Lesson study in Asia Pacific classrooms: local responses to a global movement

Japanese Lesson Study is a model for teacher professional learning that has recently attracted world attention particularly within the mathematics education community. It is a highly structured process of teacher collaboration, observation, reflection and practice. The world focus has been mainly due to the work of American researchers such as Stigler and Hiebert (Am Educ Winter:1–10, 1998; The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. Free Press, New York 1999), Lewis and Tsuchida (Am Educ Winter:14–17; 50–52, 1998) and Fernandez [J Teach Educ 53(5):395–405, 2002]. These researchers have documented Lesson Study from the perspective of their social, cultural and educational contexts. In order to develop a deeper understanding of Lesson Study in a post-modern global world, there is a need to seek views beyond those presented from an American perspective. This paper will provide further additional perspectives from an Australian state view and a Malaysian state district view and a university view. The aim is to develop an understanding of how the different contexts have influenced the structure and implementation of the Japanese Lesson Study model.     

Gender, technology and attitude towards mathematics: a comparative longitudinal study with Mexican students

In this paper the results of a comparative longitudinal study investigating changes in girls’ and boys’ attitudes towards mathematics, and self-confidence in mathematics are presented. A 5-point Likert scale, AMMEC, was used to measure attitudes towards mathematics (AM), computer-based mathematics (AMC), and self-confidence in mathematics (CM). A total of 430 students using technology for mathematics and 109 students not using it were monitored for 3 years. At the beginning of the study, the participants were aged about 13 years. The statistical analyses of the data showed few gender differences in the way students’ attitudes and self-confidence changed over the 3 years. Significant gender differences favouring boys were found in attitudes towards mathematics in grades 8 and 9 for the group using technology. For the group using technology, significantly more boys than girls got high scores in attitudes towards computer-based mathematics in grade 7. Significantly, more girls using technology than girls not using it got high scores in grade 8. The use of technology did not have a positive impact on students’ self-confidence. Regardless of whether they used computers or not, from grades 7 to 9, there was a decrease in the self-confidence in mathematics of both boys and girls. To enrich these results and detect possible gender differences in the way attitudes were constructed, 12 girls and 13 boys were interviewed at the end of the study. The analysis of the arguments they presented to explain and justify their attitudes towards mathematics, computer-based mathematics, and their self-confidence in working in mathematics provided evidence of important gender differences in the ways in which boys and girls construct their attitude, indicating how their constructions reflect the gender stereotypes within Mexican society.     

Self-learning K-means clustering: a global optimization approach

An appropriate distance is an essential ingredient in various real-world learning tasks. Distance metric learning proposes to study a metric, which is capable of reflecting the data configuration much better in comparison with the commonly used methods. We offer an algorithm for simultaneous learning the Mahalanobis like distance and K-means clustering aiming to incorporate data rescaling and clustering so that the data separability grows iteratively in the rescaled space with its sequential clustering. At each step of the algorithm execution, a global optimization problem is resolved in order to minimize the cluster distortions resting upon the current cluster configuration. The obtained weight matrix can also be used as a cluster validation characteristic. Namely, closeness of such matrices learned during a sample process can indicate the clusters readiness; i.e. estimates the true number of clusters. Numerical experiments performed on synthetic and on real datasets verify the high reliability of the proposed method.     

On global warming: Flow-based soft global constraints

In case a CSP is over-constrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then computing a minimum-weight flow in the extended graph to measure the violation. We present efficient propagation algorithms, based on different violation measures, achieving domain consistency for the alldifferent constraint, the global cardinality constraint, the regular constraint and the same constraint. This work was for a large part carried out while the author was at the Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands     

SPT: a stochastic tunneling algorithm for global optimization

A stochastic approach to solving unconstrained continuous-function global optimization problems is presented. It builds on the tunneling approach to deterministic optimization presented by Barhen and co-workers (Bahren and Protopopescu, in: State of the Art in Global Optimization, Kluwer, 1996; Barhen et al., Floudas and Pardalos (eds.), TRUST: a deterministic algorithm for global optimization, 1997) by combining a series of local descents with stochastic searches. The method uses a rejection-based stochastic procedure to locate new local minima descent regions and a fixed Lipschitz-like constant to reject unpromising regions in the search space, thereby increasing the efficiency of the tunneling process. The algorithm is easily implemented in low-dimensional problems and scales easily to large problems. It is less effective without further heuristics in these latter cases, however. Several improvements to the basic algorithm which make use of approximate estimates of the algorithms parameters for implementation in high-dimensional problems are also discussed. Benchmark results are presented, which show that the algorithm is competitive with the best previously reported global optimization techniques. A successful application of the approach to a large-scale seismology problem of substantial computational complexity using a low-dimensional approximation scheme is also reported.     

Uniformisation in dimension four: towards a conjecture of Iitaka

Let $X$ be a compact Kähler manifold whose universal cover is $\mathbb{C }^n$ . A conjecture of Iitaka claims that some finite étale cover of $X$ is a torus. We prove this conjecture in various cases in dimension four. We also show that in the projective case Iitaka’s conjecture is a consequence of the non-vanishing conjecture.     

Attitude towards mathematics: a bridge between beliefs and emotions

Recent research in the field of affect has highlighted the need to theoretically clarify constructs such as beliefs, emotions and attitudes, and to better investigate the relationships among them. As regards the definition of attitude, in a previous study we proposed a characterization of attitude towards mathematics grounded in students’ experiences, investigating how students express their own relationship with mathematics. The data collected suggest a three-dimensional model of attitude towards mathematics that includes students’ emotional disposition, their vision of mathematics, and their perceived competence. In this paper, we discuss the relationship between beliefs and emotions, investigating the interplay among the three dimensions in the proposed model of attitude, as emerging in the students’ essays.     

An experimental study towards micro-mechanical modeling of fiber-reinforced aerogels

Fiber-reinforced aerogels are a class of reinforced aerogels characterized by very low thermal conductivity, hydrophobicity and most importantly load bearing capability. In this work, an experimental study describing the damage in these fiber-reinforced aerogels through various uniaxial compression tests is presented. While understanding the damage evolution at the micro-scale, we come across three probable sources contributing towards the damage evolution. They are: (a) matrix cracks, (b) debonding of particles due to fiber sliding, and (c) breakage of fibers. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zooming from global to local: a multiscale RBF approach

Because physical phenomena on Earth’s surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and finer scales. It also makes sense eventually to seek fine scale features locally, rather than globally. In the present work, we start with a global multiscale radial basis function (RBF) approximation, based on a sequence of point sets with decreasing mesh norm, and a sequence of (spherical) radial basis functions with proportionally decreasing scale centered at the points. We then prove that we can “zoom in” on a region of particular interest, by carrying out further stages of multiscale refinement on a local region. The proof combines multiscale techniques for the sphere from Le Gia, Sloan and Wendland, SIAM J. Numer. Anal. 48 (2010) and Applied Comp. Harm. Anal. 32 (2012), with those for a bounded region in ? ^d from Wendland, Numer. Math. 116 (2010). The zooming in process can be continued indefinitely, since the condition numbers of matrices at the different scales remain bounded. A numerical example illustrates the process.     

Meta-data envelopment analysis: Finding a direction towards marginal profit maximization

This paper discusses a new meta-DEA approach to solve the problem of choosing direction vectors when estimating the directional distance function. The proposed model emphasizes finding the “direction” for productivity improvement rather than estimating the “score” of efficiency; focusing on “planning” over “evaluation”. In fact, the direction towards marginal profit maximization implies a step-by-step improvement and “wait-and-see” decision process, which is more consistent with the practical decision-making process. An empirical study of U.S. coal-fired power plants operating in 2011 validates the proposed model. The results show that the efficiency measure using the proposed direction is consistent with all other indices with the exception of the direction towards the profit-maximized benchmark. We conclude that the marginal profit maximization is a useful guide for determining direction in the directional distance function.     

Simple linkage: Analysis of a threshold-accepting global optimization method

In a recent paper the authors introduced an infinite class of global optimization algorithms based upon random sampling from the feasible region and local searches started from selected sample points, based upon an acceptance/rejection criterion. All of the algorithms of that class possess strong theoretical properties.Here we analyze a member of that family, which, although being significantly simpler to implement and more efficient than the well known Multi-Level Single-Linkage algorithm, enjoys the same theoretical properties. It is shown here that, with very high probability, our method is able to discover from which points Multi-Level Single-Linkage will decide to start local search.     

On a global analytic Positivstellensatz

We consider several modified versions of the Positivstellensatz for global analytic functions that involve infinite sums of squares and/or positive semidefinite analytic functions. We obtain a general local-global criterion which localizes the obstruction to have such a global result. This criterion allows us to get completely satisfactory results for analytic curves, normal analytic surfaces and real coherent analytic sets whose connected components are all compact.     

Low dimensional simplex evolution: a new heuristic for global optimization

This paper presents a new heuristic for global optimization named low dimensional simplex evolution (LDSE). It is a hybrid evolutionary algorithm. It generates new individuals following the Nelder-Mead algorithm and the individuals survive by the rule of natural selection. However, the simplices therein are real-time constructed and low dimensional. The simplex operators are applied selectively and conditionally. Every individual is updated in a framework of try-try-test. The proposed algorithm is very easy to use. Its efficiency has been studied with an extensive testbed of 50 test problems from the reference (J Glob Optim 31:635–672, 2005). Numerical results show that LDSE outperforms an improved version of differential evolution (DE) considerably with respect to the convergence speed and reliability.     

The simplex method as a global optimizer: A c-programming perspective

In this paper we give a brief account of the important role that the conventional simplex method of linear programming can play in global optimization, focusing on its collaboration with composite concave programming techniques. In particular, we demonstrate how rich and powerful the c-programming format is in cases where its parametric problem is a standard linear programming problem.