Introduction

Numerous studies have demonstrated a causal relationship between spatial perception and arithmetic skills (Graß & Krammer 2018, Vogel 2021). On the one hand, this relationship is reflected in the representation of

numbers along a left-to-right oriented mental number line in Western cultures (Lindemann & Fischer 2015). The mental number line concept is supported by the SNARC effect, which associates smaller numbers with

the left side and larger numbers with the right side of mental space, as well as the distance effect, which demonstrates quicker judgements for larger numerical differences (Dehaene et al. 1993, Moyer & Landauer 1967). On the other hand, these spatial-numerical associations are also substantiated by neuroscientific findings emphasizing the central role of the intraparietal sulcus in numerical cognition, which is closely linked to spatial processes (Hawes et al. 2019). Additionally, the working memory – especially the visual-spatial component – plays a crucial role in arithmetic performance, establishing another indirect link between spatial abilities and mathematical skills (Lander, Vogel & Kaufmann 2022, Zhang et al. 2022). In consideration of these findings, the central research question guiding the present study is whether and to what extent spatial abilities play a causal role in the understanding of numbers and mathematical concepts.

Methods

To answer this research question empirically, a comprehensive longitudinal intervention study, with approximately 400 third-grade primary school children, is being conducted as part of a PhD project. The experimental

group will receive a six-week spatial perception training with three training session à 15 minutes each week implemented via the digital tool RIF 3.0. This online platform boasts over 1.600 interactive tasks to train spatial

thinking skills, with a global user base of more than 100.000 spanning 63 countries. To control for potential disadvantages related to training exposure, the control group will likewise receive a digital training program, focusing on content unrelated to mathematics or spatial perception. Pre-, post- and follow-up test will be used to measure changes in key mathematical skills resulting from the spatial thinking training. To this end, basic numerical skills such as ordinal and cardinal aspects and arithmetic skills are assessed to identify both short- and long-term effects.

Results and Discussion

Due to the timing of the study, which is scheduled to be conducted in the final quarter of 2026, only preliminary findings from the pilot phase can be presented in the research lecture. Therefore, no results will be available

at the time of the conference. According to the findings of previous studies, it is anticipated that children in the experimental group will exhibit considerably higher levels of performance in the assessments. This is indicative of the positive impact of spatial abilities on mathematical skills.

Educational Significance of the Research

The research project examines the influence of spatial abilities on arithmetic skills in primary school, thereby contributing to the empirical foundation of basic mathematics education. While arithmetic performance in school contexts is typically assessed from a numerical perspective, spatial-cognitive prerequisites for mathematical learning have received limited attention so far. Addressing this gap, this project integrates perspectives

from mathematics education, educational psychology and cognitive science. The findings are of direct relevance to primary school teachers and professionals in educational and psychological diagnostics, as the differentiated analysis of spatial abilities allows for more precise classification of arithmetic skills and supports the early identification of individual learning needs. At the level of instructional development, the project provides empirical evidence on which spatial reasoning skills are particularly relevant for core mathematical competencies, thereby informing the design of task formats that integrate spatial and numerical processing. In addition, the results contribute to the further development of diagnostic instruments and offer a scientifically grounded basis for the systematical integration of spatial abilities into university teacher education. Strengthening the competencies of future teachers in this area is key to enabling effective mathematics learning in primary school.

Introduction

The ability to recognize, evaluate, and adaptively respond to errors is a core component of learning and problem solving. These processes are conceptually subsumed under the term metacognitive regulation, which encompasses metacognitive monitoring—the evaluation of one’s own cognitive performance—and metacognitive control—behavioral adjustments aimed at optimizing performance (Nelson & Narens, 1990). Despite their central role in learning, the neural and behavioral mechanisms underlying metacognitive regulation in childhood remain poorly understood.

A behavioral index of metacognitive control is post-error slowing (PES), the tendency to slow down responses following an error. PES is typically interpreted as an adaptive adjustment reflecting increased caution or attentional control (Danielmeier & Ullsperger, 2011) and appears to depend on error awareness, with larger PES following consciously perceived compared to unperceived errors (Kirschner et al., 2021). At the neural level, error awareness is associated with the error positivity, a centro-parietal event-related potential (ERP) occurring 200–500 ms after an error. The error positivity has been linked to confidence in error judgments (Taghizadeh et al., submitted) and, importantly, is thought to contribute to PES, providing a neural mechanism through which conscious error detection informs adaptive post-error behavioral adjustments.

While these neural effects have been studied in adults, they have not been investigated in children performing arithmetic. Arithmetic provides an ideal domain for assessing metacognitive regulation, as it allows for multiple forms of performance control (Jacobs et al., 2024). In the present study, we collected behavioral and electroencephalography (EEG) data from children solving multiplication problems of varying difficulty. Here, we report behavioral findings on PES, confidence, and task difficulty, EEG data analysis are ongoing, but results will be presented at the conference.

Methods

We collected behavioral and EEG data using 64-channel active electrodes (10–20 system) from 30 children (16 girls, 14 boys; mean age = 10.9 years, range = 10–12 years). Participants completed 288 multiplication problems presented on a computer screen, selecting the correct answer from two alternatives and subsequently rating their decision confidence on a 6-point Likert scale. Three multiplication difficulty categories were implemented based on problem size and proactive memory interference (De Visscher et al., 2018). Reaction times and error rates were recorded. PES was quantified based on response times for confidence ratings (i.e., rating times), allowing assessment of adaptive behavioral adjustments following errors. EEG analyses focused on frontal-to-parietal midline electrodes (Cz, CPz, Pz), where the error positivity is typically observed. The study was approved by the Ethics Board of the University of Graz, and participants provided informed consent. Upon completion of the project, the data and analyses scripts will be made available on the Open Science Framework (https://osf.io) platform.

Results and Discussion

Behavioral results showed that reaction times and error rates for solving arithmetic problems increased with task difficulty, while confidence ratings decreased, reflecting expected task difficulty effects. Linear mixed models revealed that confidence ratings were 31.49% slower following errors compared to correct trials (t = -14.11, p<.001), indicating post-error slowing and thus adaptive behavioral adjustments. PES also interacted with task difficulty (t = 4.66, p<.001): smaller PES effects were observed for the most challenging problems. Interestingly, this effect was driven by slower confidence ratings on correct trials rather than errors, indicating that individuals’ evaluation of correct answers varied with task difficulty. Together, these findings demonstrate that children adaptively adjust their behavior on both correct and error trials in an arithmetic task, and that this adjustment is modulated by task difficulty. The results provide novel evidence for metacognitive regulation in arithmetic problem solving in children. Findings from the EEG analysis will be discussed at the conference.

Educational Significance of the research.

These findings highlight the role of metacognitive regulation in children’s problem solving. Understanding how task difficulty influences children’s metacognitive monitoring and behavioural adjustments is an important step to better understand how self-regulated learning operates during complex problem-solving situations. These behavioral findings lay the groundwork for our ongoing EEG analyses, which aim to identify the neural mechanisms underlying post-error adjustments and metacognitive monitoring in children during arithmetic problem solving. Understanding how neural error signals, such as the error positivity, relate to behavior can inform both theoretical models of learning and practical strategies to foster adaptive problem-solving and metacognitive skills in educational contexts.