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The student is absolutely correct. I don't think it's even open for debate. Cutting anything in half requires exactly one cut; cutting in thirds requires two.

The student is absolutely correct. I don't think it's even open for debate. Cutting anything in half requires exactly one cut; cutting in thirds requires two. It's as simple as that. The teacher that crafted the question, or worse yet, the publisher of a textbook that may have provided the test question, needs to take a hard look at whether or not they are in the correct profession. The fact that the teacher not only marked the answer wrong (which could have just resulted from looking at a publisher-provided answer key) but actually wrote down a completely incorrect justification for the teacher's incorrect answer is rather disturbing to me. Also, this did not occur in a vacuum. Either no other students answered the question correctly, or the teacher saw the question being answered correctly by others and repeatedly marked it wrong with the same justification. Either way, it causes concern about the teacher.

shurcooL 14y ago
You can't tell if it was a simple "whoops, I thought this question belonged to a problem category X, and I overlooked that it does not" typo-like mistake, meaning the teacher would instantly realize his/her mistake if you point it. Or if they wouldn't get it even after you try to explain it to them (what you're trying to imply here). When grading things, ppl usually face hundreds of copies at a time and it's very tedious. It's easy to scrutinize a single highlighted problem that someone got wrong in hindsight, not realizing the person might've only dedicated 7 seconds to this problem out of 1000 others that were graded correctly. I personally try to give them the benefit of doubt and assume best case scenario (but I also understand it might not be).
- downandout 14y ago
  True, but I think that maybe 1/3 or more of the students would have answered this correctly. At some point during the grading process, you would think the teacher would begin to wonder why all of these students would have answered such a seemingly simple question "incorrectly" and take a second look.
  - DanBC 14y ago
    ...because 'trick' questions are (at least, were) part of math. The justification is to make sure people read, and understand, the question.
    - mratzloff 14y ago
      It's not a trick question, just a bad one. It doesn't include enough information to give an informed answer. Telepathy is required to suss out the author's intention. In the real world, you can ask more questions and get a more complete picture. On an exam, generally you must accept what you are given.
- doorhammer 14y ago
  I agree with this. I think it's a pretty decent example of the fundamental attribution error. The context of the problem clearly sets it up as one of those "everyone gets this wrong, so make sure you think a second" situations (I had to think a second, anyway). I'd extend that to the publisher as well, though (or at least it's individual employees creating the book). First off, assuming the answer key has "15", I'm not in any way saying it's okay that we have text books teaching clearly incorrect information; I'm also not in the know on how 3rd grade math textbooks are created. That said, I've been in tons of jobs where you're expected to produce a crap ton of work at a breakneck pace and god help you if you want five minutes to check your work for dumb errors, because y'aint gettin it. Of course, it could also easily be said that this is also the publishers fault for creating a working environment that isn't sufficiently rigorous or overburdens the employees.
  - jodrellblank 14y ago
    On the topic of how math textbooks are created, you might like this commentary from Richard Feynman when he served on a school-math-textbook recommendation committee: http://www.textbookleague.org/103feyn.htm http://www.textbookleague.org/103feyn.htm
    - doorhammer 14y ago
      That was an awesome read. Thanks for the article. It makes me think about how corporations work a lot of the time.
- keithpeter 14y ago
  "When grading things, ppl usually face hundreds of copies at a time and it's very tedious." Oh, yes, been there and I have the video. Don't you work from pre-written and checked marking schemes?
  - noamsml 14y ago
    It depends. In algorithm classes, there are often many right answers, including ones you haven't thought of before. Same goes for most college math.
    - keithpeter 14y ago
      "In algorithm classes, there are often many right answers" I accept this, but I'm assuming the original algorithm that a creative student produces will pass tests/produce same output as the 'textbook' solution. My understanding of the original article is that a correct final answer was marked wrong. "Same goes for most college math." Absolutely. My favourite from 16+ maths (GCSE in UK) is the area of a trapezium. Most find the mean length of the two parallel sides and multiply that by the distance between the parallel sides (so make a rectangle of the same area). About 1 in 15 break the trapezium up into two triangles and add the areas.
      - mkopinsky 14y ago
        The third option would be to chop off both "wings" and consider it as a square plus two triangles. That is often my instinct when I forget to do it with the mean length of the parallels.
- yew 14y ago
  I'd be less worried if this seemed like a one-off thing (or if math professors were obligated to drive exclusively on bridges designed by their own students, heh). As it is, this is one case among many (not all about grade schoolers and not all 'stories on the Internet' by a long shot) and the professor doesn't always acknowledge they were wrong. Speaking as an engineer, the work is hard enough when you do understand the math.
jrabone 14y ago
It is ABSOLUTELY open for debate, and part of the clue is in the question "if she works just as fast" ie. the cutting rate is constant. Then, it is ambiguous since the SIZE of the pieces is not mentioned. It's not the teacher's fault, per se; the question is unanswerable. The student picked one interpretation but the (likely) correct one is shown in the answer http://math.stackexchange.com/a/380007 http://math.stackexchange.com/a/380007
- downandout 14y ago
  Look at the image provided with the question. It shows a saw cutting the board in a way that leaves it unambiguous - the cutting time for that cut would be identical regardless of where each cut took place.
  - jrabone 14y ago
    That's not a board...
- randlet 14y ago
  It's only open for debate if you're being extremely pedantic. There is even an illustration demonstrating exactly what the cuts look like! Yes, if you want to be very nit-picky the question is undefined, but this is a third grade math test and the only reasonable answer is 20min. The student was absolutely correct.
  - dhimes 14y ago
    I agree. If I am the principal and the student protests to me and the teacher gives some bizarre-ass interpretation of the problem to me, the teacher will have a problem with me. I've seen enough of that in high-school physics where the teacher literally doesn't understand what the hell the problem is asking to piss off the Good Humor man.
- learc83 14y ago
  There is a picture of that illustrates the cut that is being made well enough to infer. Some inferences have to be made, this is a human taking the test not a robot, and it's a 3rd grade test. Even if the size of the pieces were specified, she could be cutting a different kind of wood or using a different saw or the humidity level could be different, but she's still "working just as fast". 3rd graders would be confused if you attempted to be completely unambiguous with this time of question.
dhimes 14y ago
My god, this looks more like a 4chan troll post than stackexchange. I'm not convinced this really happened. Is this the only kid in the class that got it right? Did the teacher not then notice when the brighter kids were coming up with 20 min that there may be something to it, and reconsider the question himself/herself? So much fail in so little space. Ugh.
- wtallis 14y ago
  You're not convinced this actually happened? When I was in elementary school, I regularly (ie. several times per semester) got into arguments with my math and science teachers over stuff this dumb. There's no need to make up something like this when you can find it in the real world so easily.
  - Sunlis 14y ago
    In grade school I had an argument with my science teacher about wheels. She said that a point along the outside of a wheel moved faster than a point nearer to the center (which is absolutely correct). However, she followed that up by saying that the outside of the wheel makes more revolutions than the inside. I tried to correct her, but she wasn't having any of it. So I grabbed my bike from outside, brought it into the classroom and tied two pieces of string onto one of the spokes on the bike: one near the axel, one near the tire. A few spins of the wheel had her convinced, but I can't believe I actually had to do it.
    - dhimes 14y ago
      At least she admitted it- bravo for her (and you!)
    - mkopinsky 14y ago
      If anything, the inside should have to make more revolutions. Since the whole bike is traveling at 10 MPH, at the point with the smaller radius, you'd need more revolutions to travel that same linear speed. ;-)
- jayferd 14y ago
chacham15 14y ago
While, given the picture presented the child's solution makes the most sense, there is another close scenario in which the teacher is correct[1]. So its not really "as simple as that." [1]http://math.stackexchange.com/a/380007 http://math.stackexchange.com/a/380007
- monkeynotes 14y ago
  Yes, the question did not account for unknown specifics. There is also a 3rd answer which in which the answer accounts for the person making the cuts having to answer the phone half way through the job.
  - wyck 14y ago
    Context is everything, this is a question for a 3rd grader not someone who is in Calculus. I think it's safe to assume the student is right given the screenshot.
- mrtksn 14y ago
  this is not a plausible scenario at all. if the quantity of work done is not equal at each step the question is impossible to answer which means that the teacher is nor right, just there is a possibility to be right. but then, every answer could be right, just adjust your cutting path according to the answer you would like to be correct.
keithpeter 14y ago
Yes. This is the '10 posts, nine spaces' problem. Here is another version: A fence is made using 15 posts spaced equally along a straight line. There are 3m between each post. What is the distance between the first and last post? When I'm teaching this kind of thing, we go out and walk around the building site opposite with a few 15m measuring tapes. The physical walking out and measuring helps.
- jasomill 14y ago
  So does considering simpler cases of two posts (3), three posts (3 + 3), and four posts (3 + 3 + 3), then discovering the pattern (3(n - 1)).
  - keithpeter 14y ago
    Yes when teaching GCSE here in the UK where there is an algebra component. I've also had students in Functional Maths classes just sketching arrangements of posts and counting the spaces.
- WildUtah 14y ago
  +1 for arranging your question so that it has The answer.
- shrikant 14y ago
  Surely I can't be the only one who wondered if the posts were of non-negligible thickness!
  - keithpeter 14y ago
    OK, you got me! Change "There are 3m between each post." to "The distance from one post centre to the next is 3m" Which illustrates the general point: you need teams working the test and checking their answers against what the writer thought the answers were. You also need English specialists checking the wording of the questions.
- bigiain 14y ago
Total_Meltdown 14y ago
It is open for debate. The question does not say cut "into thirds," it says "into three pieces." This - http://i.stack.imgur.com/kEjP0.png http://i.stack.imgur.com/kEjP0.png - is a perfectly reasonable answer which, assuming the rate of cutting is constant, would result in 15 minutes. It's a bad question. Edit: That said, I would have given the same answer as the student, because I think that's the most reasonable interpretation, especially considering the illustration. But the keyword there is "interpretation." The question is ambiguous. (My argument is taken from this answer: http://math.stackexchange.com/a/380007 http://math.stackexchange.com/a/380007 )
- downandout 14y ago
  As someone said below, it's only open for debate if you want to be pedantic. The Dr. Sheldon Cooper's among us may debate it, but it's pretty obvious what the question was looking for. There is even an illustration showing the cut, which would take an identical amount of time.
  - alok-g 14y ago
    The question says "board" while the illustration shows more of a rod. I deduce the question to be at least one of inconsistent or incomplete.
- Androsynth 14y ago
  You are correct, but you can trisect that piece of wood an infinite number of ways. The logical equilibrium point is 3 even pieces. The student chose a ratio of 1,1,1; which is the logical equilibrium point. your image shows 1.5,0.75,0.75; which is the second most logical ratio because it is in the form x + 2y = 3 (which can be trisected an infinite number of ways while maintaining that ratio). The third form would be x + y + z = 3; which can also be trisected an infinite number of ways and would be the least intuitive. i am agreeing with you, i am just trying to show that it is illogical for it to be 'open for debate'. There is a game theory term for this type of equilibrium, but i forgot its name. Its the same type of equilibrium as "there are three colors and a number, which one is different?" type sesame street problems.
- 14y ago
ubernostrum 14y ago
Most likely, whoever produces and publishes the question sets changed the question for a new edition and did not notice that the new question also changed the answer. In the previous edition it was probably something like "Marie works in a factory which makes cars; it takes her 10 minutes to finish two cars. How long will it take Marie to finish three cars?" And the answer to that would be 15 minutes, and the reasoning in the answer (based on reducing fractions, which is what it's probably supposed to teach) would be correct. But probably in the next edition the question changed from putting things together to cutting them apart, and the author/editor simply didn't realize that these are not interchangeable. The teacher, meanwhile, probably didn't look too closely at it, and simply applied the answer and reasoning supplied in the teaching materials for the question set. None of which implies that the teacher can't do the math; rather, it implies systemic problems in the way the materials are produced and in the methods used by teachers to grade the work.

shurcooL 14y ago

You can't tell if it was a simple "whoops, I thought this question belonged to a problem category X, and I overlooked that it does not" typo-like mistake, meaning the teacher would instantly realize his/her mistake if you point it. Or if they wouldn't get it even after you try to explain it to them (what you're trying to imply here). When grading things, ppl usually face hundreds of copies at a time and it's very tedious. It's easy to scrutinize a single highlighted problem that someone got wrong in hindsight, not realizing the person might've only dedicated 7 seconds to this problem out of 1000 others that were graded correctly. I personally try to give them the benefit of doubt and assume best case scenario (but I also understand it might not be).

downandout 14y ago
True, but I think that maybe 1/3 or more of the students would have answered this correctly. At some point during the grading process, you would think the teacher would begin to wonder why all of these students would have answered such a seemingly simple question "incorrectly" and take a second look.
- DanBC 14y ago
  ...because 'trick' questions are (at least, were) part of math. The justification is to make sure people read, and understand, the question.
  - mratzloff 14y ago
    It's not a trick question, just a bad one. It doesn't include enough information to give an informed answer. Telepathy is required to suss out the author's intention. In the real world, you can ask more questions and get a more complete picture. On an exam, generally you must accept what you are given.
doorhammer 14y ago
I agree with this. I think it's a pretty decent example of the fundamental attribution error. The context of the problem clearly sets it up as one of those "everyone gets this wrong, so make sure you think a second" situations (I had to think a second, anyway). I'd extend that to the publisher as well, though (or at least it's individual employees creating the book). First off, assuming the answer key has "15", I'm not in any way saying it's okay that we have text books teaching clearly incorrect information; I'm also not in the know on how 3rd grade math textbooks are created. That said, I've been in tons of jobs where you're expected to produce a crap ton of work at a breakneck pace and god help you if you want five minutes to check your work for dumb errors, because y'aint gettin it. Of course, it could also easily be said that this is also the publishers fault for creating a working environment that isn't sufficiently rigorous or overburdens the employees.
- jodrellblank 14y ago
  On the topic of how math textbooks are created, you might like this commentary from Richard Feynman when he served on a school-math-textbook recommendation committee: http://www.textbookleague.org/103feyn.htm http://www.textbookleague.org/103feyn.htm
  - doorhammer 14y ago
    That was an awesome read. Thanks for the article. It makes me think about how corporations work a lot of the time.
keithpeter 14y ago
"When grading things, ppl usually face hundreds of copies at a time and it's very tedious." Oh, yes, been there and I have the video. Don't you work from pre-written and checked marking schemes?
- noamsml 14y ago
  It depends. In algorithm classes, there are often many right answers, including ones you haven't thought of before. Same goes for most college math.
  - keithpeter 14y ago
    "In algorithm classes, there are often many right answers" I accept this, but I'm assuming the original algorithm that a creative student produces will pass tests/produce same output as the 'textbook' solution. My understanding of the original article is that a correct final answer was marked wrong. "Same goes for most college math." Absolutely. My favourite from 16+ maths (GCSE in UK) is the area of a trapezium. Most find the mean length of the two parallel sides and multiply that by the distance between the parallel sides (so make a rectangle of the same area). About 1 in 15 break the trapezium up into two triangles and add the areas.
    - mkopinsky 14y ago
      The third option would be to chop off both "wings" and consider it as a square plus two triangles. That is often my instinct when I forget to do it with the mean length of the parallels.
yew 14y ago
I'd be less worried if this seemed like a one-off thing (or if math professors were obligated to drive exclusively on bridges designed by their own students, heh). As it is, this is one case among many (not all about grade schoolers and not all 'stories on the Internet' by a long shot) and the professor doesn't always acknowledge they were wrong. Speaking as an engineer, the work is hard enough when you do understand the math.

jrabone 14y ago

It is ABSOLUTELY open for debate, and part of the clue is in the question "if she works just as fast" ie. the cutting rate is constant. Then, it is ambiguous since the SIZE of the pieces is not mentioned. It's not the teacher's fault, per se; the question is unanswerable. The student picked one interpretation but the (likely) correct one is shown in the answer http://math.stackexchange.com/a/380007 http://math.stackexchange.com/a/380007

downandout 14y ago
Look at the image provided with the question. It shows a saw cutting the board in a way that leaves it unambiguous - the cutting time for that cut would be identical regardless of where each cut took place.
- jrabone 14y ago
  That's not a board...
randlet 14y ago
It's only open for debate if you're being extremely pedantic. There is even an illustration demonstrating exactly what the cuts look like! Yes, if you want to be very nit-picky the question is undefined, but this is a third grade math test and the only reasonable answer is 20min. The student was absolutely correct.
- dhimes 14y ago
  I agree. If I am the principal and the student protests to me and the teacher gives some bizarre-ass interpretation of the problem to me, the teacher will have a problem with me. I've seen enough of that in high-school physics where the teacher literally doesn't understand what the hell the problem is asking to piss off the Good Humor man.
learc83 14y ago
There is a picture of that illustrates the cut that is being made well enough to infer. Some inferences have to be made, this is a human taking the test not a robot, and it's a 3rd grade test. Even if the size of the pieces were specified, she could be cutting a different kind of wood or using a different saw or the humidity level could be different, but she's still "working just as fast". 3rd graders would be confused if you attempted to be completely unambiguous with this time of question.

dhimes 14y ago

My god, this looks more like a 4chan troll post than stackexchange. I'm not convinced this really happened. Is this the only kid in the class that got it right? Did the teacher not then notice when the brighter kids were coming up with 20 min that there may be something to it, and reconsider the question himself/herself? So much fail in so little space. Ugh.

wtallis 14y ago
You're not convinced this actually happened? When I was in elementary school, I regularly (ie. several times per semester) got into arguments with my math and science teachers over stuff this dumb. There's no need to make up something like this when you can find it in the real world so easily.
- Sunlis 14y ago
  In grade school I had an argument with my science teacher about wheels. She said that a point along the outside of a wheel moved faster than a point nearer to the center (which is absolutely correct). However, she followed that up by saying that the outside of the wheel makes more revolutions than the inside. I tried to correct her, but she wasn't having any of it. So I grabbed my bike from outside, brought it into the classroom and tied two pieces of string onto one of the spokes on the bike: one near the axel, one near the tire. A few spins of the wheel had her convinced, but I can't believe I actually had to do it.
  - dhimes 14y ago
    At least she admitted it- bravo for her (and you!)
  - mkopinsky 14y ago
    If anything, the inside should have to make more revolutions. Since the whole bike is traveling at 10 MPH, at the point with the smaller radius, you'd need more revolutions to travel that same linear speed. ;-)
jayferd 14y ago

chacham15 14y ago

While, given the picture presented the child's solution makes the most sense, there is another close scenario in which the teacher is correct[1]. So its not really "as simple as that." [1]http://math.stackexchange.com/a/380007 http://math.stackexchange.com/a/380007

monkeynotes 14y ago
Yes, the question did not account for unknown specifics. There is also a 3rd answer which in which the answer accounts for the person making the cuts having to answer the phone half way through the job.
- wyck 14y ago
  Context is everything, this is a question for a 3rd grader not someone who is in Calculus. I think it's safe to assume the student is right given the screenshot.
mrtksn 14y ago
this is not a plausible scenario at all. if the quantity of work done is not equal at each step the question is impossible to answer which means that the teacher is nor right, just there is a possibility to be right. but then, every answer could be right, just adjust your cutting path according to the answer you would like to be correct.

keithpeter 14y ago

Yes. This is the '10 posts, nine spaces' problem. Here is another version: A fence is made using 15 posts spaced equally along a straight line. There are 3m between each post. What is the distance between the first and last post? When I'm teaching this kind of thing, we go out and walk around the building site opposite with a few 15m measuring tapes. The physical walking out and measuring helps.

jasomill 14y ago
So does considering simpler cases of two posts (3), three posts (3 + 3), and four posts (3 + 3 + 3), then discovering the pattern (3(n - 1)).
- keithpeter 14y ago
  Yes when teaching GCSE here in the UK where there is an algebra component. I've also had students in Functional Maths classes just sketching arrangements of posts and counting the spaces.
WildUtah 14y ago
+1 for arranging your question so that it has The answer.
shrikant 14y ago
Surely I can't be the only one who wondered if the posts were of non-negligible thickness!
- keithpeter 14y ago
  OK, you got me! Change "There are 3m between each post." to "The distance from one post centre to the next is 3m" Which illustrates the general point: you need teams working the test and checking their answers against what the writer thought the answers were. You also need English specialists checking the wording of the questions.
bigiain 14y ago

Total_Meltdown 14y ago

It is open for debate. The question does not say cut "into thirds," it says "into three pieces." This - http://i.stack.imgur.com/kEjP0.png http://i.stack.imgur.com/kEjP0.png - is a perfectly reasonable answer which, assuming the rate of cutting is constant, would result in 15 minutes. It's a bad question. Edit: That said, I would have given the same answer as the student, because I think that's the most reasonable interpretation, especially considering the illustration. But the keyword there is "interpretation." The question is ambiguous. (My argument is taken from this answer: http://math.stackexchange.com/a/380007 http://math.stackexchange.com/a/380007 )

downandout 14y ago
As someone said below, it's only open for debate if you want to be pedantic. The Dr. Sheldon Cooper's among us may debate it, but it's pretty obvious what the question was looking for. There is even an illustration showing the cut, which would take an identical amount of time.
- alok-g 14y ago
  The question says "board" while the illustration shows more of a rod. I deduce the question to be at least one of inconsistent or incomplete.
Androsynth 14y ago
You are correct, but you can trisect that piece of wood an infinite number of ways. The logical equilibrium point is 3 even pieces. The student chose a ratio of 1,1,1; which is the logical equilibrium point. your image shows 1.5,0.75,0.75; which is the second most logical ratio because it is in the form x + 2y = 3 (which can be trisected an infinite number of ways while maintaining that ratio). The third form would be x + y + z = 3; which can also be trisected an infinite number of ways and would be the least intuitive. i am agreeing with you, i am just trying to show that it is illogical for it to be 'open for debate'. There is a game theory term for this type of equilibrium, but i forgot its name. Its the same type of equilibrium as "there are three colors and a number, which one is different?" type sesame street problems.
14y ago

ubernostrum 14y ago

Most likely, whoever produces and publishes the question sets changed the question for a new edition and did not notice that the new question also changed the answer. In the previous edition it was probably something like "Marie works in a factory which makes cars; it takes her 10 minutes to finish two cars. How long will it take Marie to finish three cars?" And the answer to that would be 15 minutes, and the reasoning in the answer (based on reducing fractions, which is what it's probably supposed to teach) would be correct. But probably in the next edition the question changed from putting things together to cutting them apart, and the author/editor simply didn't realize that these are not interchangeable. The teacher, meanwhile, probably didn't look too closely at it, and simply applied the answer and reasoning supplied in the teaching materials for the question set. None of which implies that the teacher can't do the math; rather, it implies systemic problems in the way the materials are produced and in the methods used by teachers to grade the work.