Chapter two of Fair Isn’t Always Equal talks about the concept of mastery. I particularly like the quote from Piaget: “Real comprehension of a notion or theory … implies the reinvention of this theory by the student. … True understanding manifests itself by spontaneous applications” (12). I agree with this. I feel like, when a student truly understands a concept, the best way they can show me that they have achieved this is by telling me not just that the concept is true, but why it is true. When I am a teacher, I will have my students demonstrate their knowledge in such a way that I can be sure they know why what they say is true is true. This can’t be the only criteria for understanding, though; I will feel more comfortable if my students can demonstrate to me that they understand how everything I have taught them fits together, as well. I feel that synthesis is important.
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