School mathematics has a bad reputation for being intellectually unattainable and mind-numbingly boring for many students. Proclaiming the falsity of these beliefs is usually not enough to convince kids (or people in general) of their untruth. Students need to experience their own success in mathematics and be given the opportunity to engage in curiosity-sparking mathematics. For me, one of the very best moments in a classroom is when a self-proclaimed math hater fully engages in a challenge and is motivated to work hard to arrive at a solution.
Enter January 2nd and 3rd. Students are back for a two-day week which they view as punishment and a rude-awakening from a restful winter break. To boot, the Governor Dayton announced today at about 11 am that all Minnesota schools will close Monday, January 6th due to impending dangerously cold weather. You can imagine where the motivation level was in school today.
As the CEO of room 114, I decided to make an executive decision and do a puzzle from Nrich (shocking, I know) in my probability and statistics class. Technically, the students could use the mean or median to help solve the problem, so I wasn’t veering too far off of what I had previously planned.
The Consecutive Seven puzzle starts like this:
Initially, one student began by explaining to me that she took one number from the beginning of the set, one from the middle and one from the end. Then she figured the other consecutive sums needed to be above and below that number. (Spoiler alert: These numbers actually end up being the seven consecutive sums, so I was very interested in her explanation of how she arrived at those particular answers. )
It’s worth noting that this student’s first words to me at the beginning of the trimester term were, “I hate math and I hate sitting in the front.” So you can imagine my excitement when she dove in head first into this particular task, happily and correctly.
Adding to my excitement about the class’s progress, another girl (who was equally enthusiastic about math at the beginning of the term) was the first one to arrive at a correct solution. And although she probably wouldn’t admit it, she was thrilled when I took a picture of her work. And I am more than thrilled to display it here:
If you were wondering about how math-love girl #1 fared in completing the task, she persevered and impressed her skeptical cohorts:
This phenomenon fascinates and excites me that students, when confronted with a puzzle, highly engaged and motivated throughout the lesson. Dan Meyer summarized this idea nicely on his blog recently:
“The “real world” isn’t a guarantee of student engagement. Place your bet, instead, on cultivating a student’s capacity to puzzle and unpuzzle herself. Whether she ends up a poet or a software engineer (and who knows, really) she’ll be well-served by that capacity as an adult and engaged in its pursuit as a child.”
And who knows. Maybe one of the girls featured above will become a puzzling poet.
I am impressed! And love puzzles…especially number ones.
First things first – nice redesign of the page. Jealous…
I’m wrestling with an idea and I’d love to ‘hear’ some opinions. I am inclined to think that problems like this are worthwhile and I have gone through stretches where I use such a problem every day as the class warm up. However, I have also read some compelling arguments that warm up problems should be connected to the curriculum of the particular class. I have also seen that when I use these too often, interest wanes. One of my resolutions this year – especially for my Calc BC kids – is to devote one day per week on open problems. Sometimes they will be Calculus-based, but often they will be like this one. I think that by taking a day each week I will minimize the ‘problem-solving exhaustion’ that I saw sometimes and instead will make it more of a treat each week. This also gives me more breathing room to craft meaningful problem-solving days. I’m at more of a loss with my AP Stats group who represent a MUCH wider range of math talent/logical ability/interest. I need to figure out something for them.
I got premium for Xmas 🙂
Anyway, I think it’s possible to use these tasks regularly and have them align with your curriculum, rather than just a break from the schedule. In fact, in my college algebra class, most days contain problems like this. I spent a LOT if time this summer though combing through problems and aligning them with my topics.
I think it’s ore difficult to find these types of problems for stats, so I try to give them something interesting to discuss. That way the kids at both ends of the spectrum can contribute fully. Have you ever looked at Gapminder.org? I swear I could do an entire trimester of stats just on that site alone.
Good luck with your resolution. I’m eager to see how it works for you 🙂
This is precisely what the brain is designed to do: To solve problems,to figure out puzzles. It is what I kept telling my composition students. The brain wants problems; it needs problems to get stronger. The kind of problems you pose for students is like weight lifting for the brain.