Peer tutoring can improve learning by prompting learners to reflect. To assess whether peer interactions are conducive to learning and provide peer tutoring support accordingly, what tutorial dialog types relate to student learning most? Advancements in collaborative learning analytics allow for merging machine learning-based dialog act classification with cognitive modeling of fine-grained learning processes during problem-solving to illuminate this question. We estimate how much peer-tutored students improve in a collaborative tutoring system for linear equation-solving in K-12 mathematics in relationship to the peer dialog types they engage in. This work establishes a reliable BERT classifier with an accuracy of close to 80\% to classify chat messages during peer tutoring into minimal, facilitative, and constructive, serving as instructional factors. Based on data from 394 students, peer tutor dialog was rare. Only 8\% of tutee problem-solving steps were followed by peer tutor chat messages. Still, facilitative tutor dialog was associated with an increased tutee learning rate. Meanwhile, tutor dialog classified as constructive was associated with lower learning rates. Content analysis suggested that such dialog often reinforced incorrect solutions, gave away answers, or was unrelated to the taught content. Hence, considering problem-solving solution contexts could improve the assessment of peer tutoring dialog. Peer tutors engaging in little dialog could be attributed to the high cognitive demand of learning to tutor while still learning the content they tutor on. Providing peer tutors with instructional support to engage in constructive dialog may improve the tutee's learning.