This is fascinating. I would be intrigued to see the results of asking the same question to students undergoing self-directed learning, either in a home schooling setting or in more progressive schools.
How Old Is The Shepherd?
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Re: How Old Is The Shepherd?
#32This 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.
Re: How Old Is The Shepherd?
#33I 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.
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.
Re: How Old Is The Shepherd?
#34I just asked my 2 yr old this same question. He just responded with "yellow!" /facepalm
That answer isn't really any more wrong than "His age is 25 sheep per dog".
Re: How Old Is The Shepherd?
#35This 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…
> 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.
Re: How Old Is The Shepherd?
#36We 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.
"Never attribute to malice that which is adequately explained by stupidity."
Were you taught that at school?
Re: How Old Is The Shepherd?
#37Earlier quoted context omitted.
Wait, how would having a laptop in the classroom prevent this situation?
That was sarcasm. My point was that if this level of critical thinking deficiency is really present, then there is something seriously wrong with the way kids are being taught, and calls that you hear for extra funding to pay for things like laptops in the classroom are really a giant waste of money until we fix whatever that is.
That's a good example of Poe's law. I decided to reply with (hopefully more apparent) sarcasm, because if it wasn't sarcasm, I didn't want to let it go, and if it was, I didn't want to be an ass, and I assumed you could take it as me going with the joke.
Re: How Old Is The Shepherd?
#38Re: How Old Is The Shepherd?
#39These 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:
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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 assume that it has a gestation period around 9 months. We'll also guess that a sheep reaches sexual maturity after 3 years, or four gestation periods. If we assume that all adult female sheep are kept gravid and that genders are divided evenly, we know that the number of female sheep after n gestation periods is
a(n) = a(n-1)+a(n-5)*0.5
Solving the recurrence relation and assuming that both sheep are adults when we start, there will be 60 female sheep, or 120 sheep in total, after 19 gestation periods. Thus the shepherd is around 33.
Of course, I've made several assumptions in my solution and I wouldn't expect eighth graders to come back with the same answer. However, the fact that they just threw up their hands and declared that the problem is insolvable shows that our school system is failing the next generation of entrepreneurs. We don't need people who give up and declare that nothing can be done - we need people who make guesses and take risks. Yes, expecting an eighth grader to solve a recurrence relation is beyond their ability, but they could make simpler approximations. Heck, they could have just divided the number of sheep by two and been right to within an order of magnitude. It works as a model - say a sheep is born every six month and be done with it. It may not be the best model, but the perfect is the enemy of the good. Instead, we've taught our student to be dependent on our teachers to provide them with all the information and not make any guesses on their own.
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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.
I'm not going to deny for a moment that our schools do a horrific job of teaching unit analysis - I've taught intro to physics and know how little our high school graduates know. Still, students are caught between two masters. When lacking information, students who guess are punished for lack of critical thinking and those who don't guess are punished for lack of effort and creativity. The blog post obviously indicates that the pendulum is currently swinging toward rewarding creativity over critical thinking. However, the pendulum will swing back and, in twenty years, we'll be complaining about how are students aren't doing nearly as well as the brilliant, creative children this blogger visited.
Re: How Old Is The Shepherd?
#40I weep for humanity.