Is this real?

Today, part 2 of Harry Potter and the Deathly Hallows is available in stores. When the movie opened in theaters this past July, I used it as an opportunity to write about teaching as storytelling. In this post, I want to take a look at a particular exchange between two main characters and consider what it might mean for teaching and learning mathematics. Warning - spoilers ahead.

The following happens near the end of the story. Harry has sacrificed himself to save his friends and finds himself in an ethereal version of King's Cross Station talking with his deceased mentor, Albus Dumbledore. The conversation is nearly over when this brief exchange occurs.

     "Tell me one last thing," said Harry. "Is this real? Or has this been happening inside my head?"

     Dumbledore beamed at him, and his voice sounded loud and strong in Harry's ears even though the bright mist was descending again, obscuring his figure.

     "Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real?"

There seems to be a strong push in mathematics education to attach some real-world significance to nearly every topic in the curriculum. I appreciate the effort and agree that content a learner can connect to is more likely to be engaging. For me, however, the search for context to wrap around content can sometimes be distracting and inauthentic.

How can real-world examples be inauthentic? Let me provide a personal example. As a middle school mathematics teacher, I often extolled the practicality of learning to add and subtract fractions with unlike denominators. I would say, "You'll need this skill in cooking and building." Now maybe someone else can pull this off in an authentic way, but I cannot remember ever adding or subtracting fractions outside of an educational setting. Granted, I do not cook or build anything from scratch so I may be missing something. This only reinforces that this purpose was inauthentic to me and a distraction to my learners.

My problem was that I was confusing context with purpose. I now explain to learners that the rationale behind our lessons on fractions are related to the NCTM Process Standards and not some potential future use. I do not know if my learners will ever need to add or subtract fractions while cooking. I am sure that their future success will depend on their ability to problem solve, reason, communicate their thinking, use representations, and make connections. Yes, even connections to the real-world. 

Let me be clear that I am not suggesting context is not important. In order to learn something new, we need to connect to something known. Looking back, I am not sure how many 8th-graders have experience with cooking and building. They are familiar with time, however, which is why I like using the clock model. They also have worked with whole numbers, and I often try to connect to these computational experiences. Sometimes the mathematics itself is the context.

Essentially, it is about finding what is real for my learners. Certainly, there will be times when their reality is at odds with that of the mathematical community - that is when the fun begins. I can only hope that my learners, like Harry, will begin by asking, "Is this real?"

What's the story?

Hogwart's Express?

I am a huge fan of J. K. Rowling's work. She is a fantastic writer who has introduced a new generation to the magic of reading through her Harry Potter series. My guess is that she was also an excellent teacher. While I have never seen her teach in a classroom, I believe effective teachers are essentially storytellers.

First, there is Ms. Rowling's phenomenal ability at writing backstory. This is the part of the narrative that provides background supporting a better understanding of story. She flawlessly weaves this information throughout her writing. It is akin to what effective teachers do when they help learners to activate schema during a lesson - providing a firm foundation on which to construct new ideas. The ability to make connections is fundamental to teaching and learning.

Could this hat do more than sort?

Foreshadowing is the literary device used by authors to provide readers a subtle peek at future plot points. Again, here Ms. Rowling is a master. Once I was aware that her books included clues about the upcoming story, I began reading (and rereading) the text even more deeply. Imagine teaching a lesson that has learners engaged with every moment because it has purpose - they don't want to miss something important that they can use in later learning. I see this as being related to Cambourne's ideas of engagement and immersion.

Another thing I like about the Harry Potter series is that there doesn't seem to be any wasted effort. The story always moved forward. And while there were times that we were introduced to characters, settings, or events that seemed superfluous, they almost always ended up playing an important part in the resolution of the story. This reminds me of what I have read so far in Mike Schmoker's book, Focus. In order to be effective, teaching needs to maintain momentum toward a clear set of manageable goals.

This car plays a part in several books

Certainly, storytelling is not the only simile that can apply to effective teaching. It just seems fitting to explore it the day the second part of Harry Potter and the Deathly Hallows is released in US theaters. Maybe I'll write my "teaching is like kayaking" post after my next trip to the UP. It is the rationale supporting the simile that is most important - that is where we find the characteristics of effective teaching.


(If you want more evidence of Ms. Rowling as an effective teacher, then consider her 2008 graduation speech at Harvard and her characterization of effective teachers in her writing.)