First day back in the classroom, teaching genetics, and I speculate for a bit about why so many people find the subject difficult. I’ve had smart students who struggled with the concepts. I think the answer is that many people don’t get the whole idea of chance and probability and the statistical nature of inheritance.
The autofocus on my camera was a bit goofy. Someday I’ll get this all figured out.
“The autofocus on my camera was a bit goofy. Someday I’ll get this all figured out.”
Well, you do have a partner.*
That’s the point; sometimes assistant, sometimes assisted.
Mutual thingies like that.
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* Mary Mary (not Contrary, of course)
I remember back when I was in grad school working on a MSEE. There were only two required courses. One was on random variables and noise. That stuff turns up everywhere it seems.
Ooo, you might be interested in two citations.
Andrew Gelman and Deborah Nolan, “You Can Load a Die, But You Can’t Bias a Coin,” The American Statistician 56, no. 4 (2002): 308–11, https://doi.org/10.1198/000313002605
Gelman and Nolan describe a class activity where they ask students to create a biased die and coin. The students have no problem with the former, but none have yet to pull off the latter. That pairs well with:
Matthew P. A. Clark and Brian D. Westerberg, “How Random Is the Toss of a Coin?,” Holiday Review, CMAJ 181, no. 12 (2009): E306–8, https://doi.org/10.1503/cmaj.091733
A prof asked 13 residents to induce bias towards heads in a coin toss, via how they flipped it. All of them were successful, with half achieving statistical significance.
I had no problem with the variable focus because I am old and variable focus is a part of life.
I was a wise talk.
I know that many people don’t have any understanding of how statistics work, much less probability. It is annoyingly common for me to hear people say they support things 1000%, or some other nonsensical percentage.
I think many people find the idea that chance and randomness are part of evolution and human genetics disquieting.
Hj@3–
Not entirely convinced by the second paper. There’s a lot of crucial design description missing. I know it’s not meant to be a Big Serious Paper, but still. Plus, it fails to understand why coin tossing for sports (home captain tosses the coin, away captain calls the toss once it’s in midair) makes it a very good randomiser. Even if the coin-tosser can bias the toss, the caller gets to randomise the advantage. Worse, if the coin-tosser’s bias is predictable, then it gives the advantage to the caller.
Tethys@5–
I take most statements about “giving 110%” or “1000%” to be hyperbole, but it’s certainly true that probabilistic errors are commonplace, including in respected scientific journals.
People do tend to have a pretty poor innate sense of probability. Unless you get a lot of training and actively focus on using the skill. It’s a hard one to teach people
Having taught university-level Mendelian genetics for some years, I found that students had a lot of trouble understanding what gametes would come from a double heterozygote, such as AB//ab. One is tempted to think that some of the gametes will be Aa or Bb, rather than just the four types AB, Ab, aB, and ab. I was unhappy that students could not understand that, even though they had been exposed to Mendelian genetics in high school. But then I remembered that it took me being exposed to it about three different times before I understood gamete segregation from double heterozygotes.
(Oh, and I advise having a cold drink of water, juice, or pop to delay the onset of hoarseness.)
I should have said, a cold drink to keep with you and sip on.
I suspect Mendelian genetics is eminently teachable via computer gaming.
@5, 7
This is literally how our language gets decimated over time.
Our first lab is to produce double heterozygotes and then do another cross to see random assortment in the next generation. Yeah, students struggle with that, but that’s why we do it hands-on.
I passed a course of statistics but I found it to be really counter- intuitive.
It might be too much to demand ordinary schoolkids learn much statistics but at least expose them to it enough to make them understand that statistics is weird, and can be misused by demagogues to manioulate you.
@ ^ I woulda thought genes were too small to get ones hands on! ;-)
Although I guess they do make up your hands along with every other part of your body..
I think it was key that Mendel studied peas. Because there you had just simply two outcomes: Green or yellow. Usually, such characteristics are much more distributed, with in-between levels and interactions and mutations and so on.
By the way, do you have a public course website? I’m somewhat interested in the content.
chrislawson @6:
That was my biggest disappointment with the paper. I thought they had a line in there about ensuring the tosses looked “fair,” but on re-reading I couldn’t find it.
Not necessarily! If the person calling the toss is perfectly random, any degree of bias in the coin toss won’t matter. But we know human beings aren’t perfectly random, so some bias must remain. All the tosser has to do is figure out which way the caller is biased, and adjust their technique accordingly. There’s also the problem that not all coin tosses have a tosser and callee. Some just involve a toss, and for those the full amount of bias persists.
At any rate, I love bringing up that paper because it’s a good example of how terrible human beings can be at evaluating randomness. Anyone with a bit of practice can bias a coin toss, yet coin tosses have picked up a reputation for being unbiased. The fact that our intuition can’t tell the difference between a 50% and 68% success rate is an excellent argument in favour of quantifying experiments and being rigorous in their design.
My partner (physics prof) says probability is the one course that every college student should be required to take.
Funny, because in my opinion probability is one of the most fun math subjects. I took a “discrete math” elective in high school, and it was my favorite exactly because it blows ones mind to realize that naive intuitions about probability and combinatorics are wrong, and there are many “paradoxes” to resolve with clear thinking. Also, it involves a lot of games, card games, dice games etc.
I remember back at Eschaton in Ottawa in 2012, your talk at the museum was all about randomness as a factor in evolution. Which included references to the way that if you go back far enough, everybody alive back then is either the ancestor of everybody alive today or nobody, and the farther back you go the less in-between there is.
As for probabilities, yes, most people are bad at it, especially on edge cases. There’s a reason I’ve used the line ‘a one in a million chance will probably happen to about eight thousand people on the planet’. just to help drive in the way the law of large numbers plays into it. Douglas Hofstadter talked about what he called ‘the Oddmatch phenomenon’ in one of his Metamagical Themas columns: the idea that part of the problem is actually inherent to the way human memory works: the 999,999 times where everything works as expected all sort of get compressed together in your head, but the one in a million chance where something odd happens stands out in your head, meaning it seems a lot more probable than it actually is.
On top of that, I’d say the existence of conspiracy theories helps show that some people just can’t handle the fact that randomness is a thing at all. Bad things happen to bad people, and they’re good people, so bad things shouldn’t be happening to them. Religion can certainly exacerbate this (‘a plan for your life’), though it isn’t going to be the only source; that also seems to be a natural result of the way people often anthropomorphize and assign motives to inanimate objects.
When I was telling a large undergraduate class about genetic drift, I posed the following: I said we were making independent tosses of a fair coin. We tossed it 10 times and got Heads all of those times. We are about to toss it again. Which is true:
1. We are more likely to get Heads since “we’ve got a run of Heads going”. A majority of the class agreed with that.
2. We are more likely to get Tails, “because the laws of probability say that we tend towards 50% Heads”. A reasonablle number of students agreed with that.
3. A depressingly small fraction of the students agreed that “it’s 50:50, Heads of Tails”.
Do biology profs ever use the analogy of people’s physical make-up being (to first approximation anyway) the outcome of 23 coin tosses?
I have long thought that statistics and probability are subjects that should have some serious emphasis in high school – because they are the most useful thing that people do not intuit well and which helps to understand what is not obvious in the world.
@ ^ fentex : Agreed completely.
@ drdrdrdrdralhazeneuler
Being comically(~ish?) pedantic Mendel studied pea plants and they can exhibit a range of differneces beyond just pea colour for instance length of pods, hairiness of pods (a local member of the Leguminosae family the KangarooThorn or Acacia paradoxa has VERY hairy & curly seedpods), precise leaf size and shape, etc… In Mendel’s specific historical case :
Source : https://en.wikipedia.org/wiki/Gregor_Mendel#Experiments_on_plant_hybridization
About 3 years ago PZ posted his class lectures to here. They should be still Findable?