The math lesson on variables began with a simple prompt.
As Dan Rothstein, executive director of the Right Question Institute, tells the story: “The teacher presented the following equation: 24 = (smiley face) + (smiley face) + (smiley face).” Then, she asked her students to think of as many questions as they could about the equation. What did the students want to know about this expression? What were they curious about?
The rules that she gave her students were simple, Rothstein says: (1) Ask as many questions as you can. (2) Do not stop to judge, discuss, or answer the questions. (3) Write down every question exactly as stated. (4) Change any statements into questions.
With these rules established, the students began generating their questions. The first few were fairly straightforward: Why is the “24” first? What do the smiley faces mean? Why are there three smiley faces?
Then, the questions began to get more sophisticated: Can I put any number for a smiley face? Do the three faces mean something?
“And then question number eight was: Do the numbers have to be the same because the smiley faces are the same?” Rothstein says.
In just a few minutes of forming their own questions, the students had hit upon the key concepts underlying the use of variables in mathematics.
“At this point, the teacher can go home, right? She’s taught variables,” Rothstein jokes. “It’s just extraordinary.”
Something the Internet Can’t Replace
In most classrooms, the teacher supplies the questions that students must answer. Rothstein’s example shows how powerful learning can be when educators have students come up with their own questions to answer.
Years ago, I had the chance to spend most of a day with Stephan Wolfram, the genius thinker behind the knowledge engine, Wolfram Alpha. After Stephen demonstrated how students can find the answers to most of the traditional questions we ask in school, I became concerned that some teachers would not be happy with what could be interpreted to be the most powerful cheating tool ever invented.
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Stephen’s response was matter-of-fact: “The answers to essentially all of our traditional questions are available on the internet, and search technology will only become more sophisticated. What is not on the internet are the questions. The most important skill to teach students is to develop the most interesting questions.”
This is one of the reasons why Rothstein’s process of teaching students how to develop entire lines of enquiry is so important. Having access to all of the answers in the world from your cell phone will not do you any good if you do not know how to ask the questions that can lead to the answers.
Even without the web as our dominant media, teaching students to develop clear lines of inquiry goes all the way back to Socrates. The role of the teacher is not to give students the answers, but to challenge students to ask the right questions.
(Next page: Not just students asking the questions)