Knowing vs. Understanding

What is the difference between knowing something and understanding something? In this blog, I hope to differentiate between the two and provide a clearer understanding. I would like to start by defining the two terms:

knowing: 1. affecting, implying, or deliberately revealing shrewd knowledge  of secret or private information. 2. that knows;  having knowledge  or information; intelligent. 3. shrewd, sharp, or astute. 4. conscious; intentional; deliberate.

understanding: 1. mental process of a person who comprehends; comprehension; personal interpretation. 2. intellectual faculties; intelligence; mind: a quick understanding. 3. superior power of discernment; enlightened intelligence:

***Definitions came from  http://dictionary.reference.com/browse/knowing and  http://dictionary.reference.com/browse/understanding

To know something can often be achieved by simply memorizing facts or statistics, for example: She knows her multiplication tables; when asked, “what is 6 x 8?” she will reply “48.”  The child has memorized all of her multiplication facts through repetition and can regurgitate the information on demand.

Using that same example, the student truly understands multiplication when she recognizes and understands the patterns  well enough that she can explain the concept to someone else and she can apply her knowledge of multiplication in a real world situation. The child understands  6 x 8 is the same as 6 +6+6+6+6+6+6+6

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