Deep Convolutional Neural Networks (CNN) are at the backbone of the state–of–the art methods to automatically analyze Whole Slide Images (WSIs) of digital tissue slides. One challenge to train fully-supervised CNN models with WSIs is providing the required amount of costly, manually annotated data. This paper presents a semi-weakly supervised model for classifying prostate cancer tissue. The approach follows a teacher-student learning paradigm that allows combining a small amount of annotated data (tissue microarrays with regions of interest traced by pathologists) with a large amount of weakly-annotated data (whole slide images with labels extracted from the diagnostic reports). The task of the teacher model is to annotate the weakly-annotated images. The student is trained with the pseudo-labeled images annotated by the teacher and fine-tuned with the small amount of strongly annotated data. The evaluation of the methods is in the task of classification of four Gleason patterns and the Gleason score in prostate cancer images. Results show that the teacher-student approach improves significatively the performance of the fully-supervised CNN, both at the Gleason pattern level in tissue microarrays (respectively κ=0.594±0.022 and κ=0.559±0.034) and at the Gleason score level in WSIs (respectively κ=0.403±0.046 and κ=0.273±0.12). Our approach opens the possibility of transforming large weakly–annotated (and unlabeled) datasets into valuable sources of supervision for training robust CNN models in computational pathology.