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ObjectLOGO is a programming language, an extension of the educational programming language LOGO. It integrates concepts from object-oriented programming into LOGO's turtle graphics. The syntax and constructs in ObjectLOGO allow users to create objects, and classes with inheritance, polymorphism, and encapsulation. This can help learners understand foundational concepts of computer science while also reinforcing mathematical thinking through geometry and algebraic logic within the interactive environment that involves moving a turtle-shaped cursor across the screen to draw shapes or patterns.