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1.
Gail Tang Houssein El Turkey Emily Cilli-Turner Milos Savic Gulden Karakok David Plaxco 《International Journal of Mathematical Education in Science & Technology》2017,48(8):S4-S15
ABSTRACTAlthough many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity. In this paper, through aligning some characteristics of inquiry put forth by Cook, Murphy and Fukawa-Connelly with Gutiérrez's dimensions of equity, we theoretically explore the ways in which active learning teaching practices that focus on inquiry could support equity in the classroom. 相似文献
2.
Some researchers advocate a statistical modeling approach to inference that draws on students’ intuitions about factors influencing phenomena and that requires students to build models. Such a modeling approach to inference became possible with the creation of TinkerPlots Sampler technology. However, little is known about what statistical modeling reasoning students need to acquire. Drawing and building on previous research, this study aims to uncover the statistical modeling reasoning students need to develop. A design-based research methodology employing Model Eliciting Activities was used. The focus of this paper is on two 11-year-old students as they engaged with a bag weight task using TinkerPlots. Findings indicate that these students seem to be developing the ability to build models, investigate and posit factors, consider variation and make decisions based on simulated data. From the analysis an initial statistical modeling framework is proposed. Implications of the findings are discussed. 相似文献
3.
This paper sets the scene for a special issue of ZDM—The International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. 相似文献
4.
Isaac Dyner 《The Journal of the Operational Research Society》2000,51(2):136-144
The energy field has been dominated by ‘hard’ modelling approaches advocated by researchers from engineering and economics disciplines. The recent trend towards a more liberalised environment moves away from central planning to market-based resource allocation, leading to the creation and use of strategic tools, with much ‘softer’ specifications, in the ‘systems-thinking’ tradition. This paper presents the use of system dynamics in a generalised way, to provide a platform for integrated energy analysis. Issues of modularity and policy evolution are important in the design of the modelling platform to facilitate its use, and reuse. Hence the concept of a platform, rather than a model, has to be implemented in a coherent way if it is to provide sustained value for ongoing support to both government policy and corporate strategy. 相似文献
5.
Queueing theory continues to be one of the most researched areas of operational research, and has generated numerous review papers over the years. The phrase ‘queue modelling’ is used in the title to indicate a more practical emphasis. This paper uses work taken predominantly from the last 50 years of pages of the Operational Research Quarterly and the Journal of the Operational Research Society to offer a commentary on attempts of operational researchers to tackle real queueing problems, and on research foci past and future. A new discipline of ‘queue modelling’ is proposed, drawing upon the combined strengths of analytic and simulation approaches with the responsibility to derive meaningful insights for managers. 相似文献
6.
Although there have been repeated attempts to define the concept of an Archimedean algebra for individual classes of residuated lattices, there is no all-purpose definition that suits the general case. We suggest as a possible candidate the notion of a normal-valued and e-cyclic residuated lattice that has the zero radical compact property—namely, a normal-valued and e-cyclic residuated lattice in which every principal convex subuniverse has a trivial radical (understood as the intersection of all its maximal convex subuniverses). We characterize the Archimedean members in the variety of e-cyclic residuated lattices, as well as in various special cases of interest. A theorem to the effect that each Archimedean and prelinear GBL-algebra is commutative, subsuming as corollaries several analogous results from the recent literature, is grist to the mill of our proposal’s adequacy. Finally, we revisit the concept of a hyper-Archimedean residuated lattice, another notion with which researchers have engaged from disparate angles, and investigate some of its properties. 相似文献
7.
8.
《Mathematical Thinking and Learning》2013,15(2):93-111
Videotaped lessons of 5th graders on equivalent fractions from 7 American and 6 Japanese classrooms were analyzed in terms of a recurrent pattern in public discourse among a teacher and students. This pattern—called inquiry, response, feedback—occurs when a teacher initiates discourse (mostly with an inquiry), a student or students respond (often with an answer to the teacher inquiry), and the teacher provides feedback to the student's response. We found2 approaches to the teaching-learning of the criteria for evaluating mathematical arguments. In the Japanese classroom, students were encouraged to offer their own argument to the whole class and evaluate arguments proposed by other students. They seldom were given direct evaluation by their teacher. In contrast, American teachers often gave individual elaboration as well as direct evaluation to the student's responses, and some of the teachers offered their own opinions about mathematics, about valid ways of argumentation, or about both. The Japanese approach would help students acquire evaluative criteria indirectly through participating in mathematical discourse, whereas the American approach would help students learn modes of arguments through direct instruction. 相似文献
9.
Ulrich Bauer Axel Munk Hannes Sieling Max Wardetzky 《Foundations of Computational Mathematics》2017,17(1):1-33
We investigate the problem of estimating the number of modes (i.e., local maxima)—a well-known question in statistical inference—and we show how to do so without presmoothing the data. To this end, we modify the ideas of persistence barcodes by first relating persistence values in dimension one to distances (with respect to the supremum norm) to the sets of functions with a given number of modes, and subsequently working with norms different from the supremum norm. As a particular case, we investigate the Kolmogorov norm. We argue that this modification has certain statistical advantages. We offer confidence bands for the attendant Kolmogorov signatures, thereby allowing for the selection of relevant signatures with a statistically controllable error. As a result of independent interest, we show that taut strings minimize the number of critical points for a very general class of functions. We illustrate our results by several numerical examples. 相似文献
10.
S. K. Bar-Lev D. Bshouty F. A. van der Duyn Schouten 《Mathematical Methods of Statistics》2016,25(2):79-98
A nonhomogeneous Poisson process (NHPP) plays an important role in a variety of applications as reliability of repairable systems, software reliability and actuarial studies. An NHPP is characterized by its intensity function m(t), which provides information on the time-dependent nature of the reliability of the system. Various intensity functions, which describe different behavior (from reliability decay to reliability growth along with monotonicity, convexity or concavity), have been suggested for NHPP’s for modeling repairable systems. Perhaps one of the most frequently utilized NHPP is the power lawprocess (PLP) in which m(t) is a power function of t. Inthis studywe present a general method for constructing new intensity functions for NHPP’s yielding new classes of NHPP’s. This method utilizes certain operators L n , n ∈ N0, acting on some suitable functions L 0 = f (termed base functions). We call these classesOBIF’s (operator-based intensity functions). These classes are represented in terms of three parameters of which one is an indexing parameter n ∈ N0 and two others are scale and shape parameters. The fact that n ∈ N0 is also a parameter provides a flexibility in the choice of the appropriate statistical model for NHPP’s data. In particular, we consider the exponential operator acting on the PLP intensity function f and realize that L n ’s, n ≥ 2, inherit properties similar to those of L 1 (convexity and concavity) and thus are suitable for modelling bathtub data. We also consider a more comprehensive treatment of OBIF classes where both, the operator and base functions, are general. All of the introduced operators are demonstrated with illustrative examples. 相似文献
11.
Let G be a compact Lie group. In 1960, P A Smith asked the following question: “Is it true that for any smooth action of G on a homotopy sphere with exactly two fixed points, the tangent G-modules at these two points are isomorphic?” A result due to Atiyah and Bott proves that the answer is ‘yes’ for ? p and it is also known to be the same for connected Lie groups. In this work, we prove that two linear torus actions on S n which are c-cobordant (cobordism in which inclusion of each boundary component induces isomorphisms in ?-cohomology) must be linearly equivalent. As a corollary, for connected case, we prove a variant of Smith’s question. 相似文献
12.
Thomas R. Koballa Jr Michael J. Dias Jennifer Lance Atkinson 《School science and mathematics》2009,109(7):403-414
Inquiry‐focused professional development and conceptions of inquiry held by eight professional development leaders were investigated within the context of a state science teacher conference. The prominent session format involved session leaders modeling classroom experiences. In all sessions, classroom inquiry was portrayed as a teacher‐guided activity with the primary goal being to increase motivation for engaging students in classroom inquiry. The leaders’ conceptualized inquiry primarily as a teaching approach with various goals, characteristics, and potential barriers. The findings of this study provide evidence of how inquiry, a prominent feature of science education reform, was portrayed in sessions at a conference sponsored by a state affiliate of the National Science Teachers Association and thought about by persons who led these sessions. The findings have implications for teacher learning from conference‐based professional development and its potential influence on science teacher thinking and practice. 相似文献
13.
J Desrosiers N Mladenović D Villeneuve 《The Journal of the Operational Research Society》2005,56(1):60-66
In some schools and universities, students must sometimes be divided into several teams in such a way that each team provides a good representation of the classroom population. In this paper, two different ways of measuring the balance among teams are proposed: min-sum and min-max objective functions. For the first function and the L1-norm used in the space of attributes, an exact solution method based on a set partitioning formulation and on the enumeration of all possible team patterns is presented. For the second objective function, a set partitioning formulation is also considered, but as an approximation. In order to solve large problem instances, we have also developed metaheuristics based on variable neighbourhood search. Models and methods are tested on data from an MBA programme. 相似文献
14.
ABSTRACTThis research is a secondary analysis with Korean students’ data collected in the TIMSS 2015 to describe the moderation effects of instructional practices on the relationships between students’ emotional dispositions toward mathematics and mathematics achievement. From the TIMSS 2015 database, we collected mathematics achievement scores, a student-level contextual scale for students’ emotional disposition, and teacher-level contextual scales representing teachers’ instructional practices. We applied hierarchical linear modelling to construct multilevel models. The findings showed that the achievement gap between emotional dispositions – like and dislike – became smaller when teachers more frequently implemented certain instructional practices like asking students to complete challenging exercises, decide their own problem-solving procedures, and express their ideas in class. Students who disliked mathematics were likely to have higher scores as their teachers implemented each of those practices more frequently. Findings provide important implications to teachers regarding: It is important to encourage students to reason through instructional practices like asking them to decide their own problem-solving procedures and to solve challenging problems. 相似文献
15.
In a model of school choice, we allow school priorities to be weak and study the preference revelation game induced by the immediate acceptance (IA) rule (also known as the Boston rule), or the IA game. When school priorities can be weak and matches probabilistic, three stability notions—ex post stability, ex ante stability, and strong ex ante stability—and two ordinal equilibrium notions—sd equilibrium and strong sd equilibrium—become available (“sd” stands for stochastic dominance). We show that for no combination of stability and equilibrium notions does the set of stable matches coincide with the set of equilibrium matches of the IA game. This stands in contrast with the existing result that the two sets are equal when priorities are strict. We also show that in the presence of weak priorities, the transition from the IA rule to the deferred acceptance rule may, in fact, harm some students. 相似文献
16.
P. V. Chernikov 《Siberian Mathematical Journal》2007,48(1):189-190
We establish that condition (Γ) on brick decomposition is indecomposable. This answers K. Borsuk’s question [1]. We prove that there exist metric spaces X and Y and a point (a, b) ∈ X × Y such that (a, b) is an r-point of the product X × Y; moreover, a is not an r-point of X. This answers A. Kosinski’s question [2]. 相似文献
17.
Adrian Dumitrescu 《Periodica Mathematica Hungarica》2008,57(2):165-176
A set of points in the plane is said to be in general position if no three of them are collinear and no four of them are cocircular. If a point set determines only distinct vectors, it is called parallelogram free. We show that there exist n-element point sets in the plane in general position, and parallelogram free, that determine only O(n 2/√log n) distinct distances. This answers a question of Erd?s, Hickerson and Pach. We then revisit an old problem of Erd?s: given any n points in the plane (or in d dimensions), how many of them can one select so that the distances which are determined are all distinct? — and provide (make explicit) some new bounds in one and two dimensions. Other related distance problems are also discussed. 相似文献
18.
Although some of the earliest Estimation of Distribution Algorithms (EDAs) utilized bivariate marginal distribution models, up to now, all discrete bivariate EDAs had one serious limitation: they were constrained to exploiting only a limited O(d) subset out of all possible \(O(d^{2})\) bivariate dependencies. As a first we present a family of discrete bivariate EDAs that can learn and exploit all \(O(d^{2})\) dependencies between variables, and yet have the same run-time complexity as their more limited counterparts. This family of algorithms, which we label DICE (DIscrete Correlated Estimation of distribution algorithms), is rigorously based on sound statistical principles, and particularly on a modelling technique from statistical physics: dichotomised multivariate Gaussian distributions. Initially (Lane et al. in European Conference on the Applications of Evolutionary Computation, Springer, 1999), DICE was trialled on a suite of combinatorial optimization problems over binary search spaces. Our proposed dichotomised Gaussian (DG) model in DICE significantly outperformed existing discrete bivariate EDAs; crucially, the performance gap increasingly widened as dimensionality of the problems increased. In this comprehensive treatment, we generalise DICE by successfully extending it to multary search spaces that also allow for categorical variables. Because correlation is not wholly meaningful for categorical variables, interactions between such variables cannot be fully modelled by correlation-based approaches such as in the original formulation of DICE. Therefore, here we extend our original DG model to deal with such situations. We test DICE on a challenging test suite of combinatorial optimization problems, which are defined mostly on multary search spaces. While the two versions of DICE outperform each other on different problem instances, they both outperform all the state-of-the-art bivariate EDAs on almost all of the problem instances. This further illustrates that these innovative DICE methods constitute a significant step change in the domain of discrete bivariate EDAs. 相似文献
19.
Let Γg,b denote the orientation-preserving mapping class group of a closed orientable surface of genus g with b punctures. For a group G let Φf(G) denote the intersection of all maximal subgroups of finite index in G. Motivated by a question of Ivanov as to whether Φf(G) is nilpotent when G is a finitely generated subgroup of Γg,b, in this paper we compute Φf(G) for certain subgroups of Γg,b. In particular, we answer Ivanov’s question in the affirmative for these subgroups of Γg,b. 相似文献
20.
In this note, a new algorithm is presented for finding a zero of difference of two maximal monotone operators T and S, i.e., T — S in finite dimensional real Hilbert space H in which operator S has local boundedness property. This condition is weaker than Moudafi’s condition on operator S in [13]. Moreover, applying some conditions on inertia term in new algorithm, one can improve speed of convergence of sequence. 相似文献