Place Value Understanding Explains Individual Differences in Writing Numbers in Second and Third Graders But Goes Beyond

Abstract

Recent studies have shown that children’s proficiency in writing numbers as part of the so-called transcoding correlates with math skills. Typically, children learn to write numbers up to 10,000 between Grade 1 and 4. Transcoding errors can be categorized in lexical and syntactical errors. Number writing is thus considered a central aspect of place value understanding. Children’s place value understanding can be structured by a hierarchical model that distinguishes five levels. The current study investigates to what extent a profound understanding of the place value system can explain individual differences in number writing. N = 266 s and third graders (126 girls) participated in the study. The children wrote down 28 verbal given numbers up to 10,000 and completed a place value test based on a hierarchical model to assess number writing skills and place value understanding. Second graders made more number writing errors than third graders and transcoding errors were mostly syntactical errors. In both grades, transcoding performance and place value understanding correlated substantially. In particular complex numbers were more often solved correctly by children with a more elaborated place value understanding. The effect of place value understanding on error rate was smaller regarding lexical errors than syntactical errors. This effect was also comparably small regarding inversion-related errors. The results underpin that writing numbers is an integral part of early place value understanding. Writing numbers can be assumed to be mostly based on the identification of the place values. However, variance in transcoding skills cannot totally be explained by place value understanding, because children with an elaborated place value understanding differed in transcoding performance, too. The differences between the grades indicate that children’s development of writing numbers is also driven by instruction in school. Thus, writing numbers and place value understanding overlap but exceed each other. We discuss how an understanding of the place value relations can be integrated in existing frameworks of place value processing. Since writing numbers is a basic skill in place value understanding, it might serve as an efficient screening method for children, who struggle severely with understanding the decimal place value system.