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Eu e o Felipe Dib, do Você Aprende Agora, abordamos um problema polêmico envolvendo frações. Logicamente, uma analisada no enunciado já identifica a falha nele contida. O professor poderia ter explicitado que as pizzas dois dois deveriam ser do mesmo tamanho, para os propósitos da avaliação. Como não o fez, então a resposta da criança, na minha opinião, deveria ser considerada correta.
E você, o que acha?
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Every so often, we come across something so senseless, so confoundingly stupid, and so frustratingly obvious that, well, we feel like it’s something of a moral obligation to share with you.
It reads:
“Reasonableness: Marty ate 4/6 of his pizza and Luis ate 5/6 of his pizza. Marty ate more pizza than Luis. How is that possible?”
The test-taker gave this answer:
“Marty’s pizza is bigger than Luis’s pizza.”
To which the grader, after marking the answer as wrong, replied:
“That is not possible because 5/6 is greater than 4/6 so Luis ate more.”
But the problem here isn’t just math: it’s English. The question and the teacher’s response are both worded VERY poorly.
Here’s why the question and the teacher’s answer suck, and the kid is right.
A fraction is a unit of measurement. A pizza is not. There is no uniform size for a pizza. It is not an absolute unit.
The question does not explicitly state that the pizzas were the exact same size. The only information available are two statements and a question that, as worded, requires an outcome of possibility based on the preceding statements.
Here’s what the question actually says — the facts that the reader has to work with:
Marty has a pizza of unknown size that he ate 4/6 of.
Luis has a pizza of unknown size that he ate 5/6 of.
Marty ate more pizza than Luis.
Then the question:
How is that possible?
If the statements in the question are true and the facts given are to be taken at face value, then there’s really only one way that Marty could have eaten more pizza than Luis:
If his pizza was larger — that is to say, if there was more of it to begin with — than Luis’.
The only way that the teacher’s answer (“that is not possible because 5/6 is greater than 4/6 so Luis ate more”) could be correct is if the second statement (“Marty ate more pizza than Luis”) is false.
Mind you, there are other answers that one could cook up (a third pizza is just one idea), but given the evidence/facts and assuming the veracity of the two statements, the only possible answer for the question as worded is that Marty’s pizza was bigger than Luis’.
One counterargument, as expressed by Redditor akatherder, revolves around the material on which the student is “actually” being tested: the concept of reasonableness in the context of how the lesson had been presented in the time leading up to the test:
The problem is that to claim that the student “ignored a given/assumption (that the pizzas are the same size) to make an unreasonable answer seem reasonable” is an assumption. There’s no evidence in the question to suggest that the students were taught as much.
Moreover, this doesn’t address the fact that what this student’s answer hinges on — that Marty did, in fact, eat more pizza than Luis — would have to be a gross deception.
Is it reasonable to believe that the data on a test may be false and that you should navigate all test questions accordingly? I’d say it’s not.
If the question was “if both pizzas are the same size, is this possible?” then it would have approached reasonability — it would, at the very least, have left the possibility open.
Naturally, Reddit caught fire over this. Read the entire thread here.
What do you think? Who’s right in this situation? Should the student have been marked wrong? Let us know in the comments below.
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Criado pelo Professor Rafael Procopio:
► Pós-graduação Lato Sensu em Ensino de Matemática (UFRJ)
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