Philosophers like Dear and Mahoney have argued that pedagogical mathematization in Renaissance Aristotelianism was a transitional form of genuine mathematization, not merely illustration.

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Dear and Mahoney(as referenced philosophers making an argument about Renaissance education): Historians of philosophy and science who studied how mathematics was taught and used in European universities during the Renaissance period.
Genuine mathematization(as a contrast to merely using math as an illustration tool): The deep integration of mathematics as the core language and logic of a field of study, rather than just using it for explanatory purposes.
Pedagogical mathematization(as a specific educational approach in Renaissance universities): The practice of using mathematical methods and language as a teaching tool to explain ideas, rather than as the fundamental foundation of a subject.
Renaissance Aristotelianism(as the historical period and philosophical tradition being discussed): A revival of the ancient Greek philosopher Aristotle's ideas and methods that became popular in European universities from roughly the 14th-17th centuries.

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