Longtime NW tutor Sara shares an “a-ha!” teaching/learning moment she experienced with her son. It’s so wonderful when we learn as much as our own children and students!
My 7-year-old son and I watched my older child compete in a track meet. It was a chilly day, and we’d been standing outside, huddled under our coats, for about an hour. As we stood at the fence waiting for the next event to begin, my son sighed, looked up at me and said, “Mom, I’m bored.”
The teacher in me always looks for moments like these to squeeze in some mental activity, so we started talking about the track.
“Do you know how many meters long the track is?” I asked. He shook his head. “It’s 400 meters,” I said. “So when a runner does one lap around the track, he runs 400 meters.”
That seemed to make sense to him, so I figured I’d start off with an easy problem. “All right,” I said, “so if a runner does two laps around the track, how many meters is that?”
I’ll never forget the look of surprise on his expressive face. Shaking his head, his brow knit with genuine confusion, he responded, “What? Mom, I don’t know. We’ve studied meters before in school, but we’ve never studied tracks!”
This time, it was my turn to be surprised. My son was in second grade, so I knew he had the arithmetic skills necessary to compute 400 + 400. But for some reason, he didn’t recognize that this was just an addition problem. I smiled and crouched down next to him so that we could talk through how to get the answer. In the back of my mind, I was at work on a problem of my own: why was he so baffled by what I thought would be a simple problem?
The answer, I found, lies in the concept of the structures of problems, explained by Daniel Willingham in his book Why Don’t Students Like School?.
Word problems, such as the one I gave to my son, all have two elements to them: their surface structure and their deep structure. We adults recognize immediately that the ‘laps around the track’ problem is, at its core, an addition problem; that is, its deep structure is an addition problem. The fact that we’re talking about meters on a track does not change what we do to solve the problem. Actually, we could quite easily think of dozens of ways to “disguise” problems with the same deep structure:
The “disguise” is the surface structure of the problem. And, as you probably noticed in the last two examples, the surface structure need not even be familiar (or pronounceable) for you to recognize the deep structure and solve the problem.
The disconnect that arose for my son is that while he had the skills and knowledge necessary to solve the problem, he got hung up on the surface structure of the problem – laps around a track, which he had never formally studied – and failed to recognize the deep structure – addition, something he’s been practicing for months on end.
Being able to apply knowledge to new and unfamiliar problems is called transfer, and it’s something that we teachers and parents try to encourage in our kids. But, as you may have noticed with your own kids, knowledge transfer isn’t easy. There are reasons why it’s tough, and there are things we can do to promote knowledge transfer – but we’ll get into those another time. For now, see what you can do identify the surface and deep structures in problems you encounter – and have patience with your kids (or yourself!) during the countless repetitions of problems that will be necessary for successful transfer of knowledge.
Kim has a bachelor’s degree in public administration from University of Arizona, a master’s degree in special education from University of Illinois at Chicago, and a master’s degree in educational leadership from American College of Education. She previously worked as a teacher for fourteen years, and as a tutoring director for Nurturing Wisdom—we’re excited to have her back on the team! Learn more about her below.
My favorite class in high school was…geometry (although I prefer algebra) because my teacher, Mr. Warwick, was organized and explained the concepts in an engaging and understandable manner. He made me feel confident when asking questions and was always open to teaching material in a variety of ways.
I loved UIC because…it allowed me to explore Chicago and meet incredible people while working in a variety of schools and educational programs. The Graduate College of Education had teachers that provided real world context and were very supportive to students’ individual goals.
On a day off, you’ll find me…at a sporting event for one of my four daughters, floating down the DuPage River, or at the dog park with my dog, Daisy.
What sets Nurturing Wisdom apart is… the individual care we take with the families we work with and the strong team behind each tutoring decision, including tutoring plans, curriculum, and tutor matches.
Sarah graduated from Marquette University with a bachelor’s degree in education and sociology, and she’s completed coursework in childhood literacy and museum studies. After nine years as a fifth grade teacher in Wauwatosa, Portland, and Chicago, Sarah initially joined NW as a tutor. Learn more about her below!
A tip I’d give to a student to make the most of tutoring would be… that you get out of it what you put into it. If you put in time and energy, and bring a positive attitude, you’ll achieve so much!
I loved Marquette University because… it put me on the path to teaching, introduced me to amazing, life-long friends, and made me fall in love with Milwaukee.
On a day off, you’ll find me… taking a long walk to a coffee shop, chatting with friends, or going on a bike ride and cooking while listening to my latest podcast obsession.
What sets Nurturing Wisdom apart is… that everyone on the team is a life-long learner at heart, and that we care about the whole student. Everyone is dedicated to getting to know families in order to find a great fit for students and tutors.
Shannon has a degree in marketing from Creighton University. After working in the business world for over five years, she decided to go back to school to get her master’s degree in elementary education from Quincy University. Learn more about her below!
My favorite book is… The Sun Also Rises by Ernest Hemingway. This is an amazing book that made me want to travel and see more of the world.
My favorite subject in school was… history because I loved learning more about the world and how the past helped shape who we are today.
On a day off you’ll find me… hanging out with family and friends. In the summer, usually doing something fun outside.
What sets Nurturing Wisdom apart is… it’s team approach to tutoring as well as it’s individualized curriculum! Both the team approach and the curriculum make tutoring and learning more fun and efficient.