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Education is about supporting humans in their growth, with a special focus on exploring their intellectual potential. Learning to act following a given (even complex) pattern is losing its educational value very fast, because all well described activities can be automated. Education therefore should focus on developing those cognitive process dimensions of pupils where technology cannot compete with humans (Dagienė et al. (2020), Hromkovič and Lacher (2017), Hromkovič et al. (2020)). The contribution of this paper is conceptual. In the paper we show that starting with the algorithmic view on the historical development of number representations and calculations offers a natural, more understandable way for teaching mathematics in primary schools. We show that going consequently from concrete to abstract empowers pupils to be able to design own representations of numbers, rediscover the execution of arithmetic operations on their own, and even develop elementary calculations in own designed number systems. We show here how a successful process of rediscovery of arithmetic algorithms can be designed by using classical algorithm design methods as “induction” and “divide and conquer”. We show how that algorithmic thinking can essentially contribute to improving education in mathematics.

Computational Thinking (CT) is widely recognised as a transversal competence essential for learning, problem solving, and knowledge transfer across disciplines. However, its effective integration into school education remains strongly dependent on the availability of assessment instruments that are pedagogically meaningful, psychometrically sound, and applicable across diverse educational contexts. This paper presents COMATH, a cross-national assessment instrument designed to evaluate CT in students aged 9–14. The instrument adopts a phase-based development and validation framework that integrates Bebras-inspired tasks, Item Response Theory, factor-analytic methods, learning analytics, and teacher and student feedback. The assessment was iteratively developed and piloted between 2023 and 2025 in six European countries, with data collected from 6,480 students and 155 teachers. The findings demonstrate that a phased assessment approach enables systematic calibration of task difficulty, robust evaluation of item functioning, and meaningful interpretation of student performance across age groups and national contexts. The results further highlight how well-designed CT assessment can support instructional decision-making rather than serve solely as a summative measure. The study argues for conceptualising CT assessment as a dynamic and iterative process that links measurement, psychometric validation, and pedagogical use in school education.