How Old Is The Shepherd? • Hacker News Board

Re: How Old Is The Shepherd?

#51

Post by yongjik » Wed, Dec 04, 2013, 6:34 PM UTC

epochwolf wrote: post #32

This is totally unsurprising. Most word problems in textbooks are poorly written and have little to no basis in reality. My experience as a grade school student is that most teachers get annoyed when you question the logic of the questions being asked. Critical thinking is not rewarded in those situations. So that given, which student is going to stick their neck out in that situation? It's better to risk a wrong ans…

Yes, there are many poorly written problems, but on the other hand, even well-written problems can have little basis in reality. Spherical cows in vacuum, and all that. When a question asks "You throw a ball at 80 km/h at 45 degrees, how far does it travel?" you could argue endlessly about air friction, the exact height of your hand when you let the ball go, Coriolis' force, curvature of the earth, and the fact that you can never throw a ball that fast... but you are not being critical. You're just being obtuse.

The point of the question is not to indoctrinate students that air resistance is negligible. It's to let students practice their knowledge of Newtonian dynamics so that they can later proceed to more complex problems (hopefully with air resistance) if they want. Context matters.

So what about the original problem? I agree that the students' expectation that "there must be an answer" played a role, but I don't think the expectation is necessarily a bad thing. There's a reason that all the textbook problems (are supposed to) have nice answers: it actually makes it easier for the students to practice and internalize the concept they're learning.

Re: How Old Is The Shepherd?

#52

Post by tedsanders » Wed, Dec 04, 2013, 6:35 PM UTC

When I tutored sixth grade math, it was not uncommon to see kids who guessed that 7 + 3 was 9. When you are that far behind in math, your only possible approach to the subject can be weird heuristics that make no sense.

Re: How Old Is The Shepherd?

#53

Post by dragonwriter » Wed, Dec 04, 2013, 6:35 PM UTC

jumbled wrote: post #44

epochwolf wrote: post #32

This is totally unsurprising. Most word problems in textbooks are poorly written and have little to no basis in reality. My experience as a grade school student is that most teachers get annoyed when you question the logic of the questions being asked. Critical thinking is not rewarded in those situations. So that given, which student is going to stick their neck out in that situation? It's better to risk a wrong ans…

"If two sides of a triangular garden are 3 and 4 feet respectively, find the length of the third side." Okay, hand me a tape measure. In a middle school algebra class we had a word problem on a test that had us divide by the number of cards in a deck of cards. I didn't think this was a fair question, because it assumed that everyone knew how many cards were in a deck of cards. I went to the teacher's desk and whisper…

> In a middle school algebra class we had a word problem on a test that had us divide by the number of cards in a deck of cards. I didn't think this was a fair question, because it assumed that everyone knew how many cards were in a deck of cards. I went to the teacher's desk and whispered this concern to her and she said "Come on, even my 5 year old knows how many cards are in a deck of cards."

Just for reasonably-common playing card decks, I can think of at least three possibilities -- 48 (standard pinochle deck), 52 (poker deck w/o jokers), and 54 (poker deck w/jokers). And in middle school -- since there was a lot of card playing in my house -- I probably would have been aware of all three.

Re: How Old Is The Shepherd?

#54

Post by recuter » Wed, Dec 04, 2013, 6:36 PM UTC

rprospero wrote: post #39

These kids were in something of a no win situation. I'm imagining a different class where 75% of the students said that there wasn't enough information to complete the problem: --- Our younger generation is doomed because they clearly don't understand math. After all, this is a fairly basic Fermi problem. The shepard probably started his own flock at around 18 and with two sheep. A sheep is a large mammal, so I'll as…

I up voted you despite the forgotten 2 dogs who cannot possibly have both survived for 15+ years.

Re: How Old Is The Shepherd?

#55

Post by tedsanders » Wed, Dec 04, 2013, 6:37 PM UTC

x0054 wrote: post #50

The problem is teachers! One of my relatives is taking Community College level math right now. I was helping her with some homework, which was multiple choice. The problem was simple, find an area of a triangle. We did the problem, and the answer was not among one of the possible solutions. I quickly double checked my work, making sure I was right, and we decided to mark none on the problem sheet and give the right a…

I think students (who are themselves a product of their parents and their culture) are also part of the problem. When students don't try, they fall behind, and when they fall behind, they have no choice but to make silly guesses.

Re: How Old Is The Shepherd?

#56

Post by dragonwriter » Wed, Dec 04, 2013, 6:37 PM UTC

arbitrarilyHigh wrote: post #8

nimble wrote: post #5

This would never happen if there was a laptop in every classroom. (EDIT: Sarcasm alert -- see my response below before you downvote me) EDIT: Just watched the video. Scary.

Wait, how would having a laptop in the classroom prevent this situation?

Well, if students could use the laptop during the test, since its a no-answer question that comes directly from well-publicized earlier research, at least some of them would google it and probably get the correct answer.

This doesn't, of course, address the fundamental issue that the test reveals, but it would impact the results of the test.

Re: How Old Is The Shepherd?

#57

Post by yongjik » Wed, Dec 04, 2013, 6:41 PM UTC

lasermike026 wrote: post #10

We can learn from Descartes, Aristotle, and others to develop a curriculum teaching children how to think and process. The idiots that run this country do not want that. It's about the curriculum. We can develop the world we want by teaching the next generation.

I don't really understand this kind of categorical bashing of public education. Descartes, Aristotle, and most "others" you're thinking of lived in societies where the majority couldn't even read, and they didn't consider that a problem. Reading without moving your lips was considered an exceptional skill during the middle ages (or so I've heard).

Are you sure they really knew much more about a practical system of education than we do now?

Re: How Old Is The Shepherd?

#58

Post by recuter » Wed, Dec 04, 2013, 6:41 PM UTC

C1D wrote: post #47

rprospero wrote: post #39

These kids were in something of a no win situation. I'm imagining a different class where 75% of the students said that there wasn't enough information to complete the problem: --- Our younger generation is doomed because they clearly don't understand math. After all, this is a fairly basic Fermi problem. The shepard probably started his own flock at around 18 and with two sheep. A sheep is a large mammal, so I'll as…

Is this honestly a joke. How on earth could you expect a student to come up with an answer to a question with no information even slightly relevant to the answer; that is not a basis to judge math skills. Also your above calculation is no better than the ones the grade eights had made. If you had any knowledge of farms you would know that the Shepard probably bought a lot of sheep too and maybe some of them belonged…

His assumptions may be faulty but that isn't the point, he constructed at least a somewhat reasonable model and extrapolated some number crunching.

The OP link claims a few students tried (for no reason) to divide 125 by 5 and failed to do even that. There is no right answer obviously, it is how you play and tinker with it - the more mathematical tools you have in your toolbox the more you could improvise, see also Credit Default Swaps.

Nerds like to conflate basic competence at technical skills with intelligence. :)

However, while being able to muck about like this doesn't necessarily prove one is smart it at least demonstrates some capacity for learning and exploration. I think that is the gist of the lament - that schools don't play with math, they drill - and agree with its spirit.

Re: How Old Is The Shepherd?

#59

Post by tedsanders » Wed, Dec 04, 2013, 6:41 PM UTC

jessaustin wrote: post #27

I think many eighth graders would be sophisticated enough for some dimensional analysis if it were presented in the right way. It's hard to imagine students who had been taught that, making these sorts of mistakes.

It's important not to confuse understanding a topic with having been taught the topic. If someone understands dimensional analysis, sure, they won't make the mistake. But it's easy to imagine students who were taught dimensional analysis making these kinds of mistakes.

I think it's a mistake to argue that because students don't understand method X to solve a problem, they should be taught method Y. The problem is the lack of understanding, not the method.

Re: How Old Is The Shepherd?

#60

Post by Dru89 » Wed, Dec 04, 2013, 6:42 PM UTC

hyperpape wrote: post #7

I thint there is an unfortunate temptation to look at the students and think "how stupid are they?", but I wonder if the issue is more about familiarity of tasks. If students are going along solving word problems that always make sense, they have zero practice in identifying which questions are well posed and which aren't. It may not be that they're bad at reasoning through word problems, so much as they aren't used…

I think perhaps a better setup to the problem for a child might be to make a question that is possible to answer, but has extraneous information. Something like: "There are 12 children, 3 bats, 15 balls, and 2 swings. If everyone is holding a ball, how many balls are left over?"