Curse you, Reginald C. Punnett

Yesterday, I gave my first year students a teeny-tiny quiz over the current unit in basic genetics. No biggie, I’d been hearing some troubling concerns from the class tutor that some of the students were struggling, so this was more of an assessment of how well they were grasping the simplest concepts in Mendelian genetics. Here, I’ll even let you see the entirety of the quiz: 5 questions, 2 points each.

You have a true-breeding diploid organism with the phenotype AB, and a second true-breeding organism with the phenotype ab. A is dominant to a, and B is dominant to b.

  1. What are the genotypes of these two creatures?
  2. You cross these two and obtain a clutch of F1s. What are their genotypes and phenotypes?
  3. You cross two of the F1s with each other. Predict what the phenotypes and their proportions in the next generation should be, assuming that Mendel’s laws apply.
  4. You cross one of the F1s with another organism that has the phenotype ab. Predict what the phenotypes and their proportions in the next generation should be, assuming that Mendel’s laws apply.
  5. You actually do the experiment in #4, you get the following results:
    AB: 35%
    Ab: 15%
    aB: 15%
    ab: 35%
    Interpret this distribution.

See? If you were a student who’d just suffered through 3 weeks of an introduction to genetics, you’d probably have absolutely no problem with this. If you’ve been teaching genetics for a few decades, you could answer this quiz in seconds, in your sleep, while standing on your head. I think that might be part of the problem, because this is stuff I can totally take for granted.

I gave the students 20 minutes. Most of them used the entirety of that time. I scored the quiz that afternoon, and was aghast: mean score was 2.7/10, high score was 8. Yikes. How…? Where have I gone wrong? These are smart, hard-working students, and they missed everything. Then I saw the problem. The quizzes were covered with…

PUNNETT SQUARES. Jesus. They tried to solve every problem with a 4×4 Punnett square, which is insane. Punnett squares are a tool for graphically illustrating the outcome of a cross. They are not tools for calculating the results. They are a terrible, slow, clumsy tool for doing that. The textbook is full of ’em, I think because they’re easy to draw and give the illusion of a comprehensive answer. I’d shown a few in class, because I had to explain what the textbook was showing them, but I always told them that Punnett squares were terrible and useless, but this is what they knew, probably from high school, and then reinforced by the text, and then I made the mistake of trying to explain what the book figures were showing, and they came away with the impression that this is what geneticists do. It is not. Mendelian genetics are dead simple. You can just treat each locus independently (and they’re trivial, you can memorize all the possible results if you can hold 3 frequencies in your head), solve for A, solve for B, multiply to get the answer for A & B.

Christ, they’re trying to mechanically brute-force a solution with 4×4 Punnett squares, and it’s a disaster.

I can’t blame the students, though, it’s all on me. I remember being their age and taking Dr Sandler’s genetics course at the UW, and struggling for the first few weeks, until suddenly the light bulb flicked on in my head and I saw how easy Mendel was, and then when he started layering on the advanced stuff, like segregation distorters and epistatic interactions (seriously, try solving those kinds of problems with a Punnett square — you might be able to assemble some kind of nightmarish diagram, but it’s not efficient. You can’t even do linkage with a Punnett square.), it was all just an easy arithmetic modifier added on to the basic concept. But then, Sandler was a brilliant teacher, I’ve got some catching up to do.

So how to deal with this problem…next week, I’m going to rewind and go back to the basics, review these elementary problems without Punnett squares anywhere in sight, and actively tell the students that Reginald C. Punnett was of the devil, put on this Earth to confound generations of genetics students. Then, over Christmas break, I’m going to back over my stored presentations and notes and edit out every mention of the P word. Maybe I should print one out so I can put it on the floor the first day of class and piss all over it — nah, some administrator would probably complain.

Then, you out there — yeah, YOU, high school teachers and textbook publishers — stop poisoning students minds with these abominations. I’ve never liked them, but I keep using them because they are traditional, and because the books and students come with them preloaded. Just stop it. They’re pedagogically bad. I’ve got to explicitly unteach them now.

This is a tragic setback, because what my plan for the course was saying is that I start next week on the developmental biology unit, my favorite stuff, and now it’s getting bounced back two weeks, and is going to get slammed up against the end of the term. I’m going to blame Punnett.


  1. cartomancer says

    Piss all over it? Very off-brand for you, PZ, you’re the stick it in the bin with a rusty nail through it and some banana peels guy.

  2. steve1 says

    That explains it. I had a straight A in high school biology until Mendel and the Punnett squares. I totally flubbed it. I remember the Biology teacher handing back the assignments and the teacher asking me what happened Steve. I know now the answer was Punnett squares.

  3. hatty says

    You know, I bet they will learn and retain more from that one lesson where you explain it from the ground up, tedious as it may be, than the rest of the course.

  4. imback says

    It has been decades but let me try the test…

    I guess if they’re true-breeding, the first creature has a genotype AABB and the second has aabb. I may already be off on the notation.
    The first generation after crossing these two would all be genotype AaBb and their phenotype AB.
    The second generation should have 9/16 of AB phenotype, 3/16 of Ab, 3/16 of aB, and 1/16 of ab?
    AaBb crossing with aabb gives 25% each of phenotype AB, Ab, aB, and ab?
    Somehow A and B gene expressions are linked??

  5. robert79 says

    Now I don’t know about the biology, but I see similar stuff when teaching mathematics.

    Students will confuse the graphical illustration of some method/theory with the method/theory itself.

    The first is a teaching tool, the second is what they actually need to learn. In maths, the change happened around the time high school maths education switched from focussing more on calculation to teaching more “insight”. The end result was students couldn’t look at a “hard” problem anymore and say to themselves: “ow, this looks hard, but I can just write down all the necessary formulas and try and solve it!”

  6. says

    OK, PZ, I’m going to take you on with respect to Punnett squares. (Disclosure: I have a full page in my HS textbook explaining how to construct them from one-factor and two-factor crosses). Not only do I not think they are an “abomination,” but I find them to be useful teaching tools in my college freshman Bio class. They are useful for two reasons:

    1) They do a very good job predicting genotypic ratios of crosses like the one in your exam question for UNLINKED genes. That makes them useful for interpreting Mendel’s results.

    2) They provide an excellent means of detecting when two genes are LINKED, which is exactly what shows up in your example problem. A Punnett square would predict a 1:1:1:1 ratio of offspring. When you see something different, it’s a dead giveaway that the genes are linked. If you actually give students an example of how linked genes don’t match the predicted ratios, they get it right away.

    As my teaching example I use TH Morgan’s original crosses demonstrating that Drosophila body color and wing shape genes are linked – because they do not yield the “expected” 1:1:1:1 ration for linked genes. Therefore, they are unlinked.

    Reginald stays in my lectures – not as a devil, but as a hero!

  7. dorght says

    I tried to solve it with my dim Bio101 memories from… um, Mendal may have still been working it out then. Primed of course by the prominent Piss_on_it Square at the top of the page. Only after filling a page with square abominations did I scroll down slightly and get the gist of the post.

  8. says

    Sure, you can use a Punnett square to predict a 1:1:1:1 ratio. My point is that it’s a bad way to predict it — it’s far easier to see that 1/2 the progeny will be A, 1/2 will be a, and that 1/2 will be B and 1/2 will be b. The number of ABs will therefore be 1/4, Abs 1/4, etc. No fiddling with 16 little boxes in a 4×4 grid, no error prone tallying of the 16 boxes, it’s much more straightforward and easier. And you can still see that #5 is an observation that doesn’t fit a simple Mendelian model.

    Evidence: my students floundered over those 16 stupid boxes for an excessive period of time, and then often failed to get the right answer because they got flustered or miscounted or just ran out of time. The math is easier, clearer, and faster.

  9. dorght says

    I wonder if Endless Forms Most Beautiful: The New Science of Evo Devo by Sean B Carroll had been around when I was in HS or college if my life would have taken an entirely different track. I don’t think I have ever read a book that impacted me so much with it’s explanatory power and a desire to learn more.
    Does evolutionary development get much coverage in Bio101 equiv or Basic Genetics?

  10. says

    The course I teach is called Fundamentals of Genetics, Evolution, and Development, so yes, I’m supposed to cover evo-devo. Unfortunately, this setback means I’ve got to truncate the evo-devo part to fit everything in.

  11. Joseph Felsenstein says

    I’m glad to see that there has been debate here about Punnett Squares. Used properly they can be very helpful. Used as a mechanical ritual, not. But I do agree with you about Larry Sandler. A great teacher. He was a huge influence on the way graduate students in our department were taught to teach. For years afterwards among geneticists there was said to be a “Seattle Lecture Style”, which was a good thing. It contrasted with the High-Throughput Lecture Style that was used by the people who trained in the big molecular biology and genomics labs in places like MIT, Stanford, and Harvard. Larry used to say that the first time he taught he was terrible. I took a course from him in Advanced Genetics when I was an undergraduate at the University of Wisconsin in 1961 (60 years ago). He was great. I later found out that that actually may have been the first time he taught.

  12. chris61 says

    I agree the math is easier, cleaner and faster with one caveat. Assuming the student understands the math. In recent years I have met a number of genetics students who don’t understand the math. The ones who do understand can look at a few Punnett squares and effortlessly make the leap to the equations. The ones who don’t can look at Punnett squares for a very long time before they make the leap.

  13. Bad Bart says

    I remember sitting in high school biology and realizing that the population genetics formulae we were being asked to memorize looked exactly like the systems of equations I had just seen in algebra. And then working back to realize that by doing it as a math problem, scaling a genetics question up to 3, 4, or more factors was actually doable, whereas building an 8×8 square and trying to figure out which cells had the same values in them was tedious and virtually certain to introduce transcription errors.

  14. felixmagister says

    My experience is that some people just mentally lock up when they see math. It’s possible that these people, at least, find punnet squares (which are, after all, essentially a geometric representation of the relevant equations, but may not trigger the “it’s math, therefore I can’t do it” response) easier to work with.

  15. Russell P says

    My Junior college students act as if they’ve never heard of probability before. Or meiosis. Or Punnett squares. If they learned it in middle or high school, they’ve long since forgotten it all. So I start from scratch. My focus is always on the movement of chromosomes in meiosis and union of gametes. I avoid using letters for phenotypes–only for alleles ( I use real phenotypes in my problem sets and exams–coat color in dogs, skin color in snakes, cholesterol levels, etc). I show them by drawing diagrams that equal segregation and independent assortment produce gametes in equal proportions. Then I introduce them to the product and sum rules using non-genetic examples. Then I put the two together and emphasize the importance of the proportions of sperm and ova genotypes and that they’re just calculating the likelihoods of each possible combination. I show them both the fork method and the Punnett square, but warn them that they have to write out the proportions–otherwise it’s pointless (and will give wrong answers when we do H-W equilibrium). I use non-genetic examples so that they can see that keeping track of proportions and likelihoods isn’t anything difficult. Here’s my tutorial if anyone is interested:

  16. rpjohnston says

    Alright, at 33 it’s been awhile since I was out of school. Let’s see how I do…

    …I thought those WERE the genotypes, and the phenotype was a qualitative assessment of what actually manifests (which is usually more complicated than mere dominant and recessive traits). Uh, ok then…Organism 1 is AaBb, and organism 2 is aabb. Hmmm. No. A and B are each different traits like “Round” and “Wrinkled”. The second one I’m sure is aabb, but I don’t know what the genotype of 1 is. Unless “true-breeding” means something significant I forgot. Everything has 2 copies of a gene, right? Is it impossible for them to have 2 dominant copies? No, surely not, that would be the TL box of a Punnett square.

    F1 is the first generation right? So uh…their genotypes and phenotypes are combinations of the above? That…can’t be the right answer, it’s too vague but…oh, I guess a basic Punnett square is just an expression of ratios and you don’t need to actually know the litter size. So I could make 2 Punnett squares for those. Or…I guess theoretically, there’s nothing stopping me from making a 16-cell square or n-cell square, but I don’t remember if anything like that ever came up. Still, I don’t know the genotype of organism 1, so…

    Do I get to select which members of the F1 brood I can cross? It’d be easy enough to just select any couple cells from the previous sections (including the same one, assuming the litter size allows it) and redo the exercise.
    There’s a decent chance I would have effectively done this in the previous question lol. It’d be trivial enough. Again, if I knew the genotype of organism 1 to start the whole process.
    Hm. I’m not sure. Logically I’d think that the first organism would be AaBb (and obviously the second is aabb) but I can’t make the math work out on that. 50% of the offspring would be Aa and 50% aa, and 50% Bb and 50% bb. The models in my head say that should turn out to be 25% even for every combination. But obviously the first organism can’t be fully dominant in either trait or you’d have NO ab, nor can it be un-dominant in any trait or you’d have no A’s or B’s.

    So…I probably failed. How shameful.

  17. rpjohnston says

    Yeah, by the end of all that it was pretty obvious Punnett squares were insufficient to answer these questions, but if they ever taught me anything more advanced I’ve forgotten. I’m pretty good at math, ESPECIALLY when I can intuit what the moving parts mean and how the concepts all link together (I can never memorize a formula break it down and tell me what each of the terms relate to and I’m much better at least remember what’s being done and why), so I’m pretty sure, looking at this, that I’d grasp the concept in minutes if I was taught.

  18. rpjohnston says

    After reading imback’s comment, it looks like most of my difficulty arose from not understanding what “true-breeding” means.

  19. rpjohnston says

    Oh, also, as far as students covering their papers with Punnett squares and RE PZ @ 11: Is it still the fucking pisshit fucking asshat insufferable god damn culture in fucking highschools to “show your fucking work or get thrown into a fiery abyss and get shitty grades on your stupid god damn report card even if you can get the right fucking answer in your head in 5 seconds, you fucking assholes”?

    Yeah, I might still have an axe to grind about that, still. Point is, you probably have a lot of students conditioned value writing out an unending pedantic chart of their process rather than figuring out the answer. Cause believe me, figuring out what needs to be shown to not have that teacher take a fat dump on your paper takes up a lot more brainpower than just getting the god damn answer.

  20. wzrd1 says

    I say to print out a presentation that is rife with Punnett squares, place it in a prominent location with a rubber dog turd on it as a weight.
    After all, give the presentation the weight that it deserves.