I am home tutoring again after a long break when I was developing textbooks and other educational materials. When I returned to Wyzant, I found all these new features and doodads, including this blog function, so I figured why not tell a story about a previous rewarding tutoring experience?
DNA is a long, thin molecule, a polymer, made up of monomers joined together. My student understood that perfectly well. She also understood restriction endonucleases. These are enzymes that cut DNA only at certain recognition sequences. What she didn’t understand is that DNA molecules are objects in the real world, and they behave like similar real objects. That lack of understanding prevented her from answering homework questions about recombinant DNA techniques.
Her professor had drawn a loop and a line segment on the blackboard. The loop was a plasmid, a circle of DNA, and the segment was a piece of linear DNA. Next, her professor had drawn two separated hash marks on the plasmid and two on the linear piece. These were recognition sequences—two places on each molecule where an endonuclease would cut. Arrows showed what happened next. The circular DNA became two DNA segments, and the linear DNA became three DNA segments. My student couldn’t understand why that would happen. It had seemed obvious to the teacher, and it seemed obvious to me too, but the student was lost.
I said something like this. “Well it’s…it’s like a string…I guess it’s like this. Every time you cut the molecule, you create two more ends—a 5-prime end and a 3-prime end—but we can just call them a left end and a right end.” I began to draw more circles and lines, hash marks and arrows. “The linear molecule starts out with two ends and the circular molecule starts out with no ends. So when you cut each twice, that adds four ends to each, so six ends create three segments, and four ends create two segments.”
“But why does it happen that way?” she asked.
“Well, I think it’s…topology?” I could tell I wasn’t being much help. Math, whether it’s simple or not, is useful to describe reality and find new answers based on that reality, but math doesn’t help a student grasp reality. That’s when I thought of using toilet paper and tape.
We went to the bathroom and got two strips of toilet paper, each about a foot long, and used scotch tape to attach the ends of one piece together to make a loop. Then about a second before I could ask her to tear each piece twice, she said, “Oh! OK. I understand what will happen. We don’t have to tear them up. I understand everything now.”
She began to quickly do her homework on recombinant DNA, and the two uncut pieces of toilet paper just sat there on the kitchen table. She never looked at them, but I began to eyeball them with suspicion.
The idea that molecules have a real internal structure used to be controversial. Around the 1850s to the 1870s, some younger chemists, like Friedrich Kekulé and Jacobus vant Hoff, published articles and books where they imagined molecules as atoms arranged into specific positions in the real world. A few older chemists, like Hermann Kolbe, made fun of them. There was no direct evidence and very little indirect evidence at the time that atoms were real objects, so the idea that one unreal object in a molecule was always located over there next to that other unreal object seemed like too much of a stretch to Kolbe. He wrote that believing in the spatial arrangement of atoms in molecules was “not far removed from belief in witchcraft.” One of the fun aspects of tutoring chemistry is teaching this witchcraft and making it real using physical models.
Of course, someone had to cut those molecules, and my student no longer wanted to do it. I tore each piece of toilet paper twice and got the expected results. Could I have ever explained using only words why that had happened?