## 6 Discussion  
The present study describes the application of new software for the assessment of STM in a wide set of different conditions (varying for stimulus type, input, and response modality, sequential versus simultaneous presentation, with and without concurrent articulation to suppress phonological coding, and with or without the presence of distractors in visual-motor response). First, a number of meaningful subgroups of learning disorders were identified through a proximity-based cluster analysis. Cluster analysis was judged preferable to actual diagnoses in order to study the distribution of STM scores in subgroups defined in a transdiagnostic perspective, not strictly following the cut-off approach on which specific diagnoses of different SLD types would necessarily be based. Indeed, individuals assigned to the same nosographic category (dyslexia, dyscalculia, etc.) usually show large variability as they may have different difficulties (e.g., speed vs. accuracy in reading; number system or number sense). Moreover, there is extensive overlap between disorders that are assigned to different diagnostic categories (homotypic comorbidity). An approach based on cluster analysis allowed us to study subgroups that were as distinct as possible at the functional level, irrespective of categorical labels. It is noteworthy that the cluster analysis, beyond a group with normal performance in all domains (TD), revealed three subtypes of learning disorders that could be characterized as follows: (a) a predominant disorder of reading accuracy (cluster 2) accompanied by a less evident impairment of mathematical abilities, especially affecting number fact retrieval; (b) a predominant disorder of mathematical skills (cluster 3), especially evident in coding (number writing) and number fact retrieval, along with a moderate degree of more general writing difficulties; and (c) a mixed disorder of reading and writing skills (cluster 4), with reading speed more affected than accuracy and writing impairments, especially evident in word spelling, i.e., with a strong orthographic component. These clusters are highly representative of the literature on comorbidity in specific learning disorders (see [75; 76]). Subsequently, the different subgroups were compared with respect to their performance profile in the various STM conditions assessed through the computerized platform. Figure 11: Mean scores (Logit-transformed, see Figure 6 and Appendix A) obtained for trials without (light turquoise bars) and with (dark turquoise bars) distractors on the ML_VV STM variables (NB, the condition without distractors is not to be considered as an appropriate measure of MI but only as a reference point). For all the overall STM variables, with the exception of MI_VV, TD children performed at a higher level compared with some or all of the SLD clusters. No significant differences with respect to overall STM variables emerged among any of the SLD clusters. However, not all children with SLD showed significantly lower performances compared with TD on all variables, whereby different degrees of impairment could be observed in the different clusters. More precisely, the group with mathematical disorders (cluster 3) was not significantly impaired on MO with auditory input and oral response (the \"span-like\" task), while the group with reading and writing disorders (cluster 4) was not significantly impaired on MO with either visual input and oral response or with auditory input and the visuomotor response. This might suggest that children with mathematical disorders are not particularly impaired in purely verbal memory (indeed, children in this cluster have greater difficulties in processes related to the number system than to the calculation system, and they especially struggle with number reading and number writing, possibly pointing to a problem in coding, i.e., in the use of cross-modal translation).