AI-powered tutors that interact with students in question-answering scenarios using large language models (LLMs) as foundational models for generating responses represent a potential scalable solution to the growing demand for one-to-one tutoring. In fields like mathematics, where students often face difficulties, sometimes leading to frustration, easy-to-use natural language interactions emerge as an alternative for enhancing engagement and providing personalized advice. Despite their promising potential, the challenges for LLM-based tutors in the math domain are twofold. First, the absence of genuine reasoning and generalization abilities in LLMs frequently results in mathematical errors, ranging from inaccurate calculations to flawed reasoning steps and even the appearance of contradictions. Second, the pedagogical capabilities of AI-powered tutors must be examined beyond simple question-answering scenarios since their effectiveness in math tutoring largely depends on their ability to guide students in building mathematical knowledge. In this paper, we present a study exploring the pedagogical aspects of LLM-based tutors through the analysis of their responses in math dialogues using feature extraction techniques applied to textual data. The use of natural language processing (NLP) techniques enables the quantification and characterization of several aspects of pedagogical strategies deployed in the answers, which the literature identifies as essential for engaging students and providing valuable guidance in mathematical problem-solving. The findings of this study have direct practical implications in the design of more effective math AI-powered tutors as they highlight the most salient characteristics of valuable responses and can thus inform the training of LLMs.