Puzzling Perseverance

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:

IMG_2684 

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.  )

IMG_2668

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:

photo 2

If you were wondering about how math-love girl #1 fared in completing the task, she persevered and impressed her skeptical cohorts:

photo 1

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.

Curiosity Driven Mathematics

In my very first years of teaching, I used to have students ask me, in that age-old, cliche teenage fashion, “When are we ever going to use this?”  I vividly remember my response being, “Maybe never.  But there are plenty of other things we do in life, like play video games, that have no real-world application. That doesn’t seem to bother us too much.”

In fact, if every moment of our lives needed to apply to the bigger picture, the REAL-world, when would we do anything for pure enjoyment? or challenge?  or even spite?  I know kids are capable of this because some of them spend hours upon hours a day engaging not only with a video game but also collaborating with other people through their game system.

And furthermore, where do we think this resentment for learning math really comes from?  I have a guess…probably adults who have realized that through the course of their lives, being able to solve a polynomial equation algebraically is not all that useful! News flash, math teachers:  Our secret is out! 

There are many kids across all levels of achievement that will not engage in the learning process simply because the state mandates it or the teacher swears by its real-world relevance.  Students (and arguably people in general) are motivated by immediate consequences and results and cannot easily connect that the algebra they are learning today will be the key to success in the future.  They do not care that if they don’t nail down lines, they’ll never have a prayer understanding quadratics.  If they are bored to death by linear functions, I can’t imagine that they have even an inkling of desire to comprehend the inner workings of a parabola.  

What does resonate with learners is the satisfaction of completing a difficult task, puzzling through a complicated scenario, or engaging in something for pure enjoyment.  Kids are naturally problem-solving balls of curiosity.   There are ways to provoke curiosity and interest while simultaneously engaging in rich mathematics.  I think many teachers assume that in mathematics, especially Algebra, curiosity and deep understanding need to be mutually exclusive, and I’m positive that mindset is dead wrong.  For example, show this card trick to any group of kids, and you’d be hard-pressed to find a group who isn’t trying to figure out how it works.  I also think you’d be hard-pressed to find the real-world relevance to a card trick.  It’s still no less amazing, as well as algebraic.  

 

 

Nrich – Factors and Multiples Puzzle

Nothing gets me more excited about teaching mathematics than a task that can engage my lower level students while simultaneously challenge my high achieving students. The Factors and Multiples Puzzle from Nrich did just that. (Thanks to @drrajshah for posting this on twitter.)

I’m glad I used this in multiple classes because if nothing else, it gave students the opportunity to learn about triangular numbers! What a testament to the fact that we don’t allow students to explore with numbers nearly enough: I’ll bet only one student out of 60 had any idea what triangular numbers were.  A fantastic, interesting set of numbers, arithmetically and visually, was unbeknownst to 99% of my students.

My math recovery students were intrigued by the puzzle portion of it. In fact, I have one student in particular who is not particularly motivated by much . He’s a ‘too cool for school’ kind of kid, and he’ll tell you as much. When I bust out a puzzle, he’s all in. And when I say ‘all in,’ I mean 100%, until he solves it. It’s pretty awesome stuff to have been able to catch his attention and see how cleverly he thinks through things. Amazing.

I also gave this task to a group of advanced students. An interesting strategy these students developed was to grab a whiteboard to work out some patterns in groups of numbers.  I loved walking around and hearing their strategies.  As some groups finished, they started walking around and giving tips (not answers) to other groups.  It was wonderful.

One of my particularly eager students taped his together uniquely.  I appreciated his humor.  🙂

fmp