Following the meanders to improve understanding

Dramatic meanders in the Vltava, or Moldau, River. (Image by Imp5pa)

When I used to teach piano lessons, I would sometimes turn the page of the student’s book and get a feeling of “ugh.” The thought of explaining whatever the next page called for immediately drained my energy. Based on the student’s skill level, the leap was going to be too much.

I developed a practice of “following the meanders” by working through other books and resources with the student. By this, I don’t mean that we wandered aimlessly; I mean that instead of moving in a straight line ever forward, we proceeded as though we were going around the bends in a river or road — the meanders. We still advanced, but in a less direct way.

Instead of jumping from page 15 to 16, we’d play the song on page 15, play a dozen more songs using the same skills and techniques, and then arrive at page 16 a few days or weeks later. By that point, page 16 would be straightforward and easy, with very little explanation necessary.

I was surprised to discover that the same dynamic was present when I taught science, math, reading, and writing. Whenever a student would have required a lengthy explanation in order to understand or execute the task at hand, I took that as a sign that we were on the wrong track. Instead of trying to push forward by explaining, I set up experiences (meanders, if you will) that would allow the student to put together the pieces of a concept themselves.

For example, I had a student who was struggling with solving equations like 3x - 4(2x - 3) = 5x - 4. I could have taken her through each step and explained it thoroughly. Instead, I asked her to lead. I saw that she quickly got lost distributing -4 across 2x - 3. And not only was she struggling to understand how the distributive property worked, she was clearly shaky on adding and subtracting negative numbers.

We abandoned that problem and followed a meander. We went through simple lessons to practice adding and subtracting negative numbers fluently. Separately, we reestablished the concept of the distributive property by practicing several exercises that allowed the student to visualize the relationship between addition and multiplication, first without variables and then adding them back in. Lastly, we practiced simplifying expressions involving the distributive property and negative coefficients (like the -4(2x - 3) above).

Finally, we returned to the problem. If the student still struggled, we would have rebuilt the concept of solving linear equations with another meander (first through one-step equations, then two-step equations, then equations with variables on both sides, then equations involving parentheses). However, that part was not a problem for her. And now that she understood the component concepts of this problem more clearly and had more practice with them, she was able to solve the previously problematic problem with no difficulty.

In another situation, a student was struggling with her vocabulary words. She was having difficulty with transitive vs. intransitive verbs, making intransitive verbs transitive (“They haggled a car” instead of “they haggled over a car”) and vice versa (“I coveted over a beautiful dress”). I realized that, in order for her to make progress in learning new vocabulary words, she had to understand the concept of transitive verbs. It was a meander for us to follow, using much simpler words (eat, sit, bite, and so on, and using them to find the difference between prepositional phrases and direct objects).

There are times when portage makes sense: You take your canoe out of the water and carry it across the land to the next body of water. But other times, you might as well follow the meander as it carries you. It may take a little longer, but there is less frustration and stress. And once you get where you’re going, you have more energy and confidence to tackle the next challenge.