  Large language models (LLMs) present an opportunity to scale high-quality
personalized education to all. A promising approach towards this means is to
build dialog tutoring models that scaffold students' problem-solving. However,
even though existing LLMs perform well in solving reasoning questions, they
struggle to precisely detect student's errors and tailor their feedback to
these errors. Inspired by real-world teaching practice where teachers identify
student errors and customize their response based on them, we focus on
verifying student solutions and show how grounding to such verification
improves the overall quality of tutor response generation. We collect a dataset
of 1K stepwise math reasoning chains with the first error step annotated by
teachers. We show empirically that finding the mistake in a student solution is
challenging for current models. We propose and evaluate several verifiers for
detecting these errors. Using both automatic and human evaluation we show that
the student solution verifiers steer the generation model towards highly
targeted responses to student errors which are more often correct with less
hallucinations compared to existing baselines.
