831 resultados para Anomaly. Geometry non-Euclidean geometry. History of mathematics. Mathematics research
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Pós-graduação em Educação Matemática - IGCE
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Mode of access: Internet.
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This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.
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pt.1. Algebra.
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Mode of access: Internet.
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Caption title.
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Mode of access: Internet.
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Mode of access: Internet.
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Neural networks are statistical models and learning rules are estimators. In this paper a theory for measuring generalisation is developed by combining Bayesian decision theory with information geometry. The performance of an estimator is measured by the information divergence between the true distribution and the estimate, averaged over the Bayesian posterior. This unifies the majority of error measures currently in use. The optimal estimators also reveal some intricate interrelationships among information geometry, Banach spaces and sufficient statistics.
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In SNAP (Surface nanoscale axial photonics) resonators propagation of a slow whispering gallery mode along an optical fiber is controlled by nanoscale variation of the effective radius of the fiber [1]. Similar behavior can be realized in so - called nanobump microresonators in which the introduced variation of the effective radius is asymmetric, i.e. depends on the axial coordinate [2]. The possibilities of realization of such structures “on the fly” in an optical fiber by applying external electrostatic fields to it is discussed in this work. It is shown that local variations in effective radius of the fiber and in its refractive index caused by external electric fields can be large enough to observe SNAP structure - like behavior in an originally flat optical fiber. Theoretical estimations of the introduced refractive index and effective radius changes and results of finite element calculations are presented. Various effects are taken into account: electromechanical (piezoelectricity and electrostriction), electro-optical (Pockels and Kerr effects) and elasto-optical effect. Different initial fibre cross-sections are studied. The aspects of use of linear isotropic (such as silica) and non-linear anisotropic (such as lithium niobate) materials of the fiber are discussed. REFERENCES [1] M. Sumetsky, J. M. Fini, Opt. Exp. 19, 26470 (2011). [2] L. A. Kochkurov, M. Sumetsky, Opt. Lett. 40, 1430 (2015).
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The angle concept is a multifaceted concept having static and dynamic definitions. The static definition of the angle refers to “the space between two rays” or “the intersection of two rays at the same end point” (Mitchelmore & White, 1998), whereas the dynamic definition of the angle concept highlights that the size of angle is the amount of rotation in direction (Fyhn, 2006). Since both definitions represent two diverse situations and have unique limitations (Henderson & Taimina, 2005), students may hold misconceptions about the angle concept. In this regard, the aim of this research was to explore high achievers’ knowledge regarding the definition of the angle concept as well as to investigate their erroneous answers on the angle concept.
104 grade 6 students drawn from four well-established elementary schools of Yozgat, Turkey were participated in this research. All participants were selected via a purposive sampling method and their mathematics grades were 4 or 5 out of 5, and. Data were collected through four questions prepared by considering the learning competencies set out in the grade 6 curriculum in Turkey and the findings of previous studies whose purposes were to identify students’ misconceptions of the angle concept. The findings were analyzed by two researchers, and their inter-rater agreement was calculated as 0.91, or almost perfect. Thereafter, coding discrepancies were resolved, and consensus was established.
The angle concept is a multifaceted concept having static and dynamic definitions.The static definition of the angle refers to “the space between two rays” or“the intersection of two rays at the same end point” (Mitchelmore & White, 1998), whereas the dynamicdefinition of the angle concept highlights that the size of angle is the amountof rotation in direction (Fyhn, 2006). Since both definitionsrepresent two diverse situations and have unique limitations (Henderson & Taimina, 2005), students may holdmisconceptions about the angle concept. In this regard, the aim of thisresearch was to explore high achievers’ knowledge regarding the definition ofthe angle concept as well as to investigate their erroneous answers on theangle concept.
104grade 6 students drawn from four well-established elementary schools of Yozgat,Turkey were participated in this research. All participants were selected via a purposive sampling method and their mathematics grades were 4 or 5 out of 5,and. Data were collected through four questions prepared by considering the learning competencies set out in the grade 6 curriculum in Turkey and the findings of previous studies whose purposes were to identify students’ misconceptions of the angle concept. The findings were analyzed by two researchers, and their inter-rater agreement was calculated as 0.91, or almost perfect. Thereafter, coding discrepancies were resolved, and consensus was established.
In the first question, students were asked to answer a multiple choice questions consisting of two statics definitions and one dynamic definition of the angle concept. Only 38 of 104 students were able to recognize these three definitions. Likewise, Mitchelmore and White (1998) investigated that less than10% of grade 4 students knew the dynamic definition of the angle concept. Additionally,the purpose of the second question was to figure out how well students could recognize 0-degree angle. We found that 49 of 104 students were unable to recognize MXW as an angle. While 6 students indicated that the size of MXW is0, other 6 students revealed that the size of MXW is 360. Therefore, 12 of 104students correctly answered this questions. On the other hand, 28 of 104students recognized the MXW angle as 180-degree angle. This finding demonstrated that these students have difficulties in naming the angles.Moreover, the third question consisted of three concentric circles with center O and two radiuses of the outer circle, and the intersection of the radiuses with these circles were named. Then, students were asked to compare the size of AOB, GOD and EOF angles. Only 36 of 104 students answered correctly by indicating that all three angles are equal, whereas 68 of 104 students incorrectly responded this question by revealing AOB<GOD< EOF. These students erroneously thought the size of the angle is related to either the size of the arc marking the angle or the area between the arms of the angle and the arc marking angle. These two erroneous strategies for determining the size of angles have been found by a few studies (Clausen-May,2008; Devichi & Munier, 2013; Kim & Lee, 2014; Mithcelmore, 1998;Wilson & Adams, 1992). The last question, whose aim was to determine how well students can adapt theangle concept to real life, consisted of an observer and a barrier, and students were asked to color the hidden area behind the barrier. Only 2 of 104students correctly responded this question, whereas 19 of 104 students drew rays from the observer to both sides of the barrier, and colored the area covered by the rays, the observer and barrier. While 35 of 104 students just colored behind the barrier without using any strategies, 33 of 104 students constructed two perpendicular lines at the both end of the barrier, and colored behind the barrier. Similarly, Munier, Devinci and Merle (2008) found that this incorrect strategy was used by 27% of students.
Consequently, we found that although the participants in this study were high achievers, they still held several misconceptions on the angle concept and had difficulties in adapting the angle concept to real life.
Keywords: the angle concept;misconceptions; erroneous answers; high achievers
ReferencesClausen-May, T. (2008). AnotherAngle on Angles. Australian Primary Mathematics Classroom, 13(1),4–8.
Devichi, C., & Munier, V.(2013). About the concept of angle in elementary school: Misconceptions andteaching sequences. The Journal of Mathematical Behavior, 32(1),1–19. http://doi.org/10.1016/j.jmathb.2012.10.001
Fyhn, A. B. (2006). A climbinggirl’s reflections about angles. The Journal of Mathematical Behavior, 25(2),91–102. http://doi.org/10.1016/j.jmathb.2006.02.004
Henderson, D. W., & Taimina,D. (2005). Experiencing geometry: Euclidean and non-Euclidean with history(3rd ed.). New York, USA: Prentice Hall.
Kim, O.-K., & Lee, J. H.(2014). Representations of Angle and Lesson Organization in Korean and AmericanElementary Mathematics Curriculum Programs. KAERA Research Forum, 1(3),28–37.
Mitchelmore, M. C., & White,P. (1998). Development of angle concepts: A framework for research. MathematicsEducation Research Journal, 10(3), 4–27.
Mithcelmore, M. C. (1998). Youngstudents’ concepts of turning and angle. Cognition and Instruction, 16(3),265–284.
Munier, V., Devichi, C., &Merle, H. (2008). A Physical Situation as a Way to Teach Angle. TeachingChildren Mathematics</i>, 14(7), 402–407.
Wilson, P. S., & Adams, V.M. (1992). A Dynamic Way to Teach Angle and Angle Measure. ArithmeticTeacher, 39(5), 6–13.
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The CD209 gene family that encodes C-type lectins in primates includes CD209 (DC-SIGN), CD209L (L-SIGN) and CD209L2. Understanding the evolution of these genes can help understand the duplication events generating this family, the process leading to the repeated neck region and identify protein domains under selective pressure. We compiled sequences from 14 primates representing 40 million years of evolution and from three non-primate mammal species. Phylogenetic analyses used Bayesian inference, and nucleotide substitutional patterns were assessed by codon-based maximum likelihood. Analyses suggest that CD209 genes emerged from a first duplication event in the common ancestor of anthropoids, yielding CD209L2 and an ancestral CD209 gene, which, in turn, duplicated in the common Old World primate ancestor, giving rise to CD209L and CD209. K(A)/K(S) values averaged over the entire tree were 0.43 (CD209), 0.52 (CD209L) and 0.35 (CD209L2), consistent with overall signatures of purifying selection. We also assessed the Toll-like receptor (TLR) gene family, which shares with CD209 genes a common profile of evolutionary constraint. The general feature of purifying selection of CD209 genes, despite an apparent redundancy (gene absence and gene loss), may reflect the need to faithfully recognize a multiplicity of pathogen motifs, commensals and a number of self-antigens
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Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.
