Tag: innovation

  • 10 Questions to Ask About a Math Problem

    10 Questions to Ask About a Math Problem

    I’m substitute teaching 5th grade Language Arts today. I just found a handout with a set of questions titled “Peck’s Questions.” I quickly figured out (with my amazing powers of deduction) that they were questions you could ask about a novel.

    After reading them, though, I thought, “Why don’t they have something like that for math?!”

    So I did some research.

    Before creating the super math list, I thought I would find out a little more about the original list.

    Apparently this Richard Peck guy is pretty famous in young adult literature. The list is officially titled, “Ten Questions To Ask About a Novel” and was published in the The ALAN Review in the Spring, 1978 edition. Here it is:

    1. What would this story be like if the main character were of the opposite sex?
    2. Why is this story set where it is (not what is the setting)?
    3. If you were to film this story, what characters would you eliminate if you couldn’t use them all?
    4. Would you film this story in black and white or in color?
    5. How is the main character different from you?
    6. Why would or wouldn’t this story make a good TV series?
    7. What’s one thing in this story that’s happened to you?
    8. Reread the first paragraph of Chapter 1. What’s in it that makes you read on?
    9. If you had to design a new cover for this book, what would it look like?
    10. What does the title tell you about the book? Does it tell the truth?

    The list allows students to dig in a little deeper to the novel. It helps them get creative and think about the story in ways they wouldn’t normally.

    And it trains them to do this with novels throughout their lives.

    Why a list of questions about math problems?

    Before creating them, I decided the questions should do the following:

    • Allow the student to dig in deeper to the math problem, and the math behind the problem.
    • Help the student to think about the problem in ways they wouldn’t normally.
    • Let the student get creative in thinking about the problem.

    And of course doing these things regularly will train them to continue to do this with all math problems through their lives.

    Ten Questions to Ask About a Math Problem

    1. Who do you think created this math problem? Was it a man or woman? How old were they?
    2. Who do you think first figured out how to do a problem like this? How long ago?
    3. Imagine this is a real problem asked by a real person. What is that person’s job? Why are they asking this question?
    4. Why does this problem use the scenario that it does?
    5. If you could rewrite the problem using the same numbers and getting the same numeric answer, what scenario would you use?
    6. What numbers would you use in the problem to make it easier? What numbers would you use to make it funny?
    7. Is there a story that can be created before or after this math problem that makes sense?
    8. Has the situation in the problem ever happened to you or someone you know?
    9. What about this math problem appeals to you? If nothing, why did you continue to work on it?
    10. If you had to illustrate this math problem, what would it look like?
    11. (UPDATE Nov 5 from suggestion in comments) Can you develop some sort of theory as a result of solving this problem?
    12. (UPDATE Nov 5 from suggestion in comments) How does this problem relate to problems you have encountered before?

    Will it work?

    Try using it yourself first. Get a feel for what each question means and how it might be answered.

    Then try it on your children. Which questions work? What questions should be changed — and to what?

    Share what you find in the comments or on twitter/x so we can have a super solid list of Ten Questions to Ask About a Math Problem!

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  • Dumb Questions? Aren't They All?

    Dumb Questions? Aren't They All?

    I was labeled an “airhead” in high school. Until today, I’ve avoided telling people that. The moniker had a real negative effect on me.

    I was known as the kid who asks dumb questions. If my peers wanted to waste the last five minutes of class and not have to start another topic, they’d whisper at me, “Ask one of your dumb questions.”

    “There are no dumb questions.”

    If you’ve never said these words, email me now and I’ll send you $10.

    You’ve said them, haven’t you?

    Yup — we all have.

    The fact is that every question is a dumb question. Because someone else knows the answer.

    And the more people who know the answer, the dumber the question is. And the more valuable it is to ask it.

    Just because everyone knows the answer to a question, doesn’t mean it’s the right answer. It’s just the safe answer.

    I asked a question with an obvious answer.

    The story of how I earned my “airhead” nickname is a rather curious one. It happened like this:

    We had a guest speaker, a grownup, in our debate class. He was explaining details of the debate topic, which involved transporting water across some distance.

    He drew a series of pumps and downward sloping pipes on the chalk board. He explained that water had to be pumped up every so many feet so it could continue traveling the decline.

    I watched and listened. I wondered why they didn’t just pump the water straight through a horizontal pipe.

    I asked, “So why do the pipes have to be tilted?”

    The grownup responded with a snicker, “Because water runs downhill.”

    In retrospect, it is clear to me that I was dealing with an idiot. He lacked the novel thought, as well as nurturing behavior, to wonder what a 14 year old might be thinking when she asked the question.

    My classmates joined in on the grownup’s joke. “Wow, you don’t know that water runs downhill,” they jeered, “What an airhead!”

    Who knows what would have happened…

    Suppose that grownup would have encouraged my line of questioning.

    “The pipes have to be tilted because we let gravity do most of the work.”

    “But why can’t we just pump it straight through horizontal pipes?”

    “It’s not efficient to do it that way.”

    “What does it mean to be efficient? Do we have numbers on that?”

    “I’m not sure. Maybe that bears some investigation.”

    Perhaps I would have proposed that we create a pumping system so powerful, and efficient, that we didn’t need thousands of pumping stations? That might have led to other innovations.

    There’s no telling.

    And yet his snide remark, which gave the other students encouragement to be mean, shut down all routes of novel thinking for me.

    At least in that class.

    The airhead learns best.

    Novel thought — creative thought — is the foundation of innovation. It’s the foundation of learning.

    In math, thinking outside the proverbial box is an efficient way for a student to learn. Asking crazy, airheaded, dumb questions gets a student thinking about all sorts of things.

    The effort put into this novel thinking to solve a math problem will seem high. But the depth and breadth of a student’s understanding when they do this is incredible.

    And that understanding will carry to other things — decreasing the effort to learn even more!

    So why not be an airhead?

    Kids start out being airheads — thinking novelly and creatively. And grownups (like the guest speaker in the debate class) have an uncanny knack for destroying it.

    When your kids ask a dumb question, refrain from being a grownup. Ignore the fact that everyone knows the answer to that. See what happens.

    Encourage your kids to ask dumb questions. Give prizes for the most dumb question of the day — the one that sparks the most novel and innovative thinking.

    Epi-blog

    By the way, my peers continued this nonsense for years. It might be easy for me to say that I stopped wasting my dumb questions on those idiots. But in fact, they were just as squashed as I was.

    They were covertly given permission to do it by our teachers (except for Mr. Berkebile), therefore they continued.

    Share your thoughts in the comments or on twitter/x.

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