Investigating Conceptual Place Value Understanding and Its Interplay with Arithmetic Skills at the End of Primary School

Place value understanding is a crucial foundation for learning arithmetic in primary and secondary school. This study investigates how conceptual place value understanding for three- and four-digit numbers can be reliably and validly assessed. The study was conducted with N = 630 grade 4 students (mean age 10.3 years) from primary schools in Germany, using a cross-sectional design. A test instrument was developed, comprising 13 items across three task types, all requiring the change of pictorial or symbolic non-canonical representations into numerals. The psychometric structure of the instrument was examined using confirmatory factor analysis, and reliability was assessed using McDonald’s ω, demonstrating the instrument’s statistical quality (robust CFI/TLI = .98, SRMR = .027, robust RMSEA = .031, 90% CI [.024, .037]). In addition, the study examines the interplay between conceptual place value understanding and key arithmetic skills, including number sequencing, mental calculation, and number line estimation (both number-to-position and position-to-number tasks). Results indicated moderate positive correlations between place value understanding and arithmetic skills ranging from r = .27 to r = .46.