In previous posts, Sara introduced the concept of surface structure & deep structure when it comes to problem solving. She then went on to describe the ways the surface structure of problems can help students understand certain aspects of those problems or concepts. Now Sara goes into more detail about how, through knowledge transfer, we can help students move beyond the surface structure of problems to understand their underlying deep structure.
When we transfer, we apply past knowledge to new situations or problems. This is an essential part of how we define learning. We can’t say that we’ve really mastered a concept or skill until we can apply our knowledge in different situations. The question is: how can we promote transfer?
As I explained in my last post, students have an easier time recognizing deep structure if the surface structure is familiar. The key point here is that familiar surface structure is not necessary to solve a problem. But it is helpful. I’ve noticed that when working with ACT students over the years, most of them have an easier time tackling percentage word problems when they have a familiar context. Take these examples:
Even though the calculations are identical, most high school students have an easier time with the first problem because they’ve had experience with leaving a tip at a restaurant. It’s rare that you’ll find a high school student who has experience determining retail prices based on wholesale cost!
In the same vein, if my son had had more experience with track and field, he probably wouldn’t have balked at the ‘laps around the track’ addition problem. He’d probably have more confidence tackling this problem: “If an artist uses 2 cans of paint to make one mural, how many cans of paint would he need to make 2 murals?” than he would this problem: “If there are 2 hydrogen atoms in one molecule of H2O, how many hydrogen atoms are in 2 molecules of H2O?”
What we can take away from this is that the more exposure a student has to different subjects, the easier it will be to transfer knowledge. And the easier it will be to learn new information, period! Encourage your children to expand their base of knowledge by going to museums, reading books, participating in extracurricular activities, and engaging them in conversation on different topics. This is a case where more is definitely better!
As helpful as a wide base of knowledge is, a student doesn’t need to be familiar with the surface structure of a problem in order to recognize its deep structure. How can we promote knowledge transfer to unfamiliar contexts?
The answer: lots of practice!
This may seem oversimplified, but the truth is that it’s easier said than done. I think most of us know that practice is a necessary part of learning. It follows that the more practice a student has with different types of problems, the more apparent the deep structure of those problems becomes. After all, when I think of the variety of addition problems that I’ve seen in my lifetime, the amount of exposure my 7-year-old has had seems minuscule. With more practice, the ‘laps around the track’ problem will become as simple to him as it was to me, and the deep structure of addition problems will eventually be unmistakable.
Practice has other benefits in addition to promoting transfer. It helps students retain information for longer periods of time. It also helps basic skills become automatic, which frees up “thinking space” in the brain for performing higher-level problem solving.
The tricky part is keeping students engaged during all that practice! Here are some tips from Willingham in Why Don’t Students Like School?:
At Nurturing Wisdom, our guideline is to provide an immense amount of practice, distributed over time, and across varied contexts. Looping, a technique we use when tutoring math, is one way we’ve managed to apply these guidelines with excellent results. I’ve begun using looping with my son for addition, subtraction, and now multiplication problems, whenever teachable moments arise. As a rising third grader, he’s hardly seen the end of stumping math problems – and I’m sure I’ve hardly scratched the surface of moments that I will be surprised and confused as a parent! – but we’re at least one step further along the path of his growth as a student, and I have a much better understanding of how to guide him along in the future.
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.