Computational thinking (CT) is increasingly incorporated into curricular planning across various educational levels in numerous countries. Presently, CT is being integrated into preschool and primary education. To effectively implement CT at the classroom level, the design and study of techniques and tasks are crucial. This research empirically evaluates a didactic sequence using programmable educational robots for problem-solving challenges rooted in mathematical concepts. The study consists of two sets of activities: computational localisation of elements on a regular grid, where students program robots to navigate, and problem-solving tasks involving sum calculations using distinct pre-operational strategies. The study sample is a class of 16 students at the preschool level. The results indicate an increasing complexity in the success of the designed sequence, with the ’counting all’ strategy demonstrating higher efficacy. These promising findings highlight the potential for further research, aiming to establish a strong foundation for early educational levels through the integration of CT via programmable robots and engaging problem-solving challenges.

Project Euclid - mathematics and statistics online

In this paper, we will consider matrices with entries in the space of operators 𝓑(H), where H is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a finite number of diagonals. We will use the Schur product with Toeplitz matrices generated by summability kernels to describe such a class and show that in the case of Toeplitz matrices it can be identified with the space of continuous functions with values in 𝓑(H). We shall also introduce matricial versions with operator entries of classical spaces of holomorphic functions such as H∞(𝔻) and A(𝔻) when dealing with upper triangular matrices.