A holistic investigation of fraction learning: examining the hierarchy of fraction skills, misconceptions, mathematics anxiety and response confidence

This study aimed to holistically investigate fraction knowledge by considering pupils’ fraction performance on various tasks (i.e. mapping, equivalence, comparison, and arithmetic) and in relation to whole number arithmetic, fraction misconceptions, mathematics anxiety, and confidence in responses. Northern Irish pupils (N = 123; 77 girls; Mage = 11.1 years) demonstrated a strong understanding of fraction magnitudes with few pupils showcasing misconceptions across magnitude tasks. In contrast, fraction arithmetic knowledge, which was uniquely predicted by whole number arithmetic and fraction comparison, was still developing with many pupils incorrectly applying whole number strategies to arithmetic problems. Mathematics anxiety was low, but negatively correlated with performance, and confidence reports were more closely aligned with performance on whole number arithmetic compared to fraction tasks. Overall, researchers and educators need to consider not just fraction performance, but also foundational skills, the presence of misconceptions, and pupils’ feelings and beliefs to better understand fraction learning.