Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

How Old Is The Shepherd?

robertkaplinsky.com

Post reply on HN
Print view View original

71–80 of 100 posts

Re: How Old Is The Shepherd?

#71

Post by scotty79 »

I have an idea for whenever I'll have my own kids. I'll buy them as toys as many measurement devices as I possibly can. This will show them, I hope, that numbers are not an abstract thing. They are everywhere. Not visible at first glance but with proper device you can see them.

I think the fact that my grandfather (electrician by trade and self-taught carpenter, shoemaker and general DIY guy) owned and used vernier scale, micrometer, folding rule, voltmeters and ammeters contributed to my ability at mathematics, physics, chemistry, computer science and being a reasonable person.

Surely I used a vernier scale as a makeshift futuristic gun, micrometer to squish my fingers, folding rule as kind of pretend switchblade but later also for seeing numbers in the world.

Re: How Old Is The Shepherd?

#72

Post by dublinben »

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…

It sounds like you just had a bad math teacher. The Pythagorean Theorem has quite a few proofs, a number of which are understandable to students with only basic geometry knowledge. I'm almost certain I had to prove it in my math class at the time.

Re: How Old Is The Shepherd?

#73

Post by yongjik »

pbhjpbhj wrote: post #68
yongjik wrote: post #51

Earlier quoted context omitted.

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…

>* ... 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 i…

> 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."

Re: How Old Is The Shepherd?

#75

Post by niuzeta »

yongjik wrote: post #57
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 e…

> Reading without moving your lips was considered an exceptional skill during the middle ages (or so I've heard).

You are refering to what contemporaries wrote about Thomas Aquinas, a well-renowned theologist in medieval era. I believe he was considered a genius because he could read without moving your lips.

While it is a good food for thought for intellectual capabilities, one should also take note that in his time books were not what books as we know. No typography existed and whitespacing blocks between words were non-existent. Truly, they were mostly transcribed words with sometimes bad spelling and without a paragraph break. To read without reading out aloud meant that the reader had a mental capability to quickly parse out words, form a sentence, understand what the author meant out of context.

Re: How Old Is The Shepherd?

#76

Post by bentcorner »

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…

Everyone is clearly reading too much into the question. There is no shepherd. Our fictional herd here is actually an allegory for the struggle between the lower class "the sheep" and the upper class "the dogs". A sheep can only do as a sheep does, and despite its best efforts can never ever be a dog. The belief that there is a shepherd, there to control the dogs, is a false hope given to the sheep by the dogs themselves.

Besides, even if there was a shepherd, what do you think happens to the sheep anyway? That's right.

Re: How Old Is The Shepherd?

#77

Post by cunac »

mikeash wrote: post #49
NoPiece wrote: post #3

Especially with younger kids, when they are asked a question by someone with authority, there is a reasonable presumption that it can be answered. I'm all for teaching them to challenge that presumption, but I think you'd get a more fair result if the question was, "Can you figure out the age of the shepherd if you know how many dogs and sheep he has in his flock?"

Isn't that the whole point? We are teaching children badly by always giving them clear-cut problems that always have an answer, when the world is full of fuzzy problems that may not have an answer. Given the environment, why wouldn't the children guess? For years, we give them homework and tests where a guess is always equal to or better than no answer at all. But that's nearly the opposite of how the world works, so…

everything has answer we just don't know what it is :-)

Re: How Old Is The Shepherd?

#78

Post by bentcorner »

MBCook wrote: post #14
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 the last kid was extremely revealing. There are two numbers, and they didn't say "product", "sum", or "difference", so it must be division. Clearly the problems she gets in school are extremely rote and don't really require reading the problem much. Just look for a keyword or two and you can 'solve' it.

I feel bad for this child. Clearly she has gotten through her schooling through sheer brute force without applying very much understanding. She is likely at a grade level where building the basics back up is not possible without 1:1 attention.

Re: How Old Is The Shepherd?

#79

Post by McLeopold »

will_work4tears wrote: post #46
McLeopold wrote: post #25

Let's assume the shepherd graduated high school at 18 then bought 2 lambs and a farm. He was nice to his sheep so didn't breed them until 2 years and not after 7. The average litter size is 2 and the average age is 11. Let's assume an even number of male and female sheep. At year 2 he'll have 4 sheep (2 original and 2 new lambs). 2 more at year 3 and then 4 at year 3 (the first litter can now breed). At year 7 the or…

Or, conversely, the shepherd is 16 and they are the father's sheep. Nobody said they were his sheep.

You're right, nobody did say that. The point I was trying to make is that with the absence of data, you have to make assumptions and they should be clearly defined. My assumptions defined his starting age and how he obtained the first 2 sheep and the fact they were his.

I guess I would want my kids too look at any math problem with the following things in mind: * identify units of measurement * identify useful data * identify non-useful data * identify assumptions needed to complete answer

There are more or different assumptions I could make, such as cooperative breeding amoungst other breeders or a larger flock to start with, or a completely different model of breeding sheep. I could have described a scenario where he started with 2 sheep and went through several trading and auction rounds until he had 125 with some bonus dogs like the guy that got a house from a paper clip.

We don't have a time measurement in years, so we need some type of sheep per time or time per sheep unit. I choose an assumption of breeding and came up with about 1 sheep per year per sheep.

The original question is very close to a nonsense question, which requires so many assumptions that probably most answers can be well defended with the right set of assumptions. But at the very least you would hope a student could identify an answer in years could not be obtained with the given data of # of sheep and # of dogs.

(And, no, I don't think the units method is beyond an eight grader, even if the educational system thinks it is. The fermi problem may be.)

Re: How Old Is The Shepherd?

#80

Post by CodeMage »

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…

Obviously, the above is exaggerated, but the point remains that any answer or non-answer by the students can be interpreted as a lack of math skills and evidence of poor critical thinking.

That point remains wrong. You can treat the question as a Fermi problem, but when you do that, it's because you realize and acknowledge that there isn't enough information in the problem to complete it by other means.

Post reply on HN