In her previous post, Sara described the difference between surface and deep structure in math word problems. Here, she talks about how students transfer prior knowledge to new situations.
Applying past knowledge to new situations or problems is called transfer.
As many of us have experienced, getting a child to transfer knowledge isn’t always easy. The ‘laps around the track’ problem that I gave my 7-year-old son was a poignant example for me. Students will often focus so much on the unfamiliar surface structure of word problems that they miss the deep structure. They don’t realize that they actually have the skills to solve the problem.
Why do students put so much emphasis on surface structure? Because it’s the clearest part of the problem. The surface structure is written out and obvious, whereas the deep structure is hidden and unclear. It seems more efficient to work with obvious and concrete information rather than take haphazard stabs at what the deep structure might be.
It is important to remember, however, that paying attention to surface structure – the content of the words, the meaning of the story – is actually a necessary step when we’re learning new information. We learn new information by connecting it to information we already know.
For example, the other day my son was reading a children’s non-fiction book about murals. I know that he already has some background knowledge on the concept of art: painting and sculpture are kinds of art, Picasso and Van Gogh are famous artists, paintings are done on paper or canvas, etc. After reading the book, he fit the new information about murals into his conceptual understanding of art. Since he already had some context of what art is, he was able to fit this new art form into his previous understanding of art. As time goes on and he gains more knowledge and exposure to this topic, this understanding will grow and deepen.
If there’s no background knowledge or context for understanding a new fact or idea, the chances of a student learning is pretty slim.
When a student focuses on the surface structure of a problem (like laps around a track), he’s recalling related background knowledge (laps, tracks, runners) to see if it will help to solve it, or to see if there’s anything new that can be attached to what he already knows. If this is how we learn and understand, we can hardly fault a student for placing so much emphasis on the surface structure. Though surface structure can be helpful for absorbing new conceptual information, it wasn’t enough to help my son solve the “laps around the track” addition problem that I presented to him.
How can we help students recognize deep structure, which is also a very important skill, and promote transfer?
The short answer: lots of practice.
In my next post, I’ll go into more depth about how to help transition from surface structure to deep structure.