Data points: N ellipsis, ambiguity 7/31/10

Just in, from my daughter, about her daughter:

On Friday, Opal does work that she brings home. Yesterday’s included the word problem: Mother cat had 6 kittens. 5 kittens went to new owners. How many were left?

Opal’s answer, duly checked off by the teacher, was “2 cats were left.”

Thank goodness she gave a complete non-elliptical sentence as an answer. That’s what you’re expected to do in school talk, even though it totally goes against ordinary language use, which sensibly enough goes for brevity.

Opal’s answer, which chooses one of the two ways of filling in the N ellipsis in the question’s how many? — ‘how many cats?’ vs. ‘how many kittens?’ — does, however, opt for the contextually less likely reading of the question: the set-up for the question is about kittens — the discourse topic is kittens — so the expected fill-in for the ellipsis would be kittens, not cats, even though the N cat is out there in the context. That is, the expected elliptical answer would be “1”, or somewhat less elliptically, “1 kitten”, or the complete sentence “1 kitten was left”. (Ok, a kid who responded with any of these might still have the answer marked WRONG by a stickler teacher, since they all have “1”, the numeral, instead of “one”, the number word. My god, school is a minefield.)

I suspect that Opal might have learned, by experience rather than explicit teaching, to anticipate pitfalls and tricks in test questions, which you can avoid only by talking with utter explicitness. It’s still an open question whether she honestly (and unconsciously) interpreted the question in the contextually less appropriate way, or whether she was (perhaps without thinking it through) being clever and tweaking the person who wrote the question, or whether she meta-reasoned (unconsciously) that 6-minus-5 was just too stupidly easy a question, so that some answer less obvious than “1” was called for. (Not that we could find out by asking her: if she could supply an answer to the question “Why did you say ‘2 cats’?” at all, the answer she gave would be likely to be a construction based on her interpretation of the reasons behind our question, since she would have been extremely unlikely to have had insight into the springs of her behavior at the time she wrote her answer — whatever they might believe, people aren’t at all good at getting access to their unconscious thought processes — and she’s even less likely to remember these details now. So I’m having breakfast with Opal and her mother in a few minutes but won’t ask her why she gave that answer.)

Oh dear, this has gone way past just a brief reporting of a data point. So goes the academic life!

3 Responses to “Data points: N ellipsis, ambiguity 7/31/10”

  1. Michael Paul Goldenberg Says:

    All the more reason that the worship of standardized multiple-choice tests is clear evidence that the worshipers have little or no interest in helping teachers get formative feedback. Trying to figure out which mathematical issue (if it WAS a mathematical issue at all) that a student failed to get based on the answer to such questions is well-nigh impossible even when individual responses are provided to teachers (which doesn’t in fact happen with high-stakes tests).

  2. Elizabeth Zwicky Says:

    I did ask if the teacher had commented on her answer and she gave me the “Adults ask stupid questions” look and said “No”. I suggested maybe one was a possible answer but she was not amenable to this concept.

  3. arnold zwicky Says:

    Points to the teacher who, without wrangling, counted the answer as correct. Many teachers would have marked it just wrong, saying (if challenged) something like, “It’s true that there are two cats left; but that’s not what the question was asking.” And there’s some point in that, though I’d hate to have to explain that point to Opal, who would of course have hotly replied, “If you meant to ask how many kittens were left, why didn’t you say that?”

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