OK, VCAA, you can take a little rest. We’re going to pick on other states for a bit, beginning with Queensland. A colleague has alerted us to some nonsenses in the 2024 QLD Methods “Technology-free” Exam (MCQ and short answer), and here is the first nonsense, an MCQ. The subject report indicates that 63% of students gave the intended answer, B.
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I wonder about the worth of problems of this type on a state examination. They seem to be a type of question that is better given in regular quizzes given in class by a teacher or questions that are posted online that students can go to for practice and to check their work. In the days of the dinosaur, at least in my part of the world, the only examinations given external to the school were in the final year of high school. All the other testing through elementary and high school was administered either by the teacher alone or by the group of teachers in a given subject area, and some of them were written under formal examination conditions. In my estimation, this was at least as successful in maintaining standards as anything that came after.
The key to this is a corps of teachers who are competent both in their subjects and in methods of testing. One advantage of in-class testing is that the teacher can tailor it to the situation. This is where the effort needs to go.
A lot of state testing presents logistical problems (not the least of which the prevention of leaks and cheating) that are expensive and time-consuming to deal with, and lend themselves to bureaucratic snafus (which seems to be the case of a lot of stuff complained of in this blog), using up resources better deployed elsewhere.
Ignoring the worth, does the problem make any sense?
It is really a uniform distribution if the bounds, from the graph, are from 0 to 5 and P(0)=0?
Pretty funny, but not the reason the question was flagged to me.
I don’t have the experience to comment on whether this kind of question should be on an exam. Especially since I don’t see why it might not make sense. But I like the question, which I think is “enjoyable”. Personally, I would have added (E): None of the above, just to make it non-trivial.
I clearly shoulda made it a WitCH.
I believe what Marty is getting at is that the context or “real world” application of statistics is a bit silly. Hence, the question is poor. It is just getting students to follow some ritual they have learnt and not think. The context is not relevant to what is being assessed.
What would a study about family size learn when they have selected an equal amount from the narrow range of possible number of children a family can have? Most likely, the initial 20 families selected were not at random; it is very unlikely for a uniform distribution to randomly happen. So then what is the point of then randomly selecting from the non-randomly selected 20 families? What is this study trying to do? Who knows? The context is just pointless waffle that bogs students down reading pointless things.
No. I hate the question for those reasons, but that’s not the point. Read the question.
Are B and C both possible? With 5 picks you could have a total of between 1 and 24 children or averages between 0.2 to 4.8. Without regard to the probablilities of picking these values? But the question asks for “a” possible answer? I’m not certain what is being asked but it is at least, clumsy
Is the problem that “the mean number of children in the sample” is poorly defined, so could be interpreted in different ways? (The interpretation seems pretty clear to me, in context, but I agree it could be clearer.)
Yes. What does it mean? I don’t care what QCAA intended to write. I care what QCAA wrote. What does “the mean number of children in the sample” mean?
Do you think it would have been clear if they had aksed about “the average number of children per family in the sample?”
I suppose the most likely “wrong” interpretation is to find the expected value of the total number of children taken together from the five chosen familes? But then it wouldn’t make sense to ask for a “possible” value.
A more long-winded way to make this clear would be something like “For each family in the study, the variable X denotes the number of children in that family. The figure shows the distribution of X.” Then ask about the mean value of X in the sample.
Thanks, 3rM. Yes, they absolutely must say something about children per family. I don’t think the question is easy to word, and I’d have to think about how to do it. And it’s stats crap, so I’m not gonna think about it.
Writing exam questions is hard, and you don’t want to nitpick every question that is a little clumsy or technically ambiguous. But QCAA’s wording here is atrocious. It is not even in the ballpark.
Unless I have missed something (it happens, a lot) the number of children in the sample will be between 6 and 24 (inclusive) and the expected number of children/long run average (mean) of all these options would be 15.
So I say none are correct, as the question is currently written.
I remember being confused by this question when I looked at this exam some months back. I think I only realised what it was trying to ask when I looked at the answer choices.
Slightly off topic but I do recall thinking there were a couple off questions that were particularly bad in the general mathematics exam. Questions 3 and 5 in paper 2. (Question 5 mainly because I believe it is technically outside the scope of the syllabus).
Thanks, James, and that’s the point: this close-enough bullshit wording always disproportionately affects kids who think harder. It doesn’t matter if, in the end, there is only one plausible intent to the question. Because the smart kid will spend three minutes getting to that intent rather than the 3 seconds it would have taken if the question had been properly worded.
But try to get this point across to a psychometric witchdoctor.
I completely agree. Which is why I think those other two questions I referred to are particularly bad because despite the answers qcaa want and expect being immediately obvious to me (and probably any good student), any student who actually knows the material well and thinks about them is going to be disadvantaged.
Thanks again, James. I forgot to reply to that part of your comment. I’ll look tomorrow (or tonight, if the football gets boring).
James, can you say what is wrong with Q3 and Q5? (I don’t look at this crap unless I really need to.) If Q5 is mainly a syllabus thing, that’s bad but not much for me to do.