Abstract
Research has shown that a profound place value understanding is crucial for success in learning mathematics. At the same time, a substantial number of students struggles with developing a sustainable place value understanding. In this regard, two aspects of the place value system appear especially relevant: First, the knowledge of the decimal structure of numbers, and second, the relation between the bundling units. To support teaching place value understanding, a developmental model of place value understanding focusing on both aspects has been constructed and validated in Germany. The model comprises five levels of place value understanding that build upon each other hierarchically. This study aims at validating the level hierarchy in Turkey to prepare the usage of the developmental model as learning trajectory for Turkish primary schools. N=437 Turkish students from Grades 2 through 4 completed a translated version of the item collection of the German validation study as well as a Turkish place value test that is not based on a developmental model. In a Rasch analysis, most items of the translated item collection showed item difficulties as predicted by the model. In a regression analysis, item difficulties were well predicted by their allocation within the level hierarchy, while other item characteristics did not inform about the item difficulties. Substantial correlations between the translated item collection and the Turkish test underpin the claim that the model is appropriate to assess Turkish students’ place value understanding as well as structuring place value instruction in Turkish primary schools.
Highlights
Understanding the place value system is one of the important competencies for the further development of arithmetic skills such as the development of multi-digit numbers and operations with them (Dietrich et al, 2016) as well as other basic numerical competencies (Lambert & Moeller, 2019) such as mentally representing the magnitudes of numbers
Empirical studies have shown that a lack of place value understanding is a typical characteristic of children with math learning difficulties (Fuson et al, 1997; Gervasoni & Sullivan, 2007; Hart, 2009; Lambert & Moeller, 2019)
To address the first research question, to what extent item difficulties correspond to the model (RQ1), we employed a onedimensional Rasch analysis
Summary
Understanding the place value system is one of the important competencies for the further development of arithmetic skills such as the development of multi-digit numbers and operations with them (Dietrich et al, 2016) as well as other basic numerical competencies (Lambert & Moeller, 2019) such as mentally representing the magnitudes of numbers. Children who understand the decimal structure of numbers flexibly (Ladel & Kortenkamp, 2016) are more likely to solve math problems and do basic operations successfully (Gebhardt et al, 2014). Empirical studies have shown that a lack of place value understanding is a typical characteristic of children with math learning difficulties (Fuson et al, 1997; Gervasoni & Sullivan, 2007; Hart, 2009; Lambert & Moeller, 2019).
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