Is it possible to learn everything about a topic; to answer every question that can be asked?
Math teachers might point to the skill of addition, where 2 + 2 always equals 4.
But does it?
We would have to be assuming use of a decimal or base-ten numeral system, including all numbers from 0 to 10.
But what if we are using a binary numeral system; one based completely on 1's and 0's?
Can we solve this exact problem using a binary numeral system?
What if we wrote out the problem as a word problem?
We would say, "two somethings plus two somethings equal four somethings."
But can we say two glasses of water plus two glasses of water equal four glasses of water?
What if each glass had a different amount of water?
In what other ways might 2 + 2 not equal four?
This creative or divergent thinking is sometimes referred to as "out-of-the-box thinking" and is highly valued by employers and businesses worldwide. Being in the business of preparing students for college, career, and the world, shouldn't this be the kind of thinking we are inspiring in our students, not seeking to correct?
We must prepare our students for a world in which all answerable questions have been answered -- a world in which questions are more valuable than answers.
I know there are educators who value this kind of thinking. If you are one of them, please share your thoughts, in the comments section below.