A Better Mousetrap for Multiple-Choice Math Tests

Dec 19, 2007 by

We’ve been having a rather spirited discussion in my department about a common final exam for one of the math courses, and the need for an easy-to-score learning assessment (i.e. multiple choice).

The two biggest problems regarding math and multiple-choice tests are

  1. Students cannot show and get credit for work.
  2. Students can too easily “try out” answers to each problem (especially on factoring problems and equation solving problems).

Regarding #1, there is, I think, a point in the semester when students should be able to demonstrate that they can do problems, correctly, to completion. Especially in algebra-level courses, there is often not a lot of work that they could show that I might give them credit for.

If it’s a 50 question final exam, and each problem is worth 2 points for 100 points total, how much partial credit can there really be? Students who get every single problem 75% right do NOT deserve a passing grade of 75%. Every problem 75% right means 100% of the problems done with some kind of mistake. That is not a “passing” performance.

Now… on to issue #2. I think I have a solution to this problem… seriously. Why do we have to use the five choices on scantron tests as only 5 unique answers? Why not let these five choices (A,B,C,D,E) generate 25 unique answers instead? Take a look at my new take on “multiple-choice” and tell me what you think:

It’s about time we thought outside the box on these scantron forms!

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  1. Robert Foth

    I liked the first set of questions since there was a unique answer to each one of these.

    The second set would cause some confusion for the students since they will not know which one to put first. An alternative is to find one of the factors of the polynomial, but not list all the factors as choices (maybe hold back an easy factor). For example if x^2-9 was the polynomial then your list could have (x+3) as one of the factors on the bottom, but not (x-3). This way we know if they are factoring it as (x+3)(x-3) and not as (x-3)^2 (which is the common mistake for this problem.

    Great idea Maria – keep them coming.

    By the way, did you know the comment field will not allow the “sup” tag (had to use ^ to represent an exponent).

  2. Maria H. Andersen

    I like your idea for factoring… then you could actually get away with five answer choices for those, but avoid the “just multiply it out to find the answer” problem.

    I guess Blogger doesn’t like non-standard HTML. Sorry… but we all know what ^ means. Intersestingly, they do work in posts.

  3. mathmom


    I just found your blog via the Carnival of Mathematics. I love your multiple choice testing ideas, though it is news to me that you can get the scantron to accept multiple marks on a given question as the “correct” answer. 😉 I’m sure I’ll agree scanning through your other posts as well.

  4. mathmom

    uh, make that “enjoy” rather than “agree” above. I don’t know what my fingers were thinking. 😉

  5. Chip Uni

    The scantron can also be used instead of “All of the above”/”None of the above”. For example:

    Q1: 3+5 =
    A. 2+8
    B. 1+7
    C. 4+2
    D. 9-1
    E. 2*4

    The student would choose answers A, D and E.

  6. J. Sweeney

    Brilliant idea! Thank you.

    Joseph Sweeney
    Mathematics Department Chair
    Malvern Preparatory School

  7. c.j.doody

    There are actually 31 possibilites on a Scantron; the last being ABCDE. I struggled with this until I just treated the Scantron as Binary: a=10000, ab= 11000, e=00001, etc. Tonight I’ve put together a test on 50 Periodic Element symbols to be matched against 31 element names. I structured the matching using 1-50 on the left as possibilities and and 31 answers on the right. Just put the key thru with only 31 out of 50 answers filled in and the rest blank. Any or no answer on the other numbers won’t register as right or wrong. Although I teach 8th Grade science, I’ve also taught math. vp

  8. Anonymous

    I tested out this idea on Friday, giving 5 questions the following answers (A, AB, ABC, ABCD, ABCDE) and then scanning sheets with the answers A, B, C, D, and E and then A, AB, AC, ABCDE, and ABCD.

    The scantron correctly scored the first answer sheet as 1 right and the second as 3 right.

    Since I teach 7th grade math, I do not have to over worry about algebra stuff, so this should work very well for me.

    Thank you for the great idea!

  9. Sarah

    I love your blog – thank you. I am looking for ideas for putting a multiple choice math test online. I might try and take a look at Robert’s idea, there. I tried to set up one of your tests on Angel and the format might be a little bit confusing for my developmental math students. I would love to hear any other ideas you might have for putting tests online. Or even just further thoughts on the multiple choice test. Scantron is definitly an idea, but it has been around for a while and we’re trying to do some new things w/computers in the classes.


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