In the panorama of modern education, one-to-one teaching holds a significant place. As the old African proverb elegantly phrases, "It takes a village to raise a child", perhaps it could be rephrased in the modern context as "It takes a great tutor to raise a scholar". The importance of a proficient and skilled tutor in shaping the academic and intellectual prowess of a student cannot be undermined. Therefore, when embarking on the quest to find a great tutor, it is essential to arm oneself with the right questions that can act as a compass in this journey. These questions will help to uncover important information about the tutor and will essentially serve as a barometer in assessing the suitability of the tutor for the student's specific needs.

Firstly, inquire about the tutor’s qualifications and specialization. The Socratic approach, considered one of the oldest and most powerful teaching methodologies, asserts that the teacher must have a deep understanding of the subject matter. This knowledge equilibrium enables the tutor to navigate the student through the labyrinth of complexity associated with the subject. It's not just about possessing a degree; it's about specialization and mastery of a certain area that dictates the efficacy of a tutor.

The second question should involve understanding the tutor's experience. Drawing from the psychological theory of experiential learning by David Kolb, experience plays an instrumental role in facilitating effective learning. A seasoned tutor will have a repository of adaptive teaching strategies to cater to different learning styles.

Thirdly, dig into the tutor's approach to teaching. A proficient tutor should be familiar with various teaching methodologies and more importantly, should be able to adapt their approach based on the student's learning style. The pedagogical strategy of differentiation, which involves tailoring instruction to meet individual needs, is noteworthy in this context.

Furthermore, it would be prudent to ask about the tutor’s approach to homework. As Duke University professor Harris Cooper suggests, homework is a vital component of the learning process, reinforcing concepts covered during tutoring sessions. A great tutor will leverage homework to enhance the student’s comprehension of the subject.

Next, probe into the feedback mechanism used by the tutor. Feedback is a significant aspect of the teaching-learning continuum. The sociocultural theory of learning espoused by Vygotsky emphasizes the importance of social interactions in learning, and feedback is a crucial element of this interaction.

Additionally, delve into the tutor's plan for a standardized test preparation if applicable. Here, the key is to understand the tutor's approach towards balancing the curriculum and the test preparation.

Subsequently, ask the tutor about their expectations from the student and the parents. This question will help to understand the tutor’s perspective on the roles and responsibilities of the key stakeholders in the tutoring process.

Inquire about the tutor's availability and flexibility. The theory of time decay in learning propounded by Ebbinghaus suggests that longer time gaps between learning sessions can lead to forgetting. Hence, a tutor's availability at regular intervals is of paramount importance.

The penultimate query should involve understanding the tutor's policy on cancellation of sessions. This is a practical question that will help to avoid any future disagreements.

Lastly, it would be beneficial to ask for references. This can provide valuable insights about the tutor from a third-party perspective.

The process of finding a great tutor might feel like navigating through the complexities of Fermat's Last Theorem. However, armed with these ten essential questions, you will be well equipped to decode this theorem and find that great tutor who can be the guiding North Star for your child's academic journey. Remember, education is not the filling of a pail, but the lighting of a fire. A great tutor will not merely fill your child's mind with information but will ignite the flame of curiosity, learning, and wisdom.