Mathematical competence in school-related contexts is a multidimensional construct that encompasses several content areas and cognitive components. Kindergarten children have experiences with different types of mathematical content. However, empirical research has focused mostly on children's numerical skills, and less is known about their…

The number line estimation task is frequently used to measure children's numerical magnitude understanding. It is unclear whether the resulting straight, horizontal, left-to-right-oriented estimate patterns indicate task constraints or children's intuitive number--space mapping. Three- to six-year-old children (N = 72, M[subscript age] = 4.89, 56%…

The approximate number system (ANS) is foundational to numerical cognition. Whereas some studies hint at intact ANS skills in individuals with Down syndrome (DS), others report impaired ANS abilities. To reconcile these discrepant findings, we investigated ANS skills of children with DS and typically developing (TD) children in a non-symbolic…

Fractions are a fundamental component of the school mathematics curriculum, and most students achieve proficiency in these concepts during their elementary education. However, a significant proportion of students still encounter challenges in this area even after entering secondary education, necessitating additional support to prevent further…

Empirical research highlights the benefits for the development of children's mathematical competencies when they play linear number board games with dice and receive feedback. We, therefore, investigated mathematical competencies in two training studies with six sessions and a 3 × 2 design. The sample in the first experiment consisted of N = 79…

It is well known that fraction knowledge is relevant for later success in mathematics. However, many students still face difficulties when dealing with fractions. Predictors of fraction knowledge have been widely examined. Systematizing "mathematical" predictors, whether their predictive contributions are direct or indirectly mediated…

This study explores a pathway from social origin at adolescence to numeracy acquisition in young adulthood. A variation associated with vocational track attendance and numeracy acquisition between two different traditions of education systems is identified; namely, between education systems of German (Austria and Germany) and English (UK and US)…

When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

The perception and manipulation of spatial information are essential for mathematical learning, and research highlights gender differences in spatial abilities. The present study contributes to the question of whether these differences are evident at earlier ages and how they interact with task complexity in mental rotation. We developed the…

Background: Differences in competence gains between academic and non-academic track schools are often attributed to selection effects based on students' primary school performance and socioeconomic status (SES). However, how the competencies of comparable students (in terms of school performance and social background) at different tracks develop…

Measurement estimation skills are relevant for our everyday life and should be addressed in the mathematics classroom. Although students' measurement estimation skills were examined in several empirical studies, a structure model to describe these skills is still missing. The current research aimed at analyzing the structure of length estimation…

This large-scale and longitudinal study examines early home support for learning, formal/informal home mathematics activities, and their associations with children's mathematical development between age two and six. Data were collected in Germany between 2012 and 2018, N = 1184 (49% girls, 51% boys), and 15% of children had parents with a…

Mathematics plays a significant role in many study programs. However, several studies show deficiencies and a decline in beginning undergraduates' skills in mathematics in many content domains. However, it remains unclear whether they have improved in so-called process competencies like modeling, mathematical reasoning, or using different…

This paper presents a replication study investigating the effectiveness of a strategy to assist students with learning difficulties in adding fractions. Drawing on the research conducted by Grünke et al. (2023), this single-case analysis extends the application of the "Look, Ask, Pick" (LAP) mnemonic technique initially introduced by…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…