Página 1 dos resultados de 1811 itens digitais encontrados em 0.141 segundos

## Desafios e perspetivas do ensino da matemática no ensino superior online : um estudo de caso

Gomes, Estela Maria Martins Teixeira
Relevância na Pesquisa
55.8%

## O ensino de estatística e a busca do equilíbrio entre os aspectos determinísticos e aleatórios da realidade; The teaching of statistics and the search for the equilibrium between deterministic and random aspects of reality

Ara, Amilton Braio
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
45.67%

## An investigation into the teaching and learning of probability at senior cycle

Murphy, Conor
Fonte: University of Limerick Publicador: University of Limerick
Tipo: Master thesis (Research); ul_published_reviewed; none
ENG
Relevância na Pesquisa
55.57%
peer-reviewed; In Ireland at present, the National Council for Curriculum and Assessment is comprehensively overhauling the Second Level Mathematics curriculum. This reformed curriculum is known as Project Maths and is a response to concerns about how Irish students are taught and learn mathematics. These concerns are based around the achievement of Irish student’s in international studies (Close and Oldham 2005; Cosgrove, Shiel, Sofroniou, Zastrutzki and Shortt 2005; Perkins, Moran, Cosgrove and Shiel 2010; Oldham 2002, 2006) as well as domestic and international literature which, highlights the problems associated with the behaviourist methodology favoured by Irish teachers (Conway and Sloane 2006; English, O’Donoghue and Bajpai 1992; Lyons, Lynch, Close, Sheerin and Boland 2003; NCCA 2005). The aim of the study was to improve the teaching and learning of Probability through the development of a resource pack. probability was chosen as the focus of the intervention due to the author’s experiences in the classroom, international literature highlighting its pedagogical difficulties (Shaughnessy 1992; Fischbein, Nello and Marino 1991; Ahlgren and Garfield 1988; Hawkins and Kapadia 1984) and its lack of popularity among Irish Leaving Certificate students (Chief Examiner 2000...

## A formação estatistica e pedagogica do professor de matematica em comunidades de pratica; The formation pedagogy and statistic of the teacher of mathematics in communities of practice

Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
45.79%
Neste trabalho discute-se a aprendizagem-ensino da Estatística na formação do Professor de Matemática, ressaltando as práticas pedagógicas nela envolvidas. Para tanto, realizou-se uma pesquisa na qual foi utilizado um instrumento da História Oral, a "Narrativa Biográfica", para a recolha de dados. Tais narrativas foram obtidas de professores experientes que têm atuado no ensino de estatística, em cursos de formação de professores de matemática (Licenciatura em Matemática) em universidades paulistas. Como instrumento de análise, utilizou-se a "Teoria Social da Aprendizagem", de Wenger, sobre comunidade de prática, a partir da perspectiva histórico-cultural vygotskiana. Para compreender as práticas de formação pedagógicas presentes na formação estatísticas do professor de matemática, tanto alunos como professores foram considerados membros de uma mesma comunidade de prática, já que os sujeitos da pesquisa narraram suas práticas de formação tanto como alunos quanto como professores formadores. Para a análise esteve também presente pelo menos duas conjecturas: uma é "toda prática de formação estatística tem imbricada uma prática de formação pedagógica" e outra, surgida a partir dos estudos de Lee Shulman...

## Come away with me: Statistics learning through collaborative work

César, Margarida
Tipo: Conferência ou Objeto de Conferência
Relevância na Pesquisa
45.7%
At a more technological and literate society statistics play a relevant role in order to allow people becoming critical and active citizens. Statistics is part of our daily life. Most media refer to statistical knowledge showing graphs, tables or means in order to sound scientifically supported and to be able to manipulate people’s opinion about what is going on in the world. Choosing the information one reads, analysing it, processing data and deciding different ways of presenting them are some of the competencies that we need to develop and mobilize. School practices play an essential role in the access pupils will have, or not, to these forms of literacy so deeply needed in a complex, changing and multicultural society. Nowadays most international and Portuguese policy documents refer that school should provide the means to develop each pupil’s competencies, namely the ones related to communication and to participant citizenship. Collaborative work is also suggested in many of them, namely related to statistical contents. Piaget and Vygotsky (Tryphon and Vonèche, 1996) underlined the role of communication in knowledge appropriation and in pupils’ performances. Social interaction, namely peer ones, played a main role in the process and could be seen as a facilitator when used within an innovative and coherent didactic contract (César...

## Efficient Mixed-Norm Regularization: Algorithms and Safe Screening Methods

Wang, Jie; Liu, Jun; Ye, Jieping
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.6%
Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1q norm with q>1 is attractive in many applications of regression and classification in that it facilitates group sparsity in the model. The resulting optimization problem is, however, challenging to solve due to the inherent structure of the mixed-norm regularization. Existing work deals with special cases with q=1, 2, infinity, and they cannot be easily extended to the general case. In this paper, we propose an efficient algorithm based on the accelerated gradient method for solving the general l1q-regularized problem. One key building block of the proposed algorithm is the l1q-regularized Euclidean projection (EP_1q). Our theoretical analysis reveals the key properties of EP_1q and illustrates why EP_1q for the general q is significantly more challenging to solve than the special cases. Based on our theoretical analysis, we develop an efficient algorithm for EP_1q by solving two zero finding problems. To further improve the efficiency of solving large dimensional mixed-norm regularized problems, we propose a screening method which is able to quickly identify the inactive groups...

## Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing

Ramdas, Aaditya; Reddi, Sashank J.; Poczos, Barnabas; Singh, Aarti; Wasserman, Larry
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.63%
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common settings as mean difference alternatives (MDA), for testing differences only in first moments, and general difference alternatives (GDA), which is about testing for any difference in distributions. A large number of test statistics have been proposed for both these settings. This paper connects three classes of statistics - high dimensional variants of Hotelling's t-test, statistics based on Reproducing Kernel Hilbert Spaces, and energy statistics based on pairwise distances. We ask the question: how much statistical power do popular kernel and distance based tests for GDA have when the unknown distributions differ in their means, compared to specialized tests for MDA? We formally characterize the power of popular tests for GDA like the Maximum Mean Discrepancy with the Gaussian kernel (gMMD) and bandwidth-dependent variants of the Energy Distance with the Euclidean norm (eED) in the high-dimensional MDA regime. Some practically important properties include (a) eED and gMMD have asymptotically equal power; furthermore they enjoy a free lunch because...

## $\ell_p$ Testing and Learning of Discrete Distributions

Waggoner, Bo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.54%
The classic problems of testing uniformity of and learning a discrete distribution, given access to independent samples from it, are examined under general $\ell_p$ metrics. The intuitions and results often contrast with the classic $\ell_1$ case. For $p > 1$, we can learn and test with a number of samples that is independent of the support size of the distribution: With an $\ell_p$ tolerance $\epsilon$, $O(\max\{ \sqrt{1/\epsilon^q}, 1/\epsilon^2 \})$ samples suffice for testing uniformity and $O(\max\{ 1/\epsilon^q, 1/\epsilon^2\})$ samples suffice for learning, where $q=p/(p-1)$ is the conjugate of $p$. As this parallels the intuition that $O(\sqrt{n})$ and $O(n)$ samples suffice for the $\ell_1$ case, it seems that $1/\epsilon^q$ acts as an upper bound on the "apparent" support size. For some $\ell_p$ metrics, uniformity testing becomes easier over larger supports: a 6-sided die requires fewer trials to test for fairness than a 2-sided coin, and a card-shuffler requires fewer trials than the die. In fact, this inverse dependence on support size holds if and only if $p > \frac{4}{3}$. The uniformity testing algorithm simply thresholds the number of "collisions" or "coincidences" and has an optimal sample complexity up to constant factors for all $1 \leq p \leq 2$. Another algorithm gives order-optimal sample complexity for $\ell_{\infty}$ uniformity testing. Meanwhile...

## On the Robustness of Regularized Pairwise Learning Methods Based on Kernels

Christmann, Andreas; Zhou, Ding-Xuan
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.66%
Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is regularized minimization of the error entropy loss which has recently attracted quite some interest from the viewpoint of consistency and learning rates. This paper shows that such RPL methods have additionally good statistical robustness properties, if the loss function and the kernel are chosen appropriately. We treat two cases of particular interest: (i) a bounded and non-convex loss function and (ii) an unbounded convex loss function satisfying a certain Lipschitz type condition.; Comment: 36 pages, 1 figure

## Two-stage Sampled Learning Theory on Distributions

Szabo, Zoltan; Gretton, Arthur; Poczos, Barnabas; Sriperumbudur, Bharath
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.65%
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their generalization performance in specific learning tasks. Learning problems formulated on distributions have an inherent two-stage sampled difficulty: in practice only samples from sampled distributions are observable, and one has to build an estimate on similarities computed between sets of points. To the best of our knowledge, the only existing method with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step (which suffers from slow convergence issues in high dimensions), and the domain of the distributions to be compact Euclidean. In this paper, we provide theoretical guarantees for a remarkably simple algorithmic alternative to solve the distribution regression problem: embed the distributions to a reproducing kernel Hilbert space, and learn a ridge regressor from the embeddings to the outputs. Our main contribution is to prove the consistency of this technique in the two-stage sampled setting under mild conditions (on separable, topological domains endowed with kernels). For a given total number of observations...

## Fast and Flexible ADMM Algorithms for Trend Filtering

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.58%
This paper presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool. It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves the minimax optimal error rate, while other popular methods like smoothing splines and kernels do not. Standing in the way of a more widespread practical adoption, however, is a lack of scalable and numerically stable algorithms for fitting trend filtering estimates. This paper presents a highly efficient, specialized ADMM routine for trend filtering. Our algorithm is competitive with the specialized interior point methods that are currently in use, and yet is far more numerically robust. Furthermore, the proposed ADMM implementation is very simple, and importantly, it is flexible enough to extend to many interesting related problems, such as sparse trend filtering and isotonic trend filtering. Software for our method is freely available, in both the C and R languages.; Comment: 22 pages, 10 figures; published in Journal of Computational and Graphical Statistics, 2015

## M@th Desktop and MD Tools - Mathematics and Mathematica Made Easy for Students

Kainhofer, Reinhold; Simonovits, Reinhard V.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.68%
We present two add-ons for Mathematica for teaching mathematics to undergraduate and high school students. These two applications, M@th Desktop (MD) and M@th Desktop Tools (MDTools), include several palettes and notebooks covering almost every field. The underlying didactic concept is so-called "blended learning", in which these tools are meant to be used as a complement to the professor or teacher rather than as a replacement, which other e-learning applications do. They enable students to avoid the usual problem of computer-based learning, namely that too large an amount of time is wasted struggling with computer and program errors instead of actually learning the mathematical concepts. M@th Desktop Tools is palette-based and provides easily accessible and user-friendly templates for the most important functions in the fields of Analysis, Algebra, Linear Algebra and Statistics. M@th Desktop, in contrast, is a modern, interactive teaching and learning software package for mathematics classes. It is comprised of modules for Differentiation, Integration, and Statistics, and each module presents its topic with a combination of interactive notebooks and palettes. Both packages can be obtained from Deltasoft's homepage at http://www.deltasoft.at/ .; Comment: 13 pages...

## Distributed Clustering and Learning Over Networks

Zhao, Xiaochuan; Sayed, Ali H.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.54%
Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different clusters that pursue different objectives. Then, indiscriminate cooperation will lead to undesired results. In this work, we propose an adaptive clustering and learning scheme that allows agents to learn which neighbors they should cooperate with and which other neighbors they should ignore. In doing so, the resulting algorithm enables the agents to identify their clusters and to attain improved learning and estimation accuracy over networks. We carry out a detailed mean-square analysis and assess the error probabilities of Types I and II, i.e., false alarm and mis-detection, for the clustering mechanism. Among other results, we establish that these probabilities decay exponentially with the step-sizes so that the probability of correct clustering can be made arbitrarily close to one.; Comment: 47 pages, 6 figures

## Learning Theory for Distribution Regression

Szabo, Zoltan; Sriperumbudur, Bharath; Poczos, Barnabas; Gretton, Arthur
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.65%
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning or point estimation problems without analytical solution such as hyperparameter or entropy estimation. Despite the large number of available heuristics in the literature, the inherent two-stage sampled nature of the problem family makes the theoretical analysis quite challenging: in practice only samples from sampled distributions are observable, and the estimates have to rely on similarities computed between sets of points. To the best of our knowledge, the only existing technique with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step (which often performs poorly in practice), and the domain of the distributions to be compact Euclidean. In this paper, we study a simple, analytically computable, ridge regression based alternative to distribution regression: we embed the distributions to a reproducing kernel Hilbert space, and learn the regressor from the embeddings to the outputs. Our main contribution is to show that this scheme is consistent in the two-stage sampled setup under mild conditions (on separable topological domains enriched with kernels). Specifically...

## Missing Entries Matrix Approximation and Completion

Shabat, Gil; Shmueli, Yaniv; Averbuch, Amir
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.53%
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank approximations, similar algorithms appears recently in the literature under different names. In this work, we introduce new theorems for matrix approximation and show that these algorithms can be extended to handle different constraints such as nuclear norm, spectral norm, orthogonality constraints and more that are different than low rank approximations. As the algorithms can be viewed from an optimization point of view, we discuss their convergence to global solution for the convex case. We also discuss the optimal step size and show that it is fixed in each iteration. In addition, the derived matrix completion flow is robust and does not require any parameters. This matrix completion flow is applicable to different spectral minimizations and can be applied to physics, mathematics and electrical engineering problems such as data reconstruction of images and data coming from PDEs such as Helmholtz equation used for electromagnetic waves.

## Dimensionality Reduction and Learning on Networks

Balachandran, Prakash
Tipo: Dissertação
Relevância na Pesquisa
55.6%

Machine learning is a powerful branch of mathematics and statistics that allows the automation of tasks that would otherwise require humans a long time to perform. Two particular fields of machine learning that have been developing in the last two decades are dimensionality reduction and semi-supervised learning.

Dimensionality reduction is a powerful tool in the analysis of high dimensional data by reducing the number of variables under consideration while approximately preserving some quantity of interest (usually pairwise distances). Methods such as Principal Component Analysis (PCA) or Isometric Feature Mapping (ISOMAP) do this do this by embedding the data, equipped with a nonnegative, symmetric, similarity kernel or adjacency matrix into Euclidean space and finding a linear subspace or low dimensional submanifold which best fits the data, respectively.

When the data takes the form of network data, how to perform such dimensionality reduction intrinsically, without resorting to an embedding, that can be extended to the case of nonnegative, non-symmetric adjacency matrices remains an important open problem. In the first part of my dissertation, using current techniques in local spectral clustering to partition the network using a Markov process induced by the adjacency matrix...

## Enhancing teaching and learning through effective feedback and assessment

Kotecha, Meena
Fonte: London School of Economics and Political Science Research Publicador: London School of Economics and Political Science Research
Tipo: Conference or Workshop Item; NonPeerReviewed Formato: video/mp4
Relevância na Pesquisa
55.64%
This video presentation is about students’ perceptions of mathematics as well as statistics and their impact on students’ engagement, enthusiasm and academic self-efficacy. The author has discussed in her presentation the strategies she developed to improve learning and teaching in statistics and mathematics courses designed for non-specialist university students. She has successfully used these strategies in classes consisting of approximately 15 students as well as in lectures to large audiences of over 200 students. She argues that such an approach could enhance students’ perceptions of the subjects and their engagement in teaching rooms. She demonstrates how it can help create and maintain students’ interest in mathematics and statistics as well as promote student interaction in classes and lectures.

## Enhancing students’ engagement through effective feedback, assessment and engaging activities

Kotecha, Meena
Fonte: Maths, Stats & OR Network Publicador: Maths, Stats & OR Network
Tipo: Article; PeerReviewed Formato: application/pdf
Relevância na Pesquisa
45.66%
This paper is about students’ perceptions of mathematics and statistics and their impact on students’ engagement, enthusiasm and academic self-efficacy. I will discuss the strategies I developed to improve learning and teaching in statistics and mathematics service course classes, consisting of 15 students each, some of which also worked extremely well in my lectures to large audiences of about 350 students. I would argue that such an approach could not only enhance students’ perceptions of the subjects and their engagement in classes/lectures but also promote critical thinking, independent learning, reasoning and several transferable skills associated with university education. I will share the outcome of my teaching approach which not only fulfilled my initial expectations but far surpassed them. It increased students’ engagement and their enthusiasm which improved their performance in class activities and coursework. Furthermore, it improved students’ perceptions and attitudes to mathematics and statistics as reflected in their feedback. I have included some of their comments to highlight the impact a teaching approach can have on students.

## New patterns in learning and teaching mathematics and statistics

Kotecha, Meena
Tipo: Book Section; NonPeerReviewed Formato: application/pdf