Although research findings have emphasized the importance of students being engaged in dialogue and co-construction of science knowledge, implementing the teaching required to promote such engagement is challenging for teachers. Co-construction is crucial not only for students' understanding of science content but also for their familiarity with some of the attributes associated with the nature of science (NOS). Inquiry-based science classroom discourses could facilitate NOS familiarization processes by promoting creativity and collaboration in upper primary school. This article presents findings from a case study of how one teacher created and navigated opportunities for students’ co-construction of science stories in a grade 6 class (age 12) working on the topic “Substances around us”. To examine the classroom dialogue and the teacher’s enablement of students’ co-construction in class, observation data were gathered over seven weeks and analysed using principles indicative of classroom dialogue. Findings show that while opportunities for co-construction were created in science class through for example open-ended questions, the teacher’s use of IRE, complemented with boosted communication for evaluation of student answers, often hampered dialogue and co-construction of novel science stories regardless of how the teaching was organized.
The totally nonnegative Grassmannian Gr≥0 k,n is the set of k-dimensional subspaces V of Rn whose nonzero Plucker coordinates all have the same sign. In their study of scattering amplitudes in N = 4 supersym- metric Yang-Mills theory, Arkani-Hamed and Trnka (2013) considered the image (called an amplituhedron) of Gr≥0 k,n under a linear map Z : Rn → Rr, where k ≤ r and the r × r minors of Z are all positive. One reason they required this positivity condition is to ensure that the map Gr≥0 k,n → Grk,r induced by Z is well defined, i.e. it takes everynelement of Gr≥0 k,n to a k-dimensional subspace of Rr. Lam (2015) gave a sufficient condition for the induced map Gr≥0 k,n → Grk,r to be well defined, in which case he called the image a Grassmann polytope. (In the case k = 1, Grassmann polytopes are just polytopes, and amplituhedra are cyclic polytopes.) We give a necessary and sufficient condition for the induced map Gr≥0 k,n → Grk,r to be well defined, in terms of sign variation. Using previous work we presented at FPSAC 2015, we obtain an equivalent condition in terms of the r × r minors of Z (assuming Z has rank r).
We study representation stability in the sense of Church and Farb. We show that products of stabilizing Sn -representations fulfill certain recursive relations which can be described by a new class of difference operators.
We classify certain non-symmetric commutative association schemes. As an application, we determine all the primitive weakly distance-regular circulant digraphs.
In this paper we develop Algebraic Morse Theory for the case where a group acts on a free chain complex. Algebraic Morse Theory is an adaption of Discrete Morse Theory to free chain complexes.
In this note, we collect mostly known formulas and methods to compute the standard and virtual Poincaré polynomials of the configuration spaces of the plane $\mathbb{C} \setminus k$ with $k$ deleted points and compare the answers.
We study the transfinite version of Welter's Game, a combinatorial game played on a belt divided into squares numbered with general ordinal. In particular, we give a straight-forward solution for the transfinite version, based on those of the transfinite version of Nim and the original version of Welter's Game.
This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.
We propose a generalization of the graphical chip-firing model allowing for the redistribution dynamics to be governed by any invertible integer matrix while maintaining the long term critical, superstable, and energy minimizing behavior of the classical model.
The Varchenko determinant is the determinant of the bilinear form associated to a real hyperplane arrangement. We show that we can obtain the exact value of this determinant for certain hyperplane arrangements if we know the edges which are relevant.
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested set complexes as well as Bergman complexes.
We apply Srivastava's spectral sparsification technique to a vector balancing version of the Kadison-Singer problem. The result is a one-sided version of the conjectured solution.
In 1962 O. A. Gross proved that the last digits of the Fubini numbers (or surjective numbers) have a simple periodicity property. We extend this result to a wider class of combinatorial numbers coming from restricted set partitions.
We prove that a certain matrix, which is not image partition regular over R near zero, is image partition regular over N. This answers a question of De and Hindman.