Recent progress in speech recognition has relied on models trained on vast amounts of labeled data. However, classroom Automatic Speech Recognition (ASR) faces the real-world challenge of abundant weak transcripts paired with only a small amount of accurate, gold-standard data. In such low-resource settings, high transcription costs make re-transcription impractical. To address this, we ask: what is the best approach when abundant inexpensive weak transcripts coexist with limited gold-standard data, as is the case for classroom speech data? We propose Weakly Supervised Pretraining (WSP), a two-step process where models are first pretrained on weak transcripts in a supervised manner, and then fine-tuned on accurate data. Our results, based on both synthetic and real weak transcripts, show that WSP outperforms alternative methods, establishing it as an effective training methodology for low-resource ASR in real-world scenarios.