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Abstract: The long‐standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from 5 years old. Algorithm is introduced early in the English computing curriculum, yet there is limited knowledge of how young pupils view this concept. This paper explores pupils' (aged 10–11) understandings of algorithm following their engagement with 1 year of ScratchMaths, a curriculum designed to develop computational and mathematical thinking skills through learning to program. A total of 181 pupils from 6 schools undertook a set of written tasks to assess their interpretations and evaluations of different algorithms that solve the same problem, with a subset of these pupils subsequently interviewed to probe their understandings in greater depth. We discuss the different approaches identified, the evaluation criteria they used, and the aspects of the concept that pupils found intuitive or challenging, such as simplification and abstraction. The paper ends with some reflections on the implications of the research, concluding with a set of recommendations for pedagogy in developing primary pupils' algorithmic thinking. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions for set-valued mappings. We construct some new iterative algorithms for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness. We prove the existence of solutions for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness and the convergence of iterative sequences generated by the algorithms. We also give an application to generalized nonlinear implicit variational inequalities. [ABSTRACT FROM AUTHOR]

Given, a graph G = (V, E), with two vertices s and t specified as the origin and destination, respectively; a positive integer K called the obstruction number; and (positive) weights l (·) on the edges; then, two players P1 and P2 play a game with the following rules. P1 starts from s, and tries to arrive at t by tracing an edge on each move. P2 cuts in his turn, P2 cuts some edges. The maximum total number of edges that P2 can cut is K during the game. It is assumed that both P1 and P2 can see the whole graph. P1 tries to minimize the sum of traveled edge weights (called the path length), and P2 tries to maximize the path length. This paper shows that the path length when the two players do their best can be determined in O(nk-l (m + n log n)) (m = |E| n = (|V|) time. It is also shown that the problem of deciding whether or not the path length when the two players do their best is not greater than a certain positive integer is P-SPACE-complete, even if the weight on each edge is 1. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(2): 13–23, 1998 [ABSTRACT FROM AUTHOR]

This paper discusses the problems of finding one of the largest similar substructures in tree Tb to tree Ta, where both Ta and Tb are rooted and ordered trees (RO-trees) or unrooted and cyclically ordered trees (CO-trees). A maximal closest common ancestor mapping and a largest similar substructure in Tb to Ta based on this mapping are defined and two algorithms are proposed for finding one of the largest similar substructures for RO-trees and that for CO-trees. The time and space complexities of the algorithm for RO-trees are OT(NaNb) and OS(NaNb), respectively; and those of the algorithm for CO-trees are OT(mambNaNb) and OS((ma + mb)NaNb), respectively, where ma(mb) and Na(Nb) are the largest degree of a vertex and the number of vertices of Ta(Tb), respectively. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 92–104, 1997 [ABSTRACT FROM AUTHOR]