Validation of a Model of Sustainable Place Value Understanding in Turkey
Mehmet Hayri Sari 1 , Moritz Herzog 2 * , Sinan Olkun 3 , Annemarie Fritz 4
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1 Nevsehir Haci Bektas Veli University, Department of Basic Education, Nevsehir, TURKEY2 University of Wuppertal, Institute of Educational Research, Wuppertal, GERMANY3 Final International University, Department of Mathematics and Science Education, Kyrenia, NORTHERN CYPRUS4 Akademie Wort + Zahl, Köln, Germany* Corresponding Author


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.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 16, Issue 3, October 2021, Article No: em0659

Publication date: 21 Oct 2021

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