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Unplugged to Plugged: An Introduction to Coding for Elementary School Children
No full textThis course introduced 4th and 5th graders to coding concepts like sequencing, loops, and decomposition through an unplugged-to-plugged learning sequence. Over four after-school learning sessions, students explored programming first through their bodies (i.e., unplugged), then in the block-based programming environment, Scratch (i.e., plugged). The goal was for learners to transition from concrete forms of programming to an abstract understanding needed for block-based programming. To achieve this goal, the plugged activities were intentionally designed around the concept of concreteness fading, where the unplugged programming challenge mirrored the plugged Scratch environment, allowing students to move from a concrete to more abstract understanding of computer science. The activities in the course drew from ready-to-use materials for computer science education (e.g., Code.org) as well as free, block-based coding websites (e.g., Scratch)
Scratch Encore: Creating and Sustaining Culturally Responsive Computer Science Education
No full textScratch Encore (Canon Lab, n.d.) is a culturally relevant, student-centered, 14 module, computer science curriculum for 4th to 8th-grade learners that introduces foundational computing topics using the Scratch environment. It employs three key design goals: (a) supporting teachers, (b) supporting learners, and (c) using culturally responsive practices to address long standing inequities in computing. The curriculum offers equitable and effective learning experiences for students who have historically not had equal opportunities to fully participate in computing while providing a wide array of supports for educators who may be inexperienced with Scratch and/or programming. This article features a high-level overview of Scratch Encore and the first 6 modules in greater detail to help teachers understand the content and pacing of the curriculum
‘Sure why would they need Irish?’: Scoil an tSeachtar Laoch, Ballymun, and working-class decolonisation, c.1970-73
No full textThis article examines the struggle carried out by working-class Irish-language activists in Ballymun to found a gaelscoil (Irish-medium school) in the early 1970s. The article is based on archival research and interviews with two key participants involved in the campaign for Scoil an tSeachtar Laoch, Éilís Uí Langáin and Colm Ó Torna. The campaign to establish the school is viewed through the lenses of class and decolonisation. Firstly, the long-term socio-economic and political contexts to the campaign are outlined. Secondly, the social base and the pre-existing networks and ideology which allowed the campaign to develop are explored. Following this, the emergence of the campaign and its politics are examined. Finally, the lasting impact of the struggle for the school both locally and nationally is discussed. The conclusion reached is one that is of the utmost importance for Irish language, gaelscoil and decolonial activists, namely that it will be difficult to replicate the success of Ballymun again today in the neoliberal context because the material basis in terms of secure housing and a tight-knit urban community does not exist. At a time when there has been much talk in Irish revivalist circles about promoting Irish in Dublin with the launch of the Baile Átha Cliath le Gaeilge (Dublin For Irish) scheme, the history of Ballymun and Scoil an tSeachtar Laoch demonstrates how a secure home is the lynchpin on which real communal progress with regard the Irish language must be based. It is therefore necessary for those who wish to see the Irish language flourish in the city to learn the lessons of history and improve, first and foremost, the day-to-day lives of ordinary Dubliners by becoming active on the burning question of housing
Godsil-McKay switchings for gain graphs
No full textWe introduce a switching operation, inspired by the Godsil-McKay switching, in order to obtain pairs of -cospectral gain graphs, that are gain graphs cospectral with respect to every representation of the gain group . For instance, for two signed graphs, this notion of cospectrality is equivalent to the cospectrality of their signed adjacency matrices together with the cospectrality of their underlying graphs. Moreover, we introduce another more flexible switching in order to obtain pairs of gain graphs cospectral with respect to some fixed unitary representation. Many existing notions of spectrum for graphs and gain graphs are indeed special cases of these spectra associated with particular representations, therefore our construction recovers the classical Godsil-McKay switching and the Godsil-McKay switching for signed and complex unit gain graphs. As in the classical case, not all gain graphs are suitable for these switchings: we analyze the relationships between the properties that make the graph suitable for the one or the other switching. Finally, we apply our construction in order to define a Godsil-McKay switching for the right spectrum of quaternion unit gain graphs
Schur stability of matrix segment via bialternate product
No full textIn this study, the problem of robust Schur stability of dimensional matrix segments by using the bialternate product of matrices is considered. It is shown that the problem can be reduced to the existence of negative eigenvalues of two of three specially constructed matrices and the existence of eigenvalues belonging to the interval of the third matrix. A necessary and sufficient condition is given for the convex combinations of two stable matrices with rank one difference to be robust Schur stable. It is shown that the robust stability of the convex hull of a finite number of matrices, where the difference between any two matrices has a rank of 1, is equivalent to the robust stability of the segments formed by these matrices. Examples of applying the obtained results are given
Construction of a solution to the rank 2 Horn problem
No full textGiven three sets of real eigenvalues satisfying the trace equality and the Horn inequalities, we know that there are real symmetric matrices and so that has the first set of eigenvalues, has the second set of eigenvalues, and has the last set of eigenvalues. Under the condition that is a rank 2 matrix, we give a construction for the matrices and . This construction is based on performing two orthogonal rank 1 updates on . We end with a discussion of the relationship between this rank 2 Horn problem and the following similar problem: given a set of real eigenvalues, a set of real eigenvalues, and a set of real eigenvalues satisfying certain conditions, find an real symmetric matrix such that the top left principal submatrix has the first set of eigenvalues, the bottom right principal submatrix has the second set of eigenvalues, and the full matrix has the last set of eigenvalues
On solutions of matrix equation over a Bezout domain
No full textLet be the set of matrices over a Bezout domain with identity and let be the zero matrix. Further, let be an ideal generated by the -th order minors of the matrix In this article, we investigate a structure of solutions of a matrix equation , where and are known matrices and is unknown matrix over . It is known that matrix equation is solvable over a Bezout domain if and only if and for all where On the other hand, is solvable over if and only if matrices and are right-equivalent, that is, the Hermitian normal forms of these matrices coincide. In this article, we give alternative necessary and sufficient conditions for the solvability of equation over a Bezout domain If a solution of this equation exists, we also give an algorithm for its construction. We prove also that the matrix equation over has a symmetric solution if and only if has a solution over and the matrix is symmetric. If symmetric solution exists, we propose the method for its construction
Semirings in which the permanent of invertible matrices is multiplicative
No full textWe show that, if holds for all elements with additive inverses in a commutative semiring , then the function of permanent is multiplicative on the matrices with multiplicative inverses over
GLT sequences and normal matrices
No full textThe theory of generalized locally Toeplitz (GLT) sequences is an apparatus for computing the asymptotic spectral distribution of matrices arising from numerical discretizations of differential equations. Indeed, when the mesh fineness parameter tends to infinity, these matrices give rise to a sequence , which often turns out to be a GLT sequence. In this paper, we extend the theory of GLT sequences in several directions: we show that every GLT sequence enjoys a normal form, we identify the spectral symbol of every GLT sequence formed by normal matrices, and we prove that, for every GLT sequence formed by normal matrices and every continuous function , the sequence is again a GLT sequence whose spectral symbol is , where is the spectral symbol of . In addition, using the theory of GLT sequences, we prove a spectral distribution result for perturbed normal matrices
On the products of commutators of real -symmetries
No full textLet . A 2-by-2 complex matrix is said to be symplectic if . If is symplectic and rank, then is called a -symmetry. It is known that every 2-by-2 complex symplectic matrix can be written as a product of commutators of -symmetries. We consider the real case and study the properties of real -symmetries and commutators of real -symmetries. We prove that if is a -by- real symplectic matrix, with , then is a product of commutators of real -symmetries if is skew-symmetric, and is a product of commutators of real -symmetries if is not skew-symmetric