Mathematics and reading are quintessential building blocks of children's primary education and they are independently predictive of educational level and income in later life (Ritchie & Bates, 2013). Already in preschool, that is before formal school entry, precursors of mathematics and reading are highly correlated, independent of general cognitive ability (Cameron et al., 2019; Cirino et al., 2018; Vanbinst et al., 2020). Many studies have investigated reading-related brain networks in preschoolers, but far less is known about mathematics-related brain networks at this age. However, studying brain networks related to both mathematics and reading in preschoolers is crucial because it can shed light on whether these networks are related to behavioral performance and whether they differ or overlap already at an early age, without influences of formal mathematics and reading instruction. This research on preschoolers in the field of reading has typically focused on the investigation of individual differences in white matter (Ozernov-Palchik & Gaab, 2016, for a review). To the best of our knowledge, there are no studies in preschool about white matter tracts that are associated with mathematics performance. There are also no studies that have investigated the white matter tracts that are correlated with preschoolers' precursors of mathematics and reading simultaneously, allowing to investigate the specificity or overlap of these white matter tracts. The current study aims to address these limitations.

Diffusion Tensor Imaging (DTI) studies in preschoolers have almost exclusively focused on reading. These studies have often investigated reading against the background of cognitive models (Coltheart et al., 2001; Jobard et al., 2003) and they have proposed two complementary reading routes, each related to specific white matter tracts (Vandermosten et al., 2012). A dorsal reading route is thought to be related to initial, phonology-based decoding strategies and is assumed to be related to the left arcuate fasciculus (AF) (Vanderauwera et al., 2018). This route is later complemented by a ventral route, associated with memory-based visual-orthographic word recognition (Vanderauwera et al., 2018). Ventral tracts connected to the visual word form area (Yeatman et al., 2013), such as the left inferior fronto-occipital fasciculus (IFOF) and left inferior longitudinal fasciculus (ILF) are assumed to sustain this reading route (Schlaggar & McCandliss, 2007). Unlike adults, preschoolers have not yet developed orthographic knowledge. It has therefore been suggested that these young children might also rely on the (bilateral) IFOF for phonological processing (Vandermosten et al., 2015; Walton et al., 2018). Indeed, given that dorsal white matter fibers, such as the AF, mature later than ventral ones (Giorgio et al., 2008; Lebel & Beaulieu, 2011; Lebel et al., 2008), young children might need to recruit ventral pathways to sustain phonological processing (Brauer et al., 2011). Longitudinal DTI research from pre-to early readers (Chyl et al., 2021, for a review) has further demonstrated an increase in fractional anisotropy (FA) in reading-related tracts (i.e., AF and IFOF) during the first two years of reading instruction (Vanderauwera et al., 2017), with the changes in white matter connectivity between the visual word form area and the parietal cortex being related to the degree of reading improvement during the first year of formal schooling (Moulton et al., 2019).

In sharp contrast to the large number of white matter studies in the field of reading, virtually nothing is known about the white matter tracts that are related to mathematics in preschoolers. The existing DTI studies, albeit all in older children, have proposed multiple white matter tracts to be correlated with individual differences in mathematical performance (Matejko & Ansari, 2015, for a review). These include the superior longitudinal fasciculus (SLF)/AF (Jolles et al., 2016; Li et al., 2013; Matejko et al., 2013; Tsang et al., 2009; Van Beek et al., 2014), IFOF (Li et al., 2013; Tsang et al., 2009), ILF (Li et al., 2013; Polspoel et al., 2019; Tsang et al., 2009; van Eimeren et al., 2008) corpus callosum (Hu et al., 2011; Tsang et al., 2009), corona radiata (Matejko et al., 2013; Tsang et al., 2009; van Eimeren et al., 2008) and internal and external capsule (Tsang et al., 2009). The existing literature suggests that the AF might play a role in arithmetic fact retrieval during for example addition and multiplication (Van Beek et al., 2014) and it has been suggested that this reflects a reliance on phonological codes during fact retrieval (De Smedt & Boets, 2010). The IFOF and ILF, on the other hand, have been suggested to be related to verbal-based processing in calculation (Li et al., 2013). Altogether, previous developmental research on mathematics suggests that fronto-parietal white matter relates to individual differences in mathematical abilities (Matejko & Ansari, 2015), yet it remains to be determined whether such pattern of associations can also be observed in younger children, that is before the start of formal school entry. On the one hand, such data allow us to study brain networks that have not been contaminated by the impact of formal instruction, as is the case in older children. On the other hand, such preschool data are relevant because they can inform us on early screening tools for learning disabilities. Children with learning disabilities are typically not diagnosed until second grade or later, when they have already failed in learning to count or read (e.g., Ozernov-Palchik & Gaab, 2016). Early identification is therefore crucial and holds important implications for remediation (Dowker, 2005).

It is important to acknowledge that all discussed DTI studies investigated mathematics or reading in isolation and independently of each other. However, from the brain imaging literature reviewed above, it is clear that the brain networks that support mathematics and reading largely overlap. Specifically, white matter tracts such as the AFdirect, AFanterior, IFOF and ILF have been frequently related to performance in both domains. Accordingly, it has been recently argued that white matter tracts often correlate with multiple cognitive domains (Forkel et al., 2022) and that they are not specific to only one given cognitive function (Thiebaut de Schotten et al., 2020). Also at the behavioral level, previous studies revealed a large overlap between mathematics and reading, which might be explained by overlapping specific cognitive skills. Phonological awareness, for instance, is a well-established predictor of reading (Melby-Lervåg et al., 2012, for a review), but it has also been associated with individual differences in mathematics (Yang et al., 2022, for a meta-analysis). This urges the need for studies that examine both abilities simultaneously. This is additionally motivated by the observation that mathematical and reading difficulties often co-occur (Landerl & Moll, 2010; Moll et al., 2019) with, for instance, arithmetic fact retrieval being less accurate in children (Miles et al., 2001) and adults (De Smedt & Boets, 2010; Göbel & Snowling, 2010; Simmons & Singleton, 2006) with dyslexia.

In the present study, we examined the white matter tracts that are correlated with precursors of mathematics and reading in 5-year-old preschoolers, none of which received formal schooling. Age, motion, verbal ability and spatial ability were included as confounding variables.

The first aim of this study was to investigate associations between white matter and precursors of mathematics. We investigated multiple precursors of mathematics that have been shown to play an important role in later mathematical performance. These precursors include the understanding of ordinality (Lyons & Ansari, 2015; Lyons & Beilock, 2011; Lyons et al., 2014), the recognition of Arabic numerals (Göbel et al., 2014; Habermann et al., 2020; Purpura et al., 2013), the comparison of symbolic and of non-symbolic numerical magnitudes (Schneider et al., 2017) and early arithmetic (Jordan et al., 2006). As was discussed above, no DTI research in preschoolers exists in the field of mathematics. Studies in older children highlighted the AFdirect, AFanterior, IFOF and ILF as critical tracts of the mathematical network (Matejko & Ansari, 2015, for a review), for which reason these tracts served as our main focus.

Our second aim was to replicate the associations between white matter tracts and precursors of reading, that is letter knowledge (Leppänen et al., 2008) and phonological awareness (Melby-Lervåg et al., 2012). Previous DTI research in the reading domain has pointed towards associations between phonological processing and white matter tracts (AF, IFOF, ILF) in prereaders (e.g., Vanderauwera et al., 2017; Vandermosten et al., 2015; Walton et al., 2018) and the current study aimed to replicate this.

Lastly, and most critically, our third aim was to investigate whether the white matter tracts under study specifically correlated with only mathematics or with reading. To verify this, we decided that if a white matter tract correlated with precursors of both domains, we would investigate whether a particular one precursor explains unique variance of the white matter tract over and above precursors from the other domain and the abovementioned confounding variables. Based on a recent review by Forkel et al. (2022) that indicated that the abovementioned white matter tracts are not specific to only one cognitive domain or function, we expected overlap to occur although we did not set a priori predictions for which white matter tracts such overlap would be observed.