The rapid digitalisation of contemporary society has profoundly impacted various facets of our lives, including healthcare, communication, business, and education. The ability to engage with new technologies and solve problems has become crucial, making CT skills, such as pattern recognition, decomposition, and algorithm design, essential competencies. In response, Switzerland is conducting research and initiatives to integrate CT into its educational system. This study aims to develop a comprehensive framework for large-scale assessment of CT skills, particularly focusing on AT, the ability to design algorithms. To achieve this, we first developed a competence model capturing the situated and developmental nature of CT, guiding the design of activities tailored to cognitive abilities, age, and context. This framework clarifies how activity characteristics influence CT development and how to assess these competencies. Additionally, we developed an activity for large-scale assessment of AT skills, offered in two variants: one based on non-digital artefacts (unplugged) and manual expert assessment, and the other based on digital artefacts (virtual) and automatic assessment. To provide a more comprehensive evaluation of students' competencies, we developed an IAS based on BNs with noisy gates, which offers real-time probabilistic assessment for each skill rather than a single overall score. The results indicate that the proposed instrument can measure AT competencies across different age groups and educational contexts in Switzerland, demonstrating its applicability for large-scale use. AT competencies exhibit a progressive development, with no overall gender differences, though variations are observed at the school level, significantly influenced by the artefact-based environment and its context, underscoring the importance of creating accessible and adaptable assessment tools.