Number line estimation (NLE) tasks are widely used to investigate numerical cognition, learning, and development, and as an instructional tool. Interpretation of these tasks generally involves an implicit expectation that responses are driven by the overall magnitudes of target numerals, in the sense that the particular digits conveying those…

This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

As one of the core skills of the 21st century, computational thinking has received increasing attention from educators and researchers. Although some research has been conducted on computational thinking, few studies examined the impact of learning activities on students' computation thinking skills from the perspective of cognitive development.…

Programming education consistently faces challenges in bridging theory with practice and fostering students' cognitive competencies. This 12-year longitudinal study (2011-2023) investigates an innovative competency-based teaching model in university C programming education that integrates six educational theories into a coherent framework with…

Young children's estimates of numerical magnitude increase approximately logarithmically with actual magnitude. The conventional interpretation of this finding is that children's estimates reflect an innate logarithmic encoding of number. A recent set of findings, however, suggests that logarithmic number-line estimates emerge via a dynamic…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…