The sphere of online learning has manifested a significant advancement in the realm of religious education, and when it comes to Islamic studies, the role of online Quran tutors has become increasingly pivotal. These tutors are specifically trained and experienced educators who facilitate the learning of the Quran via the internet, using a multitude of digital strategies and platforms to reach out to a global audience.

The online Quran tutor is essentially an educator who possesses the necessary qualifications to teach the Quran and its related studies. They are well-versed in Tajweed (the science of the rules of Quran recitation), Tafsir (interpretation of the Quran), and often the Arabic language, which is the language of the Quran. Furthermore, they have impeccable command over the digital tools, techniques, and platforms that aid in the teaching process. Given that they are dispersed across the globe, they offer unprecedented accessibility and flexibility to students of the Quran, irrespective of their geographical location.

To expound on the point of geographical accessibility, consider the Heckscher-Ohlin theorem in international economics, which postulates that countries export what they can most efficiently and plentifully produce. In the context of Quran tutors, countries with a rich Islamic educational infrastructure, such as Saudi Arabia, Egypt, and Pakistan, can 'export' their services to individuals residing in regions where access to such tutoring may be limited. This fosters a dynamic cross-border exchange of knowledge and ideas, making Quran learning a truly global endeavor.

The temporal flexibility offered by online Quran tutoring is another hallmark of this learning model. Given the asynchronous nature of many online learning platforms, students can access lessons at a time that suits them best. This deviates from the traditional model of learning the Quran, where students were required to adhere strictly to the timings set by the tutor or religious institution. Imagine the implications of this flexibility from the perspective of queuing theory, an area in mathematics which deals with the probabilities of waiting times. Asynchronous learning essentially eliminates the 'queue', maximizing the efficiency of the learning process for the student.

In terms of pedagogical delivery, online Quran tutors employ a variety of methods to facilitate learning. They use online whiteboards for visual demonstrations, audio and video communication tools for interactive sessions, and online tests and quizzes for assessments. This use of multimedia and interactivity taps into the principles of cognitive load theory, which posits that learning is optimized when extraneous cognitive load is minimized. By presenting information through various sensory channels, online Quran tutors help students absorb and retain information more effectively.

In the debate between qualitative vs. quantitative teaching methods, online Quran tutors strike a fine balance. While they focus on the qualitative aspects of Quranic learning such as understanding the meanings, context, and nuances of the verses, they also employ quantitative tools such as tracking progress and frequency diagrams, highlighting the number of repetitions or corrections required for a student to master a particular verse. This integration of both teaching methods maximizes learning outcomes.

Despite the aforementioned benefits, it’s crucial to acknowledge the potential drawbacks of online Quran tutoring. One of the primary concerns is the lack of physical presence. Traditionalists argue that this inhibits the formation of a spiritual bond between the student and the teacher, an aspect deemed important in Quranic learning. Furthermore, the digital divide can also pose challenges, as learners from low-income or rural areas may lack access to the necessary technological infrastructure.

Nevertheless, these challenges are not insurmountable. With concerted efforts towards digital inclusivity and innovative solutions to mimic the physical learning environment, online Quran tutoring can continue to thrive as a robust alternative to traditional Quran learning.

In conclusion, online Quran tutors have crafted a niche for themselves in the world of Islamic education. Their role in facilitating Quran learning by transcending geographical and temporal boundaries, employing a variety of pedagogical methods, and balancing qualitative with quantitative teaching methods is of immense value. As the digital landscape continues to evolve, so too will the role of online Quran tutors, catalyzing a dynamic and inclusive approach to Quranic learning.