All children were recruited as part of our program of research on learning disabilities, either from the community or from a school that specializes in teaching children with learning disabilities. All were monolingual, native English speakers. Participants were given informed consent prior to beginning the study and all protocols were approved by the Georgetown University Institutional Review Board. Subsets of these participants were included in prior fMRI publications (Olulade et al., 2013, 2015; Evans et al., 2014; Ashburn et al., 2020).

Behavioral assessments included the Wechsler Abbreviated Scale of Intelligence (WASI; Wechsler, 1999) and the Woodcock-Johnson III Tests of Achievement (WJ-III; Woodcock et al., 2001). To be in the study, all participants had to have a standard score for Intelligence Quotient (IQ) on the WASI of 80 or above. The WJ-III battery was used to assess single real-word reading ability (Word Identification), pseudo-word reading ability (Word Attack), simple fact retrieval (Math Fluency), and more complex mathematical functions (Calculation). A standard score of 100 represents the 50^th percentile and a score between 85 and 115 (one standard deviation above or below the mean) is considered to be the average range of performance. Children in the Control group were required to have a standard score above 92 on both the real- and pseudo- word reading subtests as well as above 92 on both the math fluency and calculation subtests of the WJ-III (28 out of 33 met these criteria). This ensured that the Control group was well within or above the average range for reading or math. Children with RD + MD were selected from a larger group of children with learning disabilities based on a standard score of 85 (16th percentile) or below on either, or both, the real- or pseudo-word reading subtest, as well as a standard score of 85 or below on either (or both) the math fluency and calculation subtests of the WJ-III (30 out of 92 met these criteria).

Children with anatomical anomalies observed on the structural MRI or those with excessive head movement in the fMRI scans (described below) were excluded. For Study 1, nine children were excluded, leaving 23 children in the Control group (13 females, 10 males, mean age = 9.7 years, standard deviation [SD] = 1.8) and 26 in the group with RD + MD (12 females, 14 males, mean age = 10.3, SD = 1.4). The groups did not differ significantly in age. However, because they differed in Verbal and Performance IQ, Full IQ was used as a covariate of no interest when analyzing the fMRI data for between-group differences on the reading task. As expected, the RD + MD group had significantly lower reading and math scores than the Control Group. All participants except one Control participant were right-handed. Group characteristics are provided in Supplementary Table 1.

For Study 2, the arithmetic task was not acquired for all participants that were in Study 1, and, after excluding one child due to head movement and another due to incomplete brain coverage, Study 2 had 16 children in the Control group (6 females, 10 males, mean age = 10.1 years, SD = 2.0) and 14 in the group with RD + MD (6 females, 8 males, mean age = 10.8, SD = 1.3). As in Study 1, the groups did not differ significantly in age, but they again differed in Verbal and Performance IQ, and therefore Full IQ was used as a covariate of no interest in the between-group analyses of the arithmetic task. As expected, the RD + MD group again had significantly lower reading and math scores than the Control Group. All participants in Study 2 were right-handed. Group characteristics are provided in Supplementary Table 2.

In Study 1, participants performed an implicit reading task (Price et al., 1996; Ashburn et al., 2020), consisting of visually presented real word and false font conditions. Real word stimuli were single five-letter, low frequency words used for the Reading task. False font stimuli were used for the Active Control condition and were created by manipulating the letters from the real word stimuli to create new, unfamiliar characters. False font strings were matched to real words for both length and location of ascenders and descenders. As such the number of elements and angles are similar across the Reading (real words) and Active Control (false fonts) conditions. Participants were instructed to indicate whether the visually presented stimulus had a “tall” character. Participants responded by pressing a button in their right hand if a tall feature was present (e.g., Figure 1A) and pressing a button in their left hand if no such feature was present (e.g., Figure 1B) in the real word or false font stimuli. They were instructed to respond as accurately and quickly as possible. Reading and Active Control stimuli were presented in separate blocks, always alternating with a block of fixation. During Fixation blocks children were instructed to keep their eyes on the cross hair in the center of the screen. We examined Reading > Fixation as a way to gauge general activation to the task and Reading > Active Control to identify activity specific to single word processing.

Each participant completed two runs and each run consisted of two blocks of each task condition (Reading and Active Control), with 10 stimuli per block. The inter- stimulus trial was 4.2 s and each task block had a duration of 42 s while interleaving Fixation blocks had a duration of 18 s blocks. Therefore, the overall length of the run was 4 min and 27 s. The number of brain volumes acquired was the same for the Reading (real words), Active Control (false fonts), and Fixation conditions (28 volumes each per run). Both runs were used for all participants except for three Control participants, where one of the two runs was removed due to excessive motion. At the conclusion of the actual scanning session, a pencil-and-paper test was performed in which participants were asked whether they had seen a given stimulus during the scans (as in Turkeltaub et al., 2003). There were 40 targets and 40 foils, for each condition.

For Study 2, participants performed a single-digit arithmetic verification task (Evans et al., 2014, 2016), which included addition and subtraction blocks. The task was a two-operand equation with a single-digit answer, and participants indicated with a right or left button press whether the math problem was correct (e.g., 2 + 3 = 5 or 7–4 = 3) or incorrect (e.g., 2 + 3 = 4 or 7–4 = 2) as shown in Figure 1. Both addition and subtraction had Active Control conditions where one of the components of the equation on either side was replaced by a symbol (symbol comparison). In this instance, children indicated whether the symbols on either side of the equal sign were the same (e.g., Figure 1C) or different (e.g., Figure 1D). Each condition (addition, addition active control, subtraction, and subtraction active control) consisted of 10 unique stimuli. Each block consisted of 50% correct and 50% incorrect problems that were randomized within each block. We examined Arithmetic > Fixation as a way to gauge general activation to the task and Arithmetic > Active Control to identify activity specific to arithmetic processing.

Each participant completed two runs and each run consisted of two blocks of each task condition, Arithmetic (addition or subtraction) and Active Control (symbol comparison), with 10 stimuli per block. The task blocks, length of the run and number of brain volumes acquired per condition (28 volumes of each, Arithmetic, Active Control and Fixation) were analogous to those used for Study 1. Both runs were used for all participants except for one Control and three RD + MD participants.

Prior to the scanning session all participants practiced the task in a mock scanner to become habituated to all of the tasks and to the scanning environment. We used Presentation software (Neurobehavioral Systems Inc., Albany, CA, United States) for stimulus presentation and recording responses. We collected reaction time (RT) and accuracy for all tasks. RT and accuracy were compared between the groups using a two-sample student t-test (Supplementary Tables 3, 4). For Study 1, one Control and one RD + MD participant did not have in-scanner performance data due to a technical malfunction while for Study 2 all participants had in-scanner performance data.

All scans were acquired at the Center for Functional and Molecular Imaging at Georgetown University on a 3 T Siemens scanner. Structural T1 images were acquired using FOV = 256, phase = 250, slices = 160, and slice resolution = 1 mm, resulting in 1.0 × 1.0 × 1.0 mm voxels. Functional images were obtained with a T2*-weighted echo planar imaging sequence using Flip Angle = 90°, TR = 3 s, TE = 30 ms, and 50 axial slices (2.8 mm with a 0.2 mm gap), FOV = 192 mm, in-plane resolution =64×64, resulting in 3 mm cubic voxels. Three RD + MD children in Study 1 and four RD + MD children in Study 2 were collected after an upgrade and this was included as a covariate of no interest for all between-group comparisons. Functional images had complete coverage of the cortex and cerebellum.

Measures for Study 1 can be considered in three parts: (i) cerebellar activity during word processing in comparison to Fixation (Reading > Fixation) and in comparison to the specific Active Control false font task (Reading > Active Control); (ii) background functional connectivity (Norman-Haignere et al., 2012); and (iii) and task-dependent (generalized psychophysiological interactions, gPPI) functional connectivity. Background functional connectivity (FC) analysis probes how the cerebellum may be intrinsically connected to cortical regions independent of the task. The task related gPPI FC analysis distinguishes whether these functional connections are specific to word processing. For all analyses, we generated within-group and between-group maps. We constrained the analyses to the cerebellum, as described in detail below.

Using a similar approach to Study 2, we examined (i) cerebellar activity during arithmetic processing in comparison to Fixation (Arithmetic > Fixation) and to the specific Active Control task (Arithmetic > Active Control); (ii) task-independent background FC; and (iii) task-dependent gPPI FC during arithmetic task.

For Study 1 and 2, there was activity in the cerebellum for the Control and the RD + MD groups during word processing and during arithmetic processing relative to a low-level baseline comparison condition (Fixation). However, there was no significant activation for either group specific to reading or arithmetic (i.e., when contrasting the reading or arithmetic task to the respective active control conditions). Importantly, there were no differences when comparing between the Control and RD + MD groups on activation for reading or for arithmetic (using either baseline comparison, and for whole-cerebellum and for cerebellar sub-region analyses) and these were largely supported with Bayesian analyses. For functional connectivity, in both Study 1 and Study 2 there were many incidences of background FC in both the Control and RD + MD groups between the cerebellar seed regions and cortical (reading- or math-related) target regions. However, there again were no differences between the Control and RD + MD groups for cerebellar-cortical connections. For task-dependent functional connectivity for reading in Study 1, there was one within-group result in the Controls (left lobule VIIb with right SMA), and two functional connections in the RD + MD group (right lobule VI with left and right SMA). However, again no between-group differences. For Study 2, there was no task-dependent FC during arithmetic task in the Control nor the RD + MD group and no between-group differences. Overall, the Control and the RD + MD groups did not differ in terms of activation or functional connectivity between the cerebellum and the target cortical regions in these studies of reading and arithmetic.

As noted in the Introduction, most studies on the neural bases of reading in typically-developing children and adolescents of alphabetic languages do not report activation in the cerebellum. This was reflected in the meta-analysis results from Martin et al. (2015), which did not find convergence of activation in the cerebellum for studies of reading in children. While both the Control and the RD + MD groups in the present study activated bilateral cerebellar regions during word processing when contrasted with a low-level fixation task, this was not the case when contrasted with the active control task (false fonts). Therefore, we do not attribute this activation to reading, but to other aspects of the task (e.g., finger pressing).

In the Martin et al. (2015) meta-analysis on reading in alphabetic languages in typical children, six of the 20 original studies reported cerebellar activation (Booth et al., 2001; Gaillard et al., 2003; Hoeft et al., 2006; Noble et al., 2006; Rimrodt et al., 2009). Adding to this, a more recent study by Liebig and colleagues reported cerebellar activation of right crus I during orthographic decision, phonological decision, and semantic organization tasks, all relative to a visual line judgment baseline (Liebig et al., 2017). Our Control and RD + MD groups both activated vermis VI and left and right lobule VI during word processing compared to fixation (but not compared to active control). Right lobule VI is one region implicated in reading disability (Stoodley, 2016), but it (nor any other region of the cerebellum) did not differ in our group with RD + MD.

Here we consider our results of no differences between the group with and without RD + MD. The only study that we are aware of to have looked at word processing in children with RD + MD was in the supplementary materials of Peters et al. (2018). In that study, children made a decision on whether visually-presented words contained a specific phoneme or were presented in upper or lower case. They found no differences in activation between groups with RD + MD, RD-only, MD-only or controls at an FDR-corrected level (Peters et al., 2018). Of note, Peters and colleagues caution against making strong conclusions due to the small sample size; however, it is currently the only functional activation study of reading in children with RD + MD. This and the other activation studies described above used a whole-brain analysis approach. However, despite our use of an analysis specifically focused on the cerebellum and a larger sample size, our findings were consistent with that of Peters et al. (2018) in that activity of the cerebellum did not differ in children with and without RD + MD during word processing.

Lastly, given the focus on the cerebellum in the context of children’s poor reading skills, we turn to the only meta-analysis constrained to children comparing functional activation studies in those with and without RD in alphabetic languages. Richlan and colleagues reported convergence for relative under-activation in cortical regions known to be involved in reading in children with dyslexia (left inferior parietal lobule, supramarginal gyrus, and fusiform gyrus), but no differences in the cerebellum (Richlan et al., 2011). Only two of the nine studies included in this meta-analyses found a difference in activity in children with RD (relatively more) in the cerebellar vermis during sentence reading (Meyler et al., 2008) and letter matching (Temple et al., 2001). A study not included in the meta-analysis reported less activation in the cerebellum in RD during semantic word matching in children using an alphabetic writing system, but this result did not meet statistical significance after correcting for multiple comparisons (Hu et al., 2010). In our own previous study comparing children with and without RD, we found no differences in cerebellar activation during the same word processing task (Ashburn et al., 2020). Therefore, the findings from the current investigation are consistent with those reported in these meta-analyses and prior studies. Since activations do not provide insight into how the cerebellum may interact with cortical regions, as is implicated by the cerebellar deficit hypothesis, we went on to examine functional connectivity, as described next.

We examined background functional connectivity and task-dependent functional connectivity between the cerebellum and regions known to be involved in reading. Background connectivity (Norman-Haignere et al., 2012) is comparable to resting-state connectivity, which measures intrinsic functional connectivity in the absence of a task (Fair et al., 2007). Resting-state studies in adults have shown intrinsic functional connectivity between the cerebellum and cortical regions involved in motor control, as well as regions within fronto–parietal and ventral attention networks (Buckner et al., 2011; Balsters et al., 2014; Riedel et al., 2015; Guell et al., 2018). These networks include the inferior frontal gyrus, temporal–parietal cortex, and occipital-temporal cortex, regions which are also known to be altered in reading disability (Gabrieli, 2009; Eden et al., 2015). Intrinsic functional connections have been shown to be stronger in adults than in children (Hoff et al., 2013; Grayson and Fair, 2017). Interestingly, intrinsic functional connections have been reported for children between the cerebellum and the angular gyrus as well as between the cerebellum and the intraparietal lobule (Dosenbach et al., 2010). Regions of interest are used to either conduct ROI-to-ROI or seed-to-voxel (ROI-to- the rest of the brain) analyses in studies on functional connectivity. To date, knowledge about cerebellar-cortical connections in children with learning disabilities are limited because very few of the studies on children with learning disabilities include the cerebellum as a region of interest. A cerebellar deficit (Nicolson et al., 2001) would be expected to manifest as aberrations in functional connections between cerebellar and cortical reading-related regions and this was the focus of the current study.

For background connectivity in the Control and RD + MD groups, we found that all cerebellar seed regions had at least one positive connection, and most had at least one with a cortical target (seed) region. The following connections were observed in both groups: left lobule VI with left occipital temporal cortex and right SMA; right lobule VI with left occipital temporal cortex, and left and right SMA. There was also left crus I and right crus I with left occipital temporal cortex; and left lobule VIIb with left and right SMA. These functional connections of lobules VI, crus I, and lobule VIIb with cortical regions have been associated with visual and motor processing fitting with prior studies in adults (Buckner et al., 2011; Riedel et al., 2015). While there were other connections specific to each group (including negative background connectivity), it was surprising that there were no findings of positive functional connections between cerebellar crus I and crus II with frontal language areas as would have been expected based on prior work in adults (Guell et al., 2018). There are few resting-state studies in typically developing children using alphabetic languages and some of these have used seed-to-voxel analysis focusing on regions known to be involved in reading and relating them to performance (Koyama et al., 2011, 2013; Cross et al., 2021). Of the few seed-to-voxel studies explicitly considering the cerebellum, Greeley and colleagues found a positive connection between right cerebellar lobule VIII and left angular gyrus to be related to reading scores in typical readers (Greeley et al., 2021).

When directly comparing the Control and the RD + MD group, there were no differences in background connectivity between the RD + MD group and the controls. We are aware of only one resting-state FC study which compared RD + MD children to RD-only, MD-only and Controls (Skeide et al., 2018). It reported weaker FC in RD + MD children between right para-hippocampal gyrus and left posterior fusiform gyrus in comparison to the other three groups. Of note, this was a ROI-to-ROI FC analysis and did not include the cerebellum.

Again, turning to the literature on children with only reading disability, most studies in alphabetic languages have examined intrinsic cortical FC at network-level with none reporting findings in the cerebellum (Koyama et al., 2013; Horowitz-Kraus et al., 2018; Twait et al., 2018; Freedman et al., 2020). However, the recent seed-to-voxel study by Greeley et al. (2021) noted above, also included children with RD. Of the 18 ROIs placed in the cerebellum, four showed multiple differences in connectivity between the two groups. Right crus I and lobule VI seeds had stronger as well as weaker functional connectivity with various cortical regions in the group with RD relative to controls. Right lobule VII and lobule VIII seeds only had stronger positive functional connectivity with various cortical regions in the group with RD. Further, a functional connection between right cerebellar lobule VIII and left angular gyrus was positively correlated with reading ability in the RD group and trending in the control group. In our previous study comparing children with and without dyslexia, we found more positive intrinsic FC between right crus I and cortical regions of the reading network (left angular, posterior superior temporal, and inferior frontal gyri) in children with RD than the controls (Ashburn et al., 2020). This was not found by Greeley et al. (2021) in their study of RD and also not in the current study of RD + MD. Lastly, an intrinsic functional connectivity study in dyslexia (and developmental coordination disorder) found that the group with RD was not characterized by impaired connectivity in the cortico-cerebellar network (Cignetti et al., 2020).

Moving on from these task-independent functional connections, we then used a gPPI analysis to test for functional connections associated with word processing using the same cerebellar seed and cortical target regions. This time there were few functional connections in the Control and in the RD + MD groups. In the Controls, the cerebellum’s left lobule VIIb had positive task-dependent functional connectivity with right SMA (consistent with the background connectivity finding as described above). In the RD + MD group, the cerebellum’s right lobule VI had positive task-dependent functional connectivity with left and right SMA (consistent with the background connectivity finding described above). However, there were no significant differences between the two groups.

Few studies have investigated task-dependent FC connections during reading in alphabetic writing systems in typical children (Wang et al., 2013; Morken et al., 2017) and of these none included the cerebellum as a region of interest. We are not aware of any task-dependent functional connectivity studies in children with RD + MD using a reading task in an alphabetic language. There have been studies that test for task-dependent FC in children with RD during reading (Richards and Berninger, 2008; Ashburn et al., 2020; Kim et al., 2022) and of these two included the cerebellum (Richards and Berninger, 2008; Ashburn et al., 2020). Richards and Berninger conducted a seed-to-voxel analysis during the visual presentation of a phoneme-mapping mapping task and found between-group differences in FC for the seed in left inferior frontal gyrus with other regions; however, most relevant to the present study, there were no differences in their cerebellar seed region with cortical regions (Richards and Berninger, 2008). Ashburn et al. (2020) also found no differences in task-dependent connectivity between the cerebellum and cortical reading-related regions for children with and without RD.

In general, not many studies on the neural bases of arithmetic in typically developing children find the cerebellum to be activated. While both the Control and the RD + MD groups in the present study had activation in bilateral cerebellum during arithmetic processing when contrasted with a low-level fixation, this was not the case when contrasted with the active control task. As in Study 1, we conclude that this more controlled comparison, which accounts for other aspects of the task, indicates that the cerebellum is not active during arithmetic, specifically, in either group, consistent with prior studies of typical children. A meta-analysis of arithmetic processing in typically developing children found no convergence of cerebellar activation during arithmetic tasks (Arsalidou et al., 2018). Of the studies included in this meta-analysis, only seven of the 17 studies found activation in the cerebellum for various math-related tasks (Meintjes et al., 2010; de Smedt et al., 2011; Mondt et al., 2011; Ashkenazi et al., 2012; Du et al., 2013; Qin et al., 2014; Peters et al., 2016). Another study not included in this meta-analysis also found activation in the cerebellum (Matejko and Ansari, 2019). Our Control and RD + MD groups both activated vermis VI, left and right lobule VI during arithmetic processing compared to fixation (but not compared to active control). These were the same regions as those identified in the two groups during word processing in Study 1, and similarly, there were no differences in cerebellar activation during arithmetic processing between our RD + MD and Control groups (irrespective of which comparison task was used). Only one empirical study has examined functional activation during arithmetic in children with RD + MD (Peters et al., 2018). Most relevant to the current study, they found no differences between the group with RD + MD and controls on their arithmetic (subtraction) task, but several differences between the two groups during a non-symbolic subtraction task (dots), yet the cerebellum was not among them. In sum, the majority of studies of arithmetic in typical children do not show activation of the cerebellum and the only study of RD + MD to date found no differences for this group in the cerebellum. Therefore, our results of no between-group differences are consistent with the literature, even though we tackled the cerebellum more directly in our analysis.

Lastly, given the focus on the cerebellum in the context of low math skills, we next consider activation studies of MD. There are two meta-analyses for MD combining children and adults (Martinez-Lincoln et al., 2023; Tablante et al., 2023) that draw from 28 studies overall, and each meta-analysis reported altered right parietal lobe regions, but neither implicated the cerebellum. Of note, these meta-analyses included a range of task types (arithmetic, magnitude comparison, visual–spatial working memory, etc.) and one of them (Martinez-Lincoln et al., 2023) included several types of brain measures (activation, connectivity, and structure), but most were activation studies. When considering the original studies that were drawn on for these meta-analyses, eight used symbolic arithmetic tasks, specifically, (three included in Tablante et al., only, two included in Martinez-Lincoln et al., only, and three shared by both). Of these eight, only two studies observed differences in the cerebellum in MD, one reporting relatively less activation in the left cerebellum during complex and simple problems (Ashkenazi et al., 2012) and another reported relatively more activation in bilateral cerebellum during arithmetic verification (Iuculano et al., 2015). In sum, as for reading in RD, the majority of activation studies included in these meta-analyses do not report differences in the cerebellum in MD, consistent with our findings in the combined RD + MD group.

As in Study 1, in Study 2 we examined task-independent background functional connectivity and task-dependent functional connectivity, this time during an arithmetic processing task and focusing on connections between the cerebellum and regions known to be involved in arithmetic. As noted above, resting-state studies have demonstrated relationships the cerebellum has with fronto–parietal and ventral attention networks in adults (Buckner et al., 2011) and these overlap in their location not only with those associated with RD as mentioned above, but also with those associated with MD (Ashkenazi et al., 2013; Peters and De Smedt, 2018). Furthermore, a resting-state study in children has shown cerebellar FC with cortical regions such as angular gyrus and intraparietal lobule (Dosenbach et al., 2010). However, there are few studies in children that chose to make the cerebellum a region of interest, and none in children with RD + MD. Here we examined functional connections between the cerebellum and cortical regions known to subserve arithmetic to test for the anomalies due to math disability.

For background connectivity in Study 2, we found that all cerebellar seed regions had at least one positive connection with another region and most had one positive connection with a cortical target region in the Control group as well as in the RD + MD group. A positive functional connection for right crus I with left middle frontal gyrus was observed in both groups. Even though each group had other connections, there were no differences when comparing the Control and the RD + MD group for cerebellar-cortical intrinsic connections. However, the RD + MD group had relatively greater positive intrinsic functional connectivity within the cerebellum, between left and right lobule VIIb. Somewhat surprisingly, we did not find in this study (or in Study 1) background connectivity between cerebellar lobule VIIb/Crus II with intraparietal lobule, which was previously discovered with an analysis utilizing Neurosynth by Alvarez and Fiez (2018).

Prior studies have probed intrinsic FC between cortical regions in typically developing children. These seed-to-seed (Emerson and Cantlon, 2012) and seed-to-voxel (Jolles et al., 2016) analyses found intrinsic FC between parietal and frontal (as well as other) regions; and the strength of these connections was predictive of gains in numerical abilities (Evans et al., 2015). However, these studies did not include the cerebellum as a region of interest. As already noted above, one resting-state FC study has compared RD + MD children to RD-only, MD-only and Controls (Skeide et al., 2018), and found that RD + MD had reduced intrinsic connectivity between right para-hippocampal gyrus and right intraparietal sulcus in comparison to the other groups, but did not include the cerebellum in their region of interest analysis (Skeide et al., 2018).

When considering the literature in children with math disability, a seed-to-voxel study found more background functional connectivity between intraparietal sulcus seed and cortical regions (including bilateral superior frontal cortex), as well as the left cerebellum (including bilateral crus I and left crus II) in the group with MD relative to controls (Michels et al., 2018). Another seed-to-voxel study also found relative hyperconnectivity between left and right intraparietal sulcus seeds and the bilateral fronto-parietal network in children with MD (Jolles et al., 2016). Jolles et al. also used an alternative method (fractional amplitude of low-frequency) to explore intrinsic brain dynamics without a priori ROIs and found an increased aberrant fluctuation within bilateral cerebellum for the MD group when compared to the control group. Therefore, although Jolles et al., did not report cerebellar FC with the seed-to-voxel analysis, both studies found increased intrinsic connections of the cerebellum in the MD group relative to controls. In contrast, our results did not find significant differences between groups for cerebellar-cortical connectivity.

Turning to the gPPI FC analysis to test for task-dependent functional connections during arithmetic using the same cerebellar seed and cortical target regions, we found no task-dependent FC during arithmetic in the Control nor the RD + MD group and no between-group differences. Although no prior task-dependent connectivity studies have been performed in RD + MD children for arithmetic tasks, task-dependent connectivity studies on MD children are useful for the interpretation of this result. One such study reported hyper-connectivity between a seed in the intraparietal sulcus and multiple brain systems including the lateral fronto-parietal and default mode networks in children with MD during arithmetic (addition and subtraction) processing (Rosenberg-Lee et al., 2015). However, the cerebellum was not one of these regions included in this seed-to-voxel analyses.

Taken together, this is the first study investigating cerebellar function in co-occurring reading and math disability. Our results are important in terms of understanding the brain-bases of these disorders as well as implications for treatment. We offer information on brain activity, task-independent background functional connectivity and task-dependent functional connectivity, all performed with special focus on the cerebellum. We found no differences between the group with RD + MD and controls on any of these measures. While our lack of a between-group difference is not unexpected given prior studies in RD or MD, it is important to discuss potential factors that may have led to the reported null results, including sample size, tasks, use of IQ as a covariate, and participants. One common concern is sample size. To ensure that the lack of results for activation of the cerebellum for reading or arithmetic when contrasted to the Active Control conditions was not due to insufficient statistical power, we conducted a post hoc analysis combining the two groups (Controls together with RD + MD group). For both real word Reading (n = 49) and Arithmetic (n = 30) relative to the Active Control tasks, we found no significant activation in the cerebellum. Moreover, we used Bayesian statistics to test for support of the alternative hypothesis and did not find it for any of the eight cerebellar sub-regions. Future studies in even larger samples would be beneficial to bolstering these findings. The tasks used here to elicit activation during reading and during arithmetic have been used previously by us and others. In our own work in children, we found them to induce robust activation in the cortex during reading (Turkeltaub et al., 2003; Olulade et al., 2013) and during arithmetic (Evans et al., 2014, 2016; Brignoni-Pérez et al., 2021); and both tasks have revealed between-group differences (Olulade et al., 2013; Evans et al., 2014). As such it is unlikely that the lack of task-specific cerebellar activation and between-group differences in the current study is related to these specific tasks. Our groups were not matched on IQ, and one may wonder if using IQ as a covariate in our analyses as we did, may have taken away from potential group differences, since IQ is correlated with our cognitive domains of interest. To address this possibility, we repeated our analyses without using IQ as a covariate, yet still found no between-group differences.

Our participants were users of an alphabetic writing system and the background literature presented here primarily reports on prior studies conducted with participants using alphabetic languages. However, as noted in the Introduction, there are reports of greater activity in the cerebellum (Feng et al., 2017; however not in Li et al., 2020); and stronger functional connectivity between the cerebellum and cortical regions known to subserve reading in Chinese children with reading disability relative to controls (Feng et al., 2017; Li et al., 2020). Future studies should investigate cerebellar involvement in children with RD + MD in logographic languages.

A challenge in the study of participants with learning disabilities is heterogeneity and even subtypes. It has been argued that the prevailing problem in RD entails poor phonological and orthographic processing, associated with left temporal–parietal and occipital-temporal regions, respectively, with poor phonological awareness being identified in the majority of children with dyslexia (Vellutino et al., 2004). While some have argued that RD can be accounted for by impairments in skill automatization due to abnormal cerebellar function, the prevalence of children with behaviors indicative of cerebellar dysfunctions (based on tests involving balance or fine manual skills) has been noted to be low among those with RD (Ramus, 2003; White et al., 2006). As such, even if there are cases of cerebellar anomaly in RD, they are likely to be in the minority and may not be detected in group analyses typically employed in brain imaging studies. Another challenge in studies of learning disabilities is that many, but not all participants will have received some intervention for their reading or math difficulties. While improvement or compensation mechanisms resulting from these efforts could obscure between-group differences, it has been noted that there is little evidence for robust, systematic brain-based changes following treatment in reading disability (Krafnick et al., 2022; Perdue et al., 2022). Even if our participants had received intervention, they were still significantly impaired in their skills, performing below the 16th percentile in reading and math.

While we set out to test for differences in the cerebellum associated with reading and differences associated with arithmetic, we did not have firm expectations as to whether these would be in the same or in separate regions of the cerebellum. The former seemed most likely given that theories on the role of the cerebellum in reading or math both focused on the same functional aspects of the cerebellum (e.g., automatization), and given the high comorbidity rate between RD and MD. While we would not have been able to attribute differences in our two groups for both tasks to the same neural populations if they had been found to be in the same region of the cerebellum, establishing whether and where such differences exist for both reading and arithmetic was an important first step, and we found this not to be the case. Also, neuroanatomical measures, such as gray matter volume, cortical thickness and white matter tracts (which were not included in our review of the literature) could also be added as measures in future studies of RD + MD.