In primary schools, Lesen durch Schreiben (LdS; “reading through writing”, known internationally as inventive spelling) is a prevalent didactic method of reading and spelling instruction. In LdS, pupils learn writing through prolonged inventive spelling, meaning that only phonological but not orthographic spelling errors are corrected. Rigorous studies of the effectiveness of LdS are scarce and have delivered inconsistent results, casting doubt on the suitability of LdS for primary school instruction. Empirical investigations of writing acquisition methods are time-consuming, costly, and are plagued by methodological evaluation difficulties, such as separating method effects from other instruction-related variables. In this work, we developed a computational framework (based on recurrent neural networks) for reading and writing acquisition. This framework enables us to extract and systematically investigate some core principles of writing acquisition methods. Focusing on two German corpora, we compared the behavior of learning agents trained using the LdS regime against agents trained using a classical, primer-based regime. Experimental results revealed that our LdS agents performed significantly worse than our primer agents in writing tasks and, to a lesser extent, in reading tasks. Our results show that the stereotypical spelling mistakes of children exposed to LdS can be replicated with neural network models. These mistakes arise naturally during writing acquisition for all learning agents but are either suppressed or reinforced depending on the learning regime. We examined the learned, internal representations of both agents and found deviations in the LdS agent that may have induced the amplified confusion of similar phonemes. While we focused on two German corpora, similar results can be expected for alphabetic languages with similar graphene-phoneme regularities. In sum, LdS does not exhibit benefits over standard instruction in our simulations. However, we urge caution in drawing immediate conclusions for human learners. Instead, our work presents a modest step towards the construction of a computational framework for writing and reading instructional methods that may inspire future research.