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Tuesday, March 15, 2011

Some thoughts on the math tests

I heard this little story about math tests from my former math professor. His math teacher friend had made a little experiment on the math tests. His philosophy concerning the tests was that the first question of every test should be easy enough to be solved by everybody in the course.

So slowly and carefully he chose every time little easier first question than last time. However, it seemed like that making of the first question easier was useless, as there was every time almost an equal number of wrong answers.

Finally he got fed up with the whole experiment of his and decided to end it once and for all. In the next test he put the first question as follows: How much do we get if we add 1 to 1? Surprisingly not everyone were able to get even this right. Some of the students thought it was a riddle and answered something else than two.

Anyway, I think it's not too rare that students face a question that isn't completely unambiguous or clear, and the students are forced to make a "sophisticated guess" about the interpretation of the problem. I have here a test question from my probability course (maybe 6 years ago) where I had a little problem:

Question: Five persons are going to be elected in a committee. There are eight candidates for the committee, 5 women and 3 men. What is the probability that the minority of the committee will be men, if five persons from eight are chosen by random?

Okay, at first let's think about all the possible combinations for the committee:
{f, f, f, f, f} = A
{f, f, f, f, m} = B
{f, f, f, m, m} = C
{f, f, m, m, m} = D, where f=female, m=male.

The problem is basically this: are men the minority in the set A even thought there's no men?

This is one of the first definitions for minority I found:  
Minority - the smaller in number of two groups forming a whole.

Some might think that the minority in A is an empty set, others that the minority doesn't exist in A. I think it doesn't actually matter, as there's anyway no such a subset of A that would contain a male as an element. So males can't be the minority in the set A.

The right interpretation according to my math teacher was that the sets A, B and C were cases where men were the minority. Fortunately enough I had let all my pedantic pride go in the test and answered interpreting A as a minority set like the teacher meant.

I guess the moral of the story is to save your clever remarks for your blog.


  1. hey you should do a blog post on how 0.999... is equal to 1. That discussion is pretty popular on the internet.
    The Nostalgia Corner.

  2. I would have thought that men wouldn't be the minority in set A if there's no men in set A.


  3. Andre: That's a good idea. I'm not too familiar with the topic thou but I'll think about it. =)

  4. It's funny how the psychology behind tests can really play with a students mind. If the first questions are extremely hard. The students can do poorly on a test due to their lack of confidence to answer questions because they see they can't even answer the first question. Yet in the exact opposite case if the question is to easy, students will tend to double guess themselves and become distracted on this question for a while or put a wrong answer.

    Even the question with the sets you've shown can mess people up. Depending if they believe a male has to be in the set or not.

  5. As usual, excellent post mate, was fun to read and got me thinking over a few things. keep up the good work man

  6. Something alont this lines is a test I had in math class in my last high school year. The first order was "read the whole test before beginning". There were about 50 questions (easy ones of course), and the 48th said "don't do anything. hand the test without any writing".
    Thank god I read it. Not everyone in my course did though.

  7. You could always ask the professor to clarify. I've never had a math professor, or any for that matter, that wouldn't clarify a question in so long as it doesn't directly provide a solution.