You want kids to hate story problems?
[probably going to be pwned by the time I post] "there seems to be something about math education that students don't think about the question critically" seems exactly wrong.
The students are operating from a view where problems given in math have mathematical solutions, have always had mathematical solutions, and are sometimes written either unclearly or with actual mistakes in them that make them absurd. You could conclude from this that students are reasoning inductively from years of experience, or you could conclude "the results were shocking" and "students don't think" but I'm going with canny students.
Well, I was pwned by the wikipedia entry anyway. Also, 4 was me.
I know what you mean. Part of every test is the Iocane Powder problem, where a clever student has to reason out, "I know there are a range of answers to this, from simplistic to complex, and I have to game out what you expect me to think the answer is, and also whether you want students to supply the "natural" answer or whether the "natural" answer is a red herring and you want us to level up, or if I'll be penalized for citing more complexity than you intended."
Pokey recently had a great example of this, and now I can't remember what it was. This is driving me nuts.
Hawaii had a slightly different thing happen: 12 questions on a geometry test. Everyone but one person missed the two hardest questions, so the teacher threw those out. Hawaii got those two problems correct. However, she made a careless error on an easy problem. So she got a 90, while her friend (who missed the hard problems) got a 100.
I got a question on the SAT thrown out because I asked the proctor a question which they have to record and report, and the SAT reviewers decided based on my question (or maybe other test takers who asked something similar) that it was in fact ambiguous and threw it out. So I probably cost some people who got it right a few points, and for a subset of those that was probably the difference in where they went to college, who they married, offspring, etc.
I think I've already told my stupidest math test story, but not lately. I was the only junior in the pre-calc math class with all seniors. Grading was on a curve and I was usually the top of that curve. So, one day when I was away from class there was a test. They all agreed to turn in a blank test so they would all get the highest score.
Yeah, everyone else has gotten here already, but someone who doesn't say "there's not enough information" hasn't failed at mathematical reasoning, they've failed at figuring out what class of answers are acceptable. I bet if you included the problem in a group of answerable questions, and explicitly told the students to say "not enough information" where it is the case, a lot more would get it right.
But also: you all are describing how you'd fail to say "insufficient info". There are plenty of students, given a coherent word problem, who just wildly grab at numbers and try to guess a plausible computation. So this isn't completely bogus, even if it's catching a wider net of students than a fairer problem.
In thinking about the methods and expectations of test creators, I am reminded of Princeton Review, a test prep company that invites you to think in terms of the average Joe --
Joe Bloggs -- and the answers he would give on standardized tests. When you don't know the answer, you want to identify the Joe Bloggs answer and -- as the questions become more difficult -- not use Joe's answer.
I didn't run across that guidance until my standardized test days were over, but I had intuited most of it in my student days.
The linked article is from 1986, and I wonder if test-makers have taken this into account.
I believe the canonical Joe Bloggs Q&A was:
You drive 60 miles to another town at 60mph. Then you drive 60 miles back at 40mph. What's your average speed for the round trip?
Joe Bloggs: Average of 40 and 60 is 50!
Nowadays he's known as Joe Substack.
I mean, students are going to try to create a math answer because they assume that there is some kind of trick that they should have been taught but weren't or didn't understand when it was explained and hence missed. They're assuming that this is supposed to be the hardest question and it will be apparent to the brightest students. This is because education in general is so often bad and cruel and about students being taught that they are basically stupid and lazy.
Students should not be presented with trick or willfully opaque questions unless the teacher is tipping them off that some questions are tricks or giving them clearly articulated strategies for solving opaque questions. Students need to trust the teacher to be honest and straightforward with them rather than constantly trying to trip them up. Any student who had been told, "sometimes it's okay to answer that there is not enough information, that can be correct" would have tools to approach this question. I, a smart kid, did not encounter "there is not enough information" as an answer until I was taking multiple choice SAT-prep type tests.
Also, kids are under a lot more pressure in China and it's just really not fair to throw a scare into them that way.
Well, I skimmed the blog and I saw that Gustave Flaubert was mentioned, so I'm guessing the answer is "Madame Bovary".
The most important thing a high school math teacher can do it tell the joke with the punch line "pie are round, cornbread are square. "
Learning to read and write in Chinese is a physiological challenge, fine print on bad paper plus a ton of necessary memorization is really hard on the eyes even in good light.
https://journals.lww.com/apjoo/Fulltext/2022/02000/China_Turns_to_School_Reform_to_Control_the_Myopia.6.aspx
I've been trying to learn a little, but have basically given up, too hard. 找 and 我 are made from the same pieces, meaning is completely different.
I can't even read English written in cursive these days.
This reminds me of examples of giving GPT-3 or a similar AI an impossible prompt (e.g., "who was president of the the United States in 1750"). You'll get all sorts of interesting answers, unless you configure the AI to reject low-confidence answers.
Once AI can figure out which parts of the picture contain bicycles, we're doomed.
Co-sign every word of Frowner's 18 (hi Frowner!).
I have spent a significant portion of my professional life trying to undo the learning trauma that adults acquired during their school years and that has poisoned their ability to approach new information in a curious and inquisitive way rather than assuming they are about to be tricked and humiliated. When I do audience presentations I have a standard line when asking for volunteers of reassuring them "I don't believe in public humiliation," and you'd be surprised (or not) how much nervous laughter that evokes.
It is a shame that more tests don't have a variation of this as the correct answer. It would be a great life lesson to teach kids.
Maybe one of the teachers here could craft a test where the answers are variations of:
I don't know.
There's not enough information to answer this question.
Any answer would just be a random/educated/bullshit guess.
Who the F knows what would happen.
Your guess is as good as mine.
I have a very vivid memory of Driver's Ed when a sub tried to teach people how to calculate miles per gallon. This involved talking about resetting the trip odometer, noticing how much gas you put in, etc. But then he was like "ok we take the miles we drove and then what do we divide by to get miles per gallon." Someone says "365!" And then someone else says "No, 52!"
That sounds like something I would have said.
The problem with questions like this is that they very often have the form "here's some verbiage and a number x, more verbiage and y, what is z?", so the student is implicitly taught that the verbiage is content-free labels for the variables in some plausible sum. It's not surprising, as others have said, that the students presumed this.
The quoted Flaubert thing is much more like a joke - it's a whole string of stuff, CS Forester nautical technicalities, generic info, with a punchline.
I was going to ask ask about the next calculus lesson, but if calculus can't tell me how old the captain is, then I just don't see the point.
Calculus is about tangents more than points.
Just bad pedagogy. A) kids learn that word problems are just narrative ways of connecting numbers, so they try to find a connection that ignores the words B) missing the "trick" doesn't teach them anything useful, or at least not as easily as saying "the first thing you ought to do is see if the problem makes sense" and C) inference to the best explanation leads to the *opposite* of the intended result.
shiv's boss has a funny story about coding an arithmetic problem generator for his kids (back when that would have been a thing for a dad to do instead of purchasing an app), where he inadvertently taught the kids to associate the varying background colors with answers. "Purple is sixteen" chimed in his 30-something daughter on the conference call.
Crap! I forgot all about Conversational Calculus! Next summer.
Just read a great tweet: "The funniest alpha male trait in America right now is being proudly afraid of American cities."
Yes some of this is bad pedagogy, but I think a bunch of it is also human nature. Most people genuinely would rather follow even complicated instructions rather than have to think about what something means. See this famous experiment.
That explains why chimpanzees suck at algebra.
38: No, I think the funniest one is caring a lot about the faithfulness of the remake of The Little Mermaid.
For example, regardless of their teacher's pedagogical approach the vast majority of people would rather memorize the quadratic formula than learn completing the square.
Speaking of urban carnage, Nextdoor had a post about poop some one found and how they think it is human because there's paper with it. I helpfully suggested that raccoons have learned to wipe.
This one has an answer, which I'll post tomorrow.
Jack is five years older than Diana. In two years, Diana's age, plus four times the age of their daughter Zoe, will be be equal to Jack's age..
Where is Jack right now? Hint: the answer is a state.
Jack & Diane but most of the lyrics are "suckin' on a chili dog":
https://www.youtube.com/watch?v=6QX57aIDbDU
The Tast-Tee Freeze caters to a very specific fetish.
44: I thought this was handled in the original post.
Of course Moby would get it. He's from one of those flat states. Joke that has not aged well, but also wasn't very funny in 1981: Where did Prince Charles spend his honeymoon? Indiana.
Probably not needed for this crowd, but for non-math people, it turns out that Zoe is -3/4 now.
Math people, there's room for improvement if you have a more elegant word problem .
I drove across Indiana in 2021 and in 2019. I'm practically an expert.
Women named Dia, Donesia, and Glewood are watching with concern.
That reminds me of the old joke, "X has spent more time in Betty Ford than Gerald Ford has", where X is the set of celebrities with both a penis and a substance abuse problem.
I just tuned in for a quick break from midterm grading and misread the post title as "How is Old Ship's Captain" and my mind was all "yeah, I love that old guy, brought out so many entertaining UnfStories."
As you were.
50: Zoe is -3/4 now
The really interesting thing is that Zoe is thus 1/8 1883, 1/16 2137, and 1/16 provably indeterminate.
I assume I am not the only one familiar with this joke which I was fond of annoying adult relatives back in the day. (Or maybe it went out of circulation sometime after the early 60s.)
"Your driving a bus. At the the first stop 8 riders get on. Second stop 3 on 1 off. Third stop 10 on 4 off. Next stop no one gets on, 2 off "... and so on through a number of stops.
"How old is the bus driver?"
Joke is conceptually similar to the "count the passes/see the gorilla" test (I think discussed here before.)
16: I was teaching the "Joe Bloggs" method for TPR as recently as 2011.
"the first thing you ought to do is see if the problem makes sense"
Further to this point, I am fresh off a project where the consultant presented me with statewide industry data that didn't make a lick of sense. (Think 10x employment in health-care sector compared to retail sector.)
After quite a bit of back and forth, I lost patience and said flat-out: The numbers have to be wrong. It doesn't pass the common-sense test.
Spoiler: the numbers were wrong. Turns out that when you try to use Census data on small businesses, you need to be really clear whether government agencies count as "businesses."
57: I can confirm that it is still in circulation among the youths of central Texas.
I just had to pass this homemade captcha on a photographer's page:
Please answer this simple question
2x3 +5 x1000=?
I answered 5006, which was wrong. The box accepts 11000. His page, his rules. I shouldn't make fun of him as I failed the Zoe test above, and order of operations rules are arbitrary anyway. But I like how he makes sure to say it's a simple question.
61. His page, his rules, sure. But if his involve ignoring the generally accepted order of operations, then I challenge the assertion that it's a simple question. It's a trick question.