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Brainteasers and College Readiness

Ben Johnson

Administrator, author and educator
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"Hey there! You like knock-knock jokes right? Ok, I got a great one for you. Here it goes. Ready? You start..."
"Ok, knock-knock..."
"Who's there?"
"Ah, ..."
"Well... say something..."
"Wait a minute! It's your knock-knock joke, why do I start it?"

I know that is how I felt when I went to college for the first time. I arrive at college and I said "Knock-knock. I'm here," and they said, "What do ya' want?" I responded, "Well, uh..."

Daniel Willingham, a cognitive scientist, wrote one of my favorite books, Why Don't Students Like School? In it he describes how students' brains work and how schools don't take advantage of how students' brains work. For example, he explains that as human beings we are full of ironies. He states that between our ears sits a magnificent memory storage and retrieval device yet it is ironic that we send students to school and when the return home, they appear to have retained very little, yet they can tell you the lyrics of the popular songs and a detailed storyline from the movie they saw last week.

It is ironic that there is such a push for higher thinking in school, but our brains were not made for thinking, they were made for remembering. It is ironic that I can remember what I ate for breakfast, but for the life of me I can't remember John Legend's name when his song "All of Me" comes on the radio.

Many of us love to do puzzles, Sudoku, crosswords, jigsaws, and the twisted nail things but can't figure out how to program the TV. The irony is that we love to pretend that we are thinking when, in fact, we are just remembering past experiences. We love puzzles that are challenging but when they get too hard -- when we have no past experience to fall back on -- we often throw in the towel.

Here, try this one (my favorite brainteasers are also the simplest): What goes up the chimney down, but not down the chimney up? There is one thing that seems to help us when we get stuck and have to think: heuristics or a process for solving problems. Draw a picture, ask questions, eliminate the obvious, brainstorm solutions, prioritize, etc. It doesn't matter what process we use, just as long as we feel we have made progress. We have two things to look at: a chimney, and a thing that can go up chimney while it is down and can't go down the chimney when it is up. What do we know about a chimney? (This is where the drawing helps.) What things go up and down by themselves and in chimneys? Hmmm...think, think!

The thing that I was most unprepared for at college was the idea that I had to come up with the ideas (knock-knock...). I didn't know how to think. I never really had to do it before. If I went to school and halfway listened, I got decent grades just because I could remember what I saw and heard. Math was a different story. I passed, but I never really understood what I was doing; it was making me think and come up with my own ideas. I was like a fish out of water -- quite uncomfortable. I'm still not really good at math, but I have more experience and things to remember that help me get by. Anyway, when I got to college, the lectures and labs were not enough to give me what I needed to know. I had to learn how to go out and get more knowledge.

In my book, Teaching Students to Dig Deeper, I listed ten college readiness traits that I wish I had when I went to college. So after all I said about us not being good thinkers, here is the list of what my ideal thinkers are like (derived from Dr. David Conley's research on what incoming college freshmen need to know and be able to do when they get to college):

  1. Analytic thinkers break things down in to small parts that are easier to understand.
  2. Critical thinkers judge the information and choose the most worthy things to know.
  3. Creative thinkers seek solutions to problems by synthesizing what they know.
  4. Inquisitive thinkers are always learning new things about the world around them.
  5. Opportunistic thinkers take advantage of learning from people who know more.
  6. Flexible thinkers are willing to admit they are wrong, and resilient enough to keep at it.
  7. Open-minded thinkers will listen and observe but reserve judgment for later.
  8. Teachable thinkers are thirsty for knowledge and are actively seeking answers.
  9. Risk-taking thinkers aren't afraid of looking at things in a different way.
  10. Expressive thinkers know how to research their ideas and share their vision.

Now if schools concentrated on these things we'd all be geniuses . Most schools and even the state testing don't have it wrong. Our brains can hold a lot and their job is to fill them. The only thing that is amiss is that they only go half way. Students get a lot of information, but really do not have a reason to retain it. That is where the thinking comes into play -- to drive the information deep into the recesses of that huge cranium between our ears.

Students like to think, but I think they just don't get the chance to do it often enough to become good at it (ok, they will never be "good" at it because their brains aren't designed that way, but they can become better at thinking and therefore, learning). So did you get the answer to my brainteaser yet? I'd like to read your thoughts on what you do to get students to think and your answer to my brainteaser. Please share in the comments section below.

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Ben Johnson

Administrator, author and educator

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SpTeacherJames's picture
Special Education Teacher, Tutor, and Education Consultant

I think Bon makes a good point: thinking is, by definition, what the brain does. I'm sorry, but I'm going to be that guy and post a dictionary definition. "to direct one's mind toward someone or something; use one's mind actively to form connected ideas " Remembering, synthesizing, analyzing, memorizing, and learning are all different sides to the same coin. Problem solving, a la Curt seems like the issue at hand. "Solving problems when memory fails and experience is lacking." Thinking does not equal problem solving.
That being said, I agree that our schools do little to help students find creative solutions to new problems for which they have no previous heuristic. With the world of technology growing at an exponential rate, most of the problems our students will face as adults are going to be completely unknown to us now. We need to prepare students to solve unknown problems by providing them with problem solving strategies, and help them to find out which approaches (your # 1-10) work best for them.
Finally, I want to take a crack at the triangle with 2 right angles. Take 2 right angles: (angle ABC and angle DEF) If one of the segments of the first right angle (AB) passes through the center point (E) of the other right angle, and point C and F were to match up, the resulting shape would be a right triangle (triangle EBC). Its easier to draw, but I hope the letters help.
Great article!

Ben Johnson's picture
Ben Johnson
Administrator, author and educator


Way to go! You are correct. A baseball player is the answer. How did you get to that answer, may I ask? Was it a process of elimination (analytical thinking), was it categorizing all of the professions with masks (analytical thinking), or was it thinking about what masks, and turning left have in common (analytical thinking). How did you test your theory (critical thinking)? Just curious...

Thanks for posting
Ben Johnson
San Antonio, Texas

Ben Johnson's picture
Ben Johnson
Administrator, author and educator


Well done. It is an umbrella. Lets see if the answer to this one pops into your head... What jumps higher than a mountain? I got this one from my daughter, Mercedes. Have fun!

Thanks for Posting.

Ben Johnson
San Antonio, Texas

Ben Johnson's picture
Ben Johnson
Administrator, author and educator


Thanks for your comments and taking a crack at the triangle with two right angles. If I just tell you the answer, what is the fun in that? Instead, I will ask you a questions. Is Euclidean geometry the only geometry?

Ben Johnson
San Antonio, Texas

PS, I tried to draw your figure and don't think I did it right. Here is another one... draw a quadrilateral with just two right angles.

Laura Thomas's picture
Laura Thomas
Director, Antioch University New England Center for School Renewal, Author of Facilitating Authentic Learning, Director of the Antioch Critical Skills Program; Elementary Library Media Specialist

According to MY daughter, "Nothing. Mountains don't jump."

Thanks for a fun post!

Bon Crowder's picture
Bon Crowder
Math Mom & Education Advocate

I'm not sure everyone (or even nearly everyone) DOES love a good brain teaser. One of the things that fascinate me is how different people like different puzzles/games/activities. And how many of those are equally hated.

I, like anyone, need the right balance of capability and challenge. If I get the feeling there's some semantic dodge in the puzzle, I'm out. I'd rather hear about the priest that says, "Brothers and sisters, I have none, but this poor man's father is my father's son." That's logic. Not words.

When you go into a triangle with two right angles, I think, "How are you defining a triangle?" And then I wonder if there's some cutesy little thing to it. Then I quit. No fun. Game over. Move on to something else more interesting.

And then you have the case where there's some important piece of information to be discussed and someone throws a brainteaser into it. I do this to my daughter. "Let's go take a bath. Hey, your tickle bone is open... gonna tickle..." Totally gets her sidetracked and I end up tickling her into the bathroom and before you know it, her hair is sudsy.

I guess I was a bit annoyed that you used brainteasers to illustrate thinking instead of actual real-world problems. Real world problems would have illustrated your point and kept the reader (me) focused on the goal: thinking about how we think.

Instead you used brainteasers which felt more like a covert attempt to get me to like the article because I enjoyed the teaser, than to enjoy the article because of the content. (Which I DID enjoy the content, but was pull away from the content because of the teaser!)

Which makes me wonder how many times we disengage students because we're trying too hard.

Kay Butler's picture
Kay Butler
HS Mathematics and MS/HS Pre-Engineering teacher, from South Louisiana

In non-Euclidean geometry there are triangles with two right angles! :)

Kay Butler's picture
Kay Butler
HS Mathematics and MS/HS Pre-Engineering teacher, from South Louisiana

Oops! Just getting accustomed to working on an iPad -I accidentally posted twice but could not delete the extra one, so you get to read this instead! ;) I love to think and solve problems - never any time for boredom! I, too, am fascinated by the multiple degrees of interest in various puzzles!
If you haven't seen this yet, you may want to check it out - related to both real world and logic puzzles!
Check out several episodes! Neat activities!

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