Welcome back to learning about genetics with me! In my last post, I told a story about how I learned about the difference and interconnectedness of conceptual, notational, and procedural knowledge. In that story, I explained how one student’s struggles last year with the procedures inherent in Punnett squares led her class to a new procedure that was, for them, more deeply grounded in conceptual understanding. This year, my students taught me even more about the confusion that can arise between conceptual understanding and notation.
I’m using a new textbook this year, one that relies a lot more on students reading and applying and a lot less on me talking and giving examples. I was really quite terrified of how this was going to when we talked about sex-linked traits. Students saw one example of the notation in the book and then had to go on to solve inheritance problems. Practice is important, and I was not convinced they were going to get enough practice. However, this lesson fell on days when I was gone (on Thursday, I was out during biology for an IEP meeting and on Friday I was at the Knowles spring meeting in Philly) so I just went with what was in the book.
(1) I’m back in teaching mode: humans have twenty-three pairs of chromosomes. Twenty-two of them follow the patterns we’ve already talked about. The last pair is the sex chromosomes. Females are XX, and males are XY. Females can only pass on an X chromosome; it’s all they have. That means the 50/50 probability of having a boy or a girl lies with the father; he can pass on an X, creating a daughter, or a Y, creating a son. This becomes somewhat ironic when thinking about how Henry VIII blamed his wives for a lack of a male heir…but there you are.
(2) But there are other genes on the X chromosome beyond just those that create different sexes. Color blindness is one example. Almost everyone learns the story of the Russian Imperial family, and how Tsarina Alexandria, originally an English princess, carried a recessive blood disease called hemophilia and passed it on to her only son and heir Alexei, leading to an obsession with healing him and arguably contributing to the Russian Revolution. See, I’ve linked history and genetics twice in one blog post! So talking about sex-linked traits is very important.
(3) Ok, you’re looking at this Punnett square and thinking one of three things. Option A: Oh no, not another one! Oh yes, my friends, another one! Option B: I thought you didn’t like Punnett squares! I don’t like Punnett squares lacking conceptual understanding. I’m assuming you’re all brilliant and have the concepts nailed. And they really are handy tools for predicting combinations. Option C: This one looks really different.
(4) Ah, yes. It does. But it’s not! If you look at just the H’s, which represent you can see that the woman (on the left, XX) is heterozygous for this hemophilia gene. That means she’s carrying it, but she’s not affected by it (recessive, remember?) And you can see that the man is not affected by the trait because he has a dominant allele (big H) on his X chromosome. Do you see the similarities now?
(5) The interesting thing about sex-linked traits is that males are proportionally affected much more than females. In this particular case, boys have a 50% chance of having hemophilia. Girls, on the other hand, have a 0% chance of having hemophilia. Note that this is the cross for Tsarina Alexandria and Tsar Nikolai, which explains why none of their four daughters (Olga, Tatiana, Maria, and Anastasia) had issues with hemophilia, while their sone Alexei did.
(Ok, now go back to paragraphs 1-5 and see if you can find the conceptual versus notational things I taught!)
Back to the story of my students’ learning; we’d left them with a sub trying to learn sex-linked traits. After I returned, I reviewed them quickly, taught them about how incredibly complex human inheritance is, and gave them a quiz and a project as their assessments.
It was grading these projects, and watching students complete them, that led me to think again about how conceptual and notational thinking play with and against each other. The project was to choose a genetic disorder from a list of five and write a brochure that could go in a genetics counseling office about it. Two of the disorders were sex-linked, so students who chose them (and a lot chose hemophilia because it was the example in the book) gave me insight into how well they learned about sex-linked traits.
What fascinated me was that students were using different notation than was in the book, but their thinking was conceptually correct. Rather than using the superscript letters like in the Punnett square above, they were color-coding the X’s:
or using apostrophes to mark affected X chromosomes:
(note that the mother is on the top rather than the side in this case).
Now, I pulled all these images for examples from the internet, so it’s entirely possible my kids got it from there. But I think, in part, what I saw happening was my kids creating new notation to fit their conceptual understanding. They knew there were “good X’s” and “bad X’s” and they created a way to tell them apart. I gave them full credit no matter what notation they used.
Do they really understand that the Factor VIII gene, which causes hemophilia, is a short DNA sequence along the whole chromosome and there are thousands of other genes on this chromosome too? I can’t actually tell from this particular question.
(As a side note, assessment design to really show student thinking is HARD!)
But this opens up all sorts of interesting teaching questions. Do I teach kids a notation? Can I ask them to come up with their own? How would I scaffold that process? What’s the value of their own notation versus the standard notation they’ll see as they pursue science? How do I make connections between the two?
Your homework: Have you ever created notation or shorthand for something? Have you ever been annoyed or confused by someone else’s notation or shorthand? What’s the value of notation or shorthand and when does it fall short (hehe)?