What does science say?
Why understanding numbers is so crucial
Scientific studies have shown for years that a solid understanding of numbers forms the basis for successful arithmetic and mathematical thinking. On this page, you will find selected research findings that show why children should understand numbers before practising arithmetic tasks.
Jordan, N. C., Kaplan, D., Locuniak, M. N. & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades.
Scientific studies have shown for years that a solid understanding of numbers forms the basis for successful arithmetic and mathematical thinking. On this page, you will find selected research findings that show why children should understand numbers before practising arithmetic tasks.
Klaudt, Dieter (2005): Zahlvorstellung und Operieren am mentalen Zahlenstrahl
(Number perception and mental arithmetic)
This dissertation shows how children develop an understanding of the number line in early education, thereby building important mathematical foundations. A solid understanding of numbers is crucial in this regard: it supports sustainable calculation strategies, promotes flexible thinking and can prevent learning difficulties at an early stage.
PIAS – Pikas.dzlm.de: Zahlverständnis im Anfangsunterricht
(Understanding numbers in early education)
According to this source, developing a solid understanding of numbers is key to avoiding difficulties with arithmetic later on. In early lessons, particular attention should be paid to specifically promoting individual prior knowledge in the small number range. Only a solid understanding of numbers enables meaningful operation with numbers and a deeper understanding of the place value system.
Ghazali, M. u. a. (2021). A systematic review on the definition of children’s number‑sense in the primary school years.
This review examines how the term ‘number sense’ is defined in research — with many different facets: number recognition, number sets, understanding relationships, operations, estimation, etc. The authors emphasise that, although definitions vary, one thing is clear: number sense forms an essential foundation for later mathematical learning.
Krajewski: Entwicklungsmodell der Zahl-Größen-Verknüpfung (Stiftung Kinder forschen)
The developmental model shows that children first understand concepts such as ‘little’ and ‘much’ before moving on to precise counting and understanding numbers. Only when these stages have been successfully completed are children able to grasp arithmetic operations and use them meaningfully.
Träff, U. (2025). Mental arithmetic skill development in primary school.
This recent study examines which cognitive and mathematical abilities are particularly strongly linked to the development of mental arithmetic skills in primary school children. It clearly shows that it is not enough to simply teach children arithmetic strategies or have them solve lots of problems. What is crucial is that they have a solid understanding of numbers – that is, what numbers mean, how they are related and how quantities can be structured.