In recent years, programming education has gained recognition at various educational levels due to its increasing importance. As the need for problem-solving skills becomes more vital, researchers have emphasized the significance of developing algorithmic thinking (AT) skills to help students in program development and error debugging. Despite the…

Background: Data on children's ability to answer assessment questions correctly paints an incomplete portrait of what they know and can do mathematically; yet, it remains a common basis for program evaluation. Indeed, pre-post-assessment correctness is necessary but insufficient evidence for making inferences about learning and program…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…