Hannah and Her Sweets
Much has been written and tweeted about this problem from a recent math exam administered in the UK:
After the exam, students took to social media to express their outrage at the absurdity of this question. This prompted some reaction pieces from mathematicians and math teachers defending this problem as a demonstration of a link between probability and algebra and as a non-routine problem-solving challenge.
The mathematical status of this problem is less interesting to me than its status as a test item. And as a test item, I think this is not only terrible, but also damaging.
The first eight sentences of this test item clearly indicate to the student that this is a probability problem. Then, it abruptly ceases to be a probability problem and becomes a problem about quadratic equations. No meaningful connection is made between the two concepts: the entire probability story simply exists to establish algebraic conditions on the number n. (And even in a world where contrived test questions are commonplace, this silly story stands out.)
For most students, this test question just reinforces the notion that math makes no sense. And I’m sure others come away feeling cheated, or deceived, by the exam-writers. High-stakes exam questions like this damage student attitudes about mathematics and learning, and have broad, long-term consequences that few people seem to think about.
This problem reminds me of the saga of “The Pineapple and the Hare“. A few years ago, a number of questions on an 8th-grade English exam referred to an absurd passage about a talking pineapple. The passage and the questions were published online, and the ensuing public outcry led to those items being nullified on the exam.
Yet test-writers defended the passage and the items as an effective discriminator: only the highest functioning test-takers could weave their way through the absurdity to answer the questions correctly. Thus, it effectively served to identify the highest performers.
Even if that were all true, why should the navigation of nonsense be a focus of our educational program? And what of the students who come away from such tests feeling demoralized and alienated because a probability abruptly became an algebra problem?
Regardless of what people think about this particular question, I’m glad that, more and more, we seem to be asking the question, “Are these tests any good?“.