sugiere que en las evaluaciones de los alumnos y alumnas se tenga en cuenta la metacognición como factor fundamental en el aprendizaje y la enseñanza

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How can we analyze and understand affiliation networks? In this class, we will discuss properties of affiliation networks and we will investigate the use of Galois lattices for the exploration of structural patterns in bi-partite graphs. Optional : L.C. Freeman and D.R. White. Using Galois Lattices to Represent Network Data. Sociological Methodology, (23):127--146, (1993)