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How Old Is The Shepherd?

robertkaplinsky.com

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Re: How Old Is The Shepherd?

#91

Post by dragonwriter »

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 would be very surprised if that is not a rubric that was provided by an adult (whether teacher or otherwise.) Certainly, I saw this type of thing more than once when I was in school, and this was before the predominance of frequent high-stakes standardized testing on which school funding decisions were based, which increase the incentive for schools to narrowly prepare students to do well on the kinds of problems likely to appear on the tests.

Re: How Old Is The Shepherd?

#92

Post by dragonwriter »

j2kun wrote: post #20
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 agree wholeheartedly that students need to spend more time dealing with the setup of a problem (thinking about how best to express a vague idea mathematically) and in dealing with problems that don't have any known answer. I think this is a huge part of "mathematical thinking skills" that we claim we want to instill in students. It's a sad thing that most people don't really have a good definition of what a "mathem…

Honestly, I think that what you are discussing is the most basic of analytical thinking, and transcends mathematics.

Re: How Old Is The Shepherd?

#93

Post by jessaustin »

dragonwriter wrote: post #45
jessaustin wrote: post #22

Earlier quoted context omitted.

Part of the problem with this question is that many students today don't know what a "shepherd" is. Perhaps this is also a failure of education, but it isn't a failure of math education. It would be better to say a "farmer" owns these animals, since most children would have heard the word "farmer" at some point in their lives. Or maybe it would be better to say "your neighbor" has so many cats and so many dogs but th…

> Part of the problem with this question is that many students today don't know what a "shepherd" is. What a shepherd is is completely irrelevant [1] to the problem. > Perhaps this is also a failure of education, but it isn't a failure of math education. The inability to identify which things in a word problem are relevant to the question being asked is clearly a failure in education in the area of logic and reasonin…

What a shepherd is is completely irrelevant to the problem.

...says the person privileged to know what a shepherd is. I agree that math education could be improved, but this study may not be the best basis for that improvement.

Re: How Old Is The Shepherd?

#94

Post by Falling3 »

anon4 wrote: post #70
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…

Well look, all math problems have a numerical answer. I've been doing them for 8 years so far and every time they've had an answer. These problems are also very silly. But I can confidently state that every math problem has some words and numbers and you are expected to perform some kind of calculation with the numbers based on the words around them. The problem I see right now doesn't have an immediate connection be…

I'm not going to pretend to be the most intelligent person here or even that I'm more intelligent than all of those kids who came up with a number. But what I've always been willing to do is question people. Like most kids, I was given plenty of word problems in school. And there were several times where I called out the teacher or the textbook author for either leaving out information or relying on assumptions that I couldn't comfortably make. In fact, now that I think about it, later in school there were multiple choice answers that went something like "not enough information to answer".

I do not think a reasonable justification is "Well all the other problems I had that looked like this had an easy answer so this one should too". And the fact, that several students were unable to kludge an answer together supports that.

>With the information given I can do no better. You can do a lot better! You can say that the question is unanswerable.

Re: How Old Is The Shepherd?

#95

Post by brettm247 »

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?"

The "Education" system doesn't teach sheeple to be critical thinkers. It trains a subservient citizenry. You don't want your slaves to be critical thinkers, just trained enough. The student is disciplined and trained to guess based on incomplete information given to them. We have got to teach children to build upon first principles.

Poor kids, they are so afraid of being wrong! They would rather guess then take the time to figure out the fundamentals. They want to tell the teacher what he/she wants to hear regardless if it is a correct solution or not. I suppose that's what humans learn in a prison.

School Sucks. Enough with Civic Religion.

https://mises.org/daily/2937/

Re: How Old Is The Shepherd?

#96

Post by chr1 »

recuter wrote: post #58
C1D wrote: post #47

Earlier quoted context omitted.

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 C…

His solution isn't much different from solutions most of the kids were giving. That is when faced with problem you don't understand -throw away the problem -solve something you are comfortable with -try to convince others it is the solution of the original problem

We don't need people who fabricate data and make unfounded guesses.

Re: How Old Is The Shepherd?

#97

Post by lotsofcows »

bentcorner wrote: post #76
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 themsel…

Nice.

I disagree though, the sheep invented the shepherd to give themselves a purpose.

History shows that a strong dictator can keep a population down for an awfully long time with nothing but violence. There's no reason for the dogs to bother inventing anything.

Re: How Old Is The Shepherd?

#98

Post by smoyer »

dragonwriter wrote: post #62
Dru89 wrote: post #60

Earlier quoted context omitted.

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?"

Filtering out extraneous information is an important and related skill, but its slightly different thing than identifying when the problem as phrased does not have the information needed to support an answer. While it may be the case that the education system fails to do enough at both of these, I suspect it does better at getting students to identify extraneous information and use only what is necessary than it does…

+1 ... between your comment and the one you responded to, both the "non-math" skills needed to solve problems in the real world are described.

Re: How Old Is The Shepherd?

#99

Post by mistercow »

jessaustin wrote: post #89
mistercow wrote: post #33

Earlier quoted context omitted.

But dimensional analysis is just another mathematical process turned into a rote method which does not require deeper understanding. The problem is not the pile of rote techniques is too small, but that students aren't learning how to actually think mathematically.

I find this "think mathematically" concept you invoke to be a bit fuzzy. Even geniuses (not me, but I've met some) can be caught out by novel constructions if they haven't had time to consider them carefully. Much mathematical sophistication consists of adding to "the pile of techniques". If a student has too shallow a pile, the goal of educators should be to pile on more. If we suspect the research under discussion…

> I suspect that an admonition to "think mathematically" is not even wrong.

I am not suggesting that we admonish students to think mathematically. I'm suggesting that we teach them to.

Re: How Old Is The Shepherd?

#100

Post by ars_technician »

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.

>Clearly the problems she gets in school are extremely rote

Not necessarily. It could just be that she is just learning how to answer tricky questions by using logic to determine what's not exactly spelled out.

That's about the same age that I started getting word problems that don't tell you specifically what you need to do so you have to 'find the problem'.

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