The educational situation in Utopia: Why what is, is

In this response to Molly Ware’s review of our 2013 book, John Dewey and Education Outdoors, we extend her suggestion that complexity be regarded as an important, generative force in education reform. Drawing on Dewey’s 1933 Utopian Schools speech, we discuss the “level deeper” that Dewey sought as he criticized the method/subject mater dichotomy, which he saw as an artifact of social class carried forward in the form of a curricular debate rather than a natural source of tension that would be productive to democratic education. Dewey radically argued that learning itself contained similar anti-democratic potential. Eschewing the false child versus curriculum dichotomy, Dewey believed complexity as a catalyst for educational action would be achieved by engaging children in historically formed occupations, harnessing the forces that drive technological and cultural evolution in order to spur interest, effort, and the formation of social attitudes among students. Following Ware, we suggest that reformers should seek to understand at a lever deeper the many sources of complexity they encounter as they both challenge and honor what is

Application of the Parallel Dichotomy Algorithm for solving Toeplitz tridiagonal systems of linear equations with one right-hand side

Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we propose a parallel procedure for solving tridiagonal systems of equations with Toeplitz matrices. Taking the structure of the Toeplitz matrices, we may substantially reduce the number of the "preliminary calculations" of the Dichotomy Algorithm, which makes it possible to effectively solve a series as well as a single system of equations. On the example of solving of elliptic equations by the Separation Variable Method, we show that the computation accuracy is comparable with the sequential version of the Thomas method, and the dependence of the speedup on the number of processors is almost linear. The proposed modification is aimed at parallel realization of a broad class of numerical methods including the inversion of Toeplitz and quasi-Toeplitz tridiagonal matrices.Comment: New tests have been adde

Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary

Let $M$ be an $m$-dimensional differentiable manifold with a nontrivial circle action {\mathcal S}= {\lbrace S_t \rbrace}_{t \in\RR}, S_{t+1}=S_t, preserving a smooth volume $\mu$. For any Liouville number \a we construct a sequence of area-preserving diffeomorphisms $H_n$ such that the sequence H_n\circ S_\a\circ H_n^{-1} converges to a smooth weak mixing diffeomorphism of $M$. The method is a quantitative version of the approximation by conjugations construction introduced in \cite{AK}. For $m=2$ and $M$ equal to the unit disc \DD^2=\{x^2+y^2\leq 1\} or the closed annulus \AAA=\TT\times [0,1] this result proves the following dichotomy: \a \in \RR \setminus\QQ is Diophantine if and only if there is no ergodic diffeomorphism of $M$ whose rotation number on the boundary equals $\alpha$ (on at least one of the boundaries in the case of \AAA). One part of the dichotomy follows from our constructions, the other is an unpublished result of Michael Herman asserting that if \a is Diophantine, then any area preserving diffeomorphism with rotation number \a on the boundary (on at least one of the boundaries in the case of \AAA) displays smooth invariant curves arbitrarily close to the boundary which clearly precludes ergodicity or even topological transitivity.Comment: To appear in annales de l'EN

Maximising the potential of ICT to provide authentic summative assessment opportunities

This paper reports on elements of a study that was conducted in Western Australia to explore the potential of various forms of digitally based external assessments for senior secondary school courses. One problem that needed addressing was how to provide students with authentic assessment opportunities, particularly in subjects in which performance is an integral component. Traditionally, assessment in many of these subjects was by way of a three-hour paper examination. This established a dichotomy for teachers in which the pedagogy of the subject was very different from the method of assessment. In wanting to maximise their student’s potential for success, many teachers taught to the examination, consequently sacrificing a practical performance approach to the subject for a more theoretical form of delivery