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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 task

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 to word problems that make zero sense. Given that context, it makes partial sense for a child to think "I must be making a mistake--I can't see how this problem works, but it must work somehow, because these problems always do make sense, even if sometimes I get them wrong, because I am not smart enough to understand them." Is that a good attitude? Heck no. If nothing else, this experiment shows that we need to teach students that math problems aren't always going to be nicely set up so that they make sense. But that's different from thinking kids are dumb for not adapting to an unexpected wrinkle on a test. An interesting companion experiment would be to prompt the students to explain the problem first, or see whether they could accurately determine which problems made sense and which didn't, when they knew that was what they were doing. My prediction is that the results would not be great, but that they'd be better.

dragonwriter 13y ago
> I think there is an unfortunate temptation to look at the students and think "how stupid are they?" I don't see any evidence of that in the comments on the original article or here. All of it seems to be focussed on the process of education and the habits it forms and the psychology of teacher/student (or more general authority figure) relations.
- hyperpape 13y ago
  Yeah, I wasn't calling anyone out. Or if I was, I was calling out my first reaction. But the point that I still think is an issue is that we don't know how much of the effect is about what the students _understand_ as much as it's about how they see the situation they are in. What incentives are there, and what is the student actually thinking?
MBCook 13y ago
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.
- bentcorner 13y ago
  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.
  - JshWright 13y ago
    Welcome to Common Core. Obviously there won't be non-sensical questions on the test, so why bother exposing kids to them in class? Teachers are being forced, now more than ever, to optimize for test scores, at the expense of real learning. This isn't a video about stupid kids, it's a video about a stupid education system.
    - acheron 13y ago
      Opposition to Common Core? You must be a "white suburban mom"! [1] [1] http://reason.com/archives/2013/11/22/no-arne-duncan-white-suburban-moms-arent http://reason.com/archives/2013/11/22/no-arne-duncan-white-s...
- dragonwriter 13y ago
  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.
- 13y ago
aidenn0 13y ago
I know there are at least some curricula that have word problems with at least 1 bit of extraneous information to try and train that. It can be somewhat amusing to see kids try and fit the extra number into their calculations.
j2kun 13y ago
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 "mathematical thinking skill" is in the first place. Figuring out how to adequately and precisely pose questions is one of the MOST mathematical skills, but it rarely shows up in discussions of standards and curricula.
- dragonwriter 13y ago
  Honestly, I think that what you are discussing is the most basic of analytical thinking, and transcends mathematics.
Dru89 13y ago
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?"
- dragonwriter 13y ago
  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 to get them to identify and confidently report when a question posed has inadequate information to support an answer.
  - Dru89 13y ago
    That's a great point. I suppose the problem that I see here is that schools often present problems as always having a solution, even when there's none to be found.
  - smoyer 13y ago
    +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.
anon4 13y ago
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 between the statement and the question parts. I have the numbers 125 and 5 and the question "how old is the shepherd?". I can see that the answer must be a person's age. The numbers refer to how many sheep and how many dogs are in the flock, which isn't really related to the shepherd's age. Still, there's probably some lateral thinking involved, or there's an omission, because I must obviously answer with a number. If I add, subtract or multiply the two numbers in any order, I do not get a number that is plausible as a person's age. However, if I divide them, I get 25, which is totally a possible answer. 25 is also the number of sheep per dog. Assuming that that's a normal ratio for a flock, we can say that the shepherd's flock contains 5 flock-units. So if the shepherd started at 17 years old (very plausible in a rural setting) and was given a new flock-unit every two years (obviously as you get older you get to take on more responsibility), at age 25 the amount of responsibility would have grown to 5 flock-units. This answer has a nice symmetry to it. Math answers have some sort of nice symmetry in them, so this sounds plausible. With the information given I can do no better. Answer: 25 years old.
- Falling3 13y ago
  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.
hibbelig 13y ago
The students aren't stupid, just badly trained.

dragonwriter 13y ago

> I think there is an unfortunate temptation to look at the students and think "how stupid are they?" I don't see any evidence of that in the comments on the original article or here. All of it seems to be focussed on the process of education and the habits it forms and the psychology of teacher/student (or more general authority figure) relations.

hyperpape 13y ago
Yeah, I wasn't calling anyone out. Or if I was, I was calling out my first reaction. But the point that I still think is an issue is that we don't know how much of the effect is about what the students _understand_ as much as it's about how they see the situation they are in. What incentives are there, and what is the student actually thinking?

MBCook 13y ago

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.

bentcorner 13y ago
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.
- JshWright 13y ago
  Welcome to Common Core. Obviously there won't be non-sensical questions on the test, so why bother exposing kids to them in class? Teachers are being forced, now more than ever, to optimize for test scores, at the expense of real learning. This isn't a video about stupid kids, it's a video about a stupid education system.
  - acheron 13y ago
    Opposition to Common Core? You must be a "white suburban mom"! [1] [1] http://reason.com/archives/2013/11/22/no-arne-duncan-white-suburban-moms-arent http://reason.com/archives/2013/11/22/no-arne-duncan-white-s...
dragonwriter 13y ago
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.
13y ago

aidenn0 13y ago

I know there are at least some curricula that have word problems with at least 1 bit of extraneous information to try and train that. It can be somewhat amusing to see kids try and fit the extra number into their calculations.

j2kun 13y ago

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 "mathematical thinking skill" is in the first place. Figuring out how to adequately and precisely pose questions is one of the MOST mathematical skills, but it rarely shows up in discussions of standards and curricula.

dragonwriter 13y ago
Honestly, I think that what you are discussing is the most basic of analytical thinking, and transcends mathematics.

Dru89 13y ago

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?"

dragonwriter 13y ago
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 to get them to identify and confidently report when a question posed has inadequate information to support an answer.
- Dru89 13y ago
  That's a great point. I suppose the problem that I see here is that schools often present problems as always having a solution, even when there's none to be found.
- smoyer 13y ago
  +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.

anon4 13y ago

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 between the statement and the question parts. I have the numbers 125 and 5 and the question "how old is the shepherd?". I can see that the answer must be a person's age. The numbers refer to how many sheep and how many dogs are in the flock, which isn't really related to the shepherd's age. Still, there's probably some lateral thinking involved, or there's an omission, because I must obviously answer with a number. If I add, subtract or multiply the two numbers in any order, I do not get a number that is plausible as a person's age. However, if I divide them, I get 25, which is totally a possible answer. 25 is also the number of sheep per dog. Assuming that that's a normal ratio for a flock, we can say that the shepherd's flock contains 5 flock-units. So if the shepherd started at 17 years old (very plausible in a rural setting) and was given a new flock-unit every two years (obviously as you get older you get to take on more responsibility), at age 25 the amount of responsibility would have grown to 5 flock-units. This answer has a nice symmetry to it. Math answers have some sort of nice symmetry in them, so this sounds plausible. With the information given I can do no better. Answer: 25 years old.

Falling3 13y ago
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.

hibbelig 13y ago

The students aren't stupid, just badly trained.