Conceptual place value understanding: students’ errors and their consistency at the individual level

Place value understanding is a key prerequisite for learning mathematics in primary and secondary school. However, some students show inadequate place value understanding at the end of primary school, which raises the question of where the difficulties lie. Therefore, we examined errors made by fourth grade students (N = 306) using a test instrument to assess conceptual place value understanding for three- and four-digit numbers, focusing on translation tasks with nonstandard representations, including places with more than nine bundling units. The findings revealed two prevalent error patterns with nonstandard representations: (1) Lining up all digits without any bundling, and (2) Pseudo-bundling to the right, next smaller place value. In addition, the analysis revealed variability in students’ errors across tasks, suggesting that the first error pattern is more consistent at the individual level than the second. Both error patterns indicate deficits in students’ conceptual place value understanding.