Chapter one of Integrating Differentiated Instruction and Understanding by Design claimed that because of diversity within student population (differences in culture, race, language, experience, disability, learning preferences, etc.), the education system needs integration of DI and UbD. The two cannot exist sufficiently without the other. Axioms provide goals for certain aspects and expectations for teaching. Corollaries ensure that every student will have access to the axioms. For example, in my classroom there will be the axiom (or expectation) to provide opportunities for my students to explore, interpret, apply, shift perspectives, empathize, and self-assess. I will provide a constructivist environment to ensure that students will create their own meaningful experiences.
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