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Comment by epochwolf | Hacker News Reader

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 answer than to risk annoying the teacher. The students may not think in those terms. They just know they need to provide the correct answer in the correct format. Understanding why is not important or rewarded. Only the result matters.

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> This is totally unsurprising. Most word problems in textbooks are poorly written and have little to no basis in reality.

There's a difference between a basis in reality and a internal completeness.

I think the problem isn't the way "most word problems in textbooks" are written, except insofar as most are, in fact, internally complete and so students are not taught to verify that the question is complete and are instead encouraged to just throw math at the numbers in the problem until they get something that looks like an answer.

Pedagogically, there may be some sense to this at certain levels, but eventually it becomes problematic if students don't have the both the skills and the understanding that it is desirable to first evaluate whether the question is complete.

"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 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."

Not 10 minutes later, another student raised his hand and asked how many cards were in a deck of cards.

> 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.

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.

>* ... but you are not being critical. You're just being obtuse.* //

I disagree. One is being critical.

If however you try to use that as an excuse not to perform the calculation then you're definitely being obstructive.

It is absolutely right for a student performing such calculations to realise there are issues with it not being realistic. They should understand that it's an approximation and understand that even in a perfect, flat, frictionless world it's still an approximation [relativistic mechanics are not being used] but that nonetheless it's a useful model the result produced by Newtonian mechanics is useful.

Indeed I'd say the realisation and ability to express the limitations mark out a student as capable of analytical thought.

>it actually makes it easier for the students to practice and internalize the concept they're learning. //

I fear you're making the calculation the end in itself (we have computers for that!) and not the subject of critical analytical thinking which IMO defines mathematics.

> I fear you're making the calculation the end in itself (we have computers for that!)

Well, I have to disagree. Of course it's rather silly to make the calculation the goal in itself, but one needs to have a decent "feeling" of what would happen in a given domain. In math (up to college freshmen) or physics, that involves a lot of number-crunching. Until you get familiar with it.

It's same as CS students implementing quicksort, merge sort, heapsort, etc., even though when they graduate they will all use libraries. You can't really grok quicksort by reading the textbook and say "Hmm, I see."

You can grok most sorting methods remarkably well, though, by lining up a bunch of office junk on a big table and working through the sorting algorithm physically.

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