Multiple Choice Questions in Math

Discussion in 'General Education' started by teachin4ever, Sep 30, 2010.

  1. teachin4ever

    teachin4ever Cohort

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    Sep 30, 2010

    One of the things my grad school group and I discussed this week was whether or not multiple choice questions should be used in math.

    As a math teacher, I personally never use them in my class. Some of my group members said they did to help prepare their students for the state assessments.

    I thought it was an interesting discussion so I thought I'd continue it on her...what do you guys think?
     
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  3. TeachinHicks

    TeachinHicks Comrade

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    Sep 30, 2010

    I use them for tests, but I use the book tests. I do require my students to show their work though. The state tests have multiple choice here in NC even in Math, so they have to be able to work it and then find the right multiple choice answer. We do a lot of activities though that are not multiple choice and almost all of our practice is without it.
     
  4. Aliceacc

    Aliceacc Multitudinous

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    Sep 30, 2010

    I use them for our Trimester and Comprehensive exams. The scantron section is usually worth about 40% of the test.

    Other than that, I'm the Queen of Partial Credit.
     
  5. mopar

    mopar Multitudinous

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    I agree with partial credit. Sometimes I will make part of the test multiple choice, but the choices are always on a separate page. Students have to show their work and then choose the correct choice. It is good practice to learn to use the choices to help solve some problems, but I expect the work in the end.
     
  6. Cerek

    Cerek Aficionado

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    Oct 1, 2010

    I've used a mixture of multiple choice and short answer on my quizzes. I gave my first unit test this week and made it completely multiple choice. There were 25 questions and I wanted to make sure the students would have time to complete them all.

    I had a good range of grades on the test, so I feel it was a good assessment and all the students except one finished in plenty of time.

    I normally am very strict about students showing their work, but I decided to give them a break on this test. Of course, some of them STILL showed their work in the margin, so it's nice to know at least a few of them are making it a habit.

    I do give partial credit as well, but I always struggle with it. I want to give enough so the amount is fair without giving too much for an answer that is - in the end - still wrong. I'm still working on the best combination/formula for my students, but both styles seem to work fairly well so far.
     
  7. Ranchwife

    Ranchwife Companion

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    Oct 1, 2010

    Just to throw a wrench in the mix, using multiple choice tests can really help a teacher determine how students are making mistakes. If you create your own multiple choice tests, out of 4 options one is the correct answer. The other three distractors should be the answers to three different ways kids can do the problem incorrectly. If you set up multiple choice tests in this manner, you can then go back through their answers and analyze how a majority of kids are making mistakes and address those mistakes.

    Our school just administered a basic skills math test of fractions and integers that I made. The results will be analyzed by all the math teachers next week to determine areas that are low, then we will look at the individual answers to learn how the kids are thinking and what they are doing to cause mistakes. In this case, multiple choice and be a very informative way for teachers to address incorrect thinking.

    The major problem with MC tests comes when teachers simply look at the overall scores and don't look at the options the kids have chosen. And then fail (due to laziness or simply because the unit is "over") to address the incorrect thinking. At our school, the incorrect thinking can be addressed as a class, or the kids are put into an advisory class where the concepts are taught again with an enphasis on how they are doing the problems incorrectly. They then take the test again to pass out of the intervention advisory class and back into their regular advisory class.

    So, in my opinion, MC questions in math are very effective if they use distractors that can give the teacher information on how the kids is making mistakes, and then teacher uses that information to reteach.
     
  8. Cerek

    Cerek Aficionado

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    Oct 1, 2010

    I agree, RanchWife.

    The software that came with our new textbooks generates tests based on the content in specific chapters. Our recent chapter test included questions on order of operations and the distractors gave the answers students would get if they did the equations in the wrong order, so I could tell exactly which operations they were most confused about.
     
  9. Aliceacc

    Aliceacc Multitudinous

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    Oct 2, 2010

    When I do make up multiple choice, that's how I do it of course.At this point I KNOW the errors they're likely to make, and that's how I come up with the distractors. And you're right, it does make it easy for me to see where the kids went wrong.

    But it still poses two problems:
    a. I may know, but unless Tommy has shown his work elsewhere, HE doesn't know. It's a lot easierfor the kids if I circle the error in red and have him see exactly where he went wrong. Kids need to learn from their mistakes. If the mistake is on scrap that's been thrown out, that's not possible with multiple choice.

    b.The whole partial credit thing. I may know that Susie divided by 2 instead of subtracting 2, and that it was a common but minor error. But she still loses full credit. It can be discouraging for kids. Math tests normally contain fewer questions than in other disciplines, since it takes a while to get from question to answer. As a result, if my kids are to finish the test in 38 minutes, each question is worth more than a question might be in History or English class. I would hate for a kid to lose 6 or 8 (or, on yesterday's geometry test, 10) points because of one error in an extended process.

    It's just as easy for me to see the mistakes-- both those I had expected and the occasional surprise-- by giving a test that's not multiple choice.
     
  10. Cerek

    Cerek Aficionado

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    So how much credit do you give in a case like this? My view is that, although it is a common error, she still got the problem wrong even though we have covered the material in class extensively. On the homework, I would give her credit for her effort and point out where she made her mistake. I would then spend more time (as needed) on the subject until I felt all (or at least most) of the class understood the content and were not making these kind of mistakes. Once we actually get to the test, though, the mistake is still wrong.

    I'm still working on my overall grading scheme, so I am always interested to hear from more experienced teachers on the subject. Do you give Tommy half-credit for getting the process right, aside from the one operational error?


    That's true, but this is offset (on my test, at least) by the fact that the MC test has several more questions, so each one counts far less than the questions on the quiz. They only lose 4 points for getting the problem wrong on an MC test as opposed to 10 points on a quiz where they work the entire problem.

    So far, my quizzes have had around 10-15 questions, requiring them to show all of their work and some of the students were pushed to finish on time. On the MC test, I had 25 questions and only 1 student out of 40 struggled to finish on time. The extra questions also meant each problem counted less than half the value of quiz questions.

    I'm still trying to find a "happy medium" of regular questions that (a) makes them show all their work, (b) gives them enough time to finish all the problems and (c) has enough problems so that missing 1 or 2 questions doesn't drop them a letter grade.

    How many questions do you typically put on your test? My students have about 40-45 minutes to complete theirs. On the first two quizzes, they an average of 12 problems and some struggled to finish on time.

    Any suggestions on giving more questions (or partial credit for questions) is appreciated.
     
  11. mopar

    mopar Multitudinous

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    Cerek,

    I think it depends on the skill. I will make my test the way I want it. Then I take the test and time myself. If I can do the test in 15 minutes, I would give the students 45 minutes to complete it (my time times three). This general rule of thumb works well in my room.

    The number of questions depends on the types of questions. For geometry proofs, I would include less questions then if my test were on solving one or two step equations. I really base the length of the test on how long it takes me to solve it.

    Second, for partial credit: I look at each step in the process that I would take to solve the question. Then I assign each step a point value (1/2-1 point depending on the step). I expect students to show all work! So, when I grade the test, I look at the work shown and for each step they get credit. If they make a simple mistake in an early step but then follow everything correctly, they may only lose 1/2-1 point. However, if they are not following correctly for half of the problem they lose 1/2 of the points. It has worked well for me so far.
     
  12. Aliceacc

    Aliceacc Multitudinous

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    Oct 2, 2010

    I agree mopar; if I can't do it in a third of the time I give my students, too many won't finish.

    I also figure that any test that doesn't fit onto an 8x11" piece of paper, including room for work, is too long for a 38 minute period. So a kid can do a LOT of factoring problems, but typically only 4 proofs.

    I normallly take off no more than 1-2 points for an arithmetic error. And, like mopar, I break down my key into the steps of a problem. So on an Algebra test, adding instead of multiplying will carry a greater penalty, since solving the equation correctly is the point of the problem. (but adding incorrectly is a less important error, since I can assume that they KNOW the answer to 2+3). That same, error, adding instead of multiplying, will carry less weight on a a geometry test, since the point is probably to set up an equation, solve it, then find the value of each of the angles in the problem.
     
  13. Aliceacc

    Aliceacc Multitudinous

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    Oct 2, 2010

    Sorry, my computer is NOT cooperating.

    Another thing on the multiple choice issue: a kid whose mistakes aren't typical isn't going to figure out what he did wrong.

    Say the correct answer is 2x. The typical errors might yield answers of x squared, x+2, x-2, and x/2. But the kid who, for some reason, takes the square root isn't going to find his error, and is going to guess. So I lose the chance to help him figure out what he's doing wrong.
     
  14. mmswm

    mmswm Moderator

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    The right answer, while important, is not the main objective of my tests. When I give a test, I want to see whether or not my students understand the process they're supposed to be completing. Of course, the ideal is every step done correctly and no errors in the pre-requisite skills, but in error in one of those skills is not going to count against the student as much as an error in whatever skill I happen to be testing at that moment. Since I'm in complete agreement with Alice, I'll spare a rehashing of it.

    Oh, and Alice, while you may be the queen of partial credit, one of my old professors takes the title of Grand Emperor, above every King, Queen, or any other title. This teacher (he was actually a TA at the time, though he's a professor now) was, and still is, very well known for the difficulty of his exams. To say they were brutal is an understatement. In his words, his exams were designed to get students to think (for background, he's not from the States, and his testing style is more in line with his native country's style.) Well, on one particular exam, I struggled with one problem. Well, to be fair, this one problem was really closer to 5 problems. I had a hard enough time with it, that now, 15 years later, I still remember it (and occasionally still have nightmares about airplane manufacturers). My general problem is I couldn't set up the initial equation based on the information in the problem. I knew it was an optimization problem, and I knew what I needed to do, but I just couldn't get that initial equation set up. Instead of leaving it blank, I wrote a new problem, similar to the one he was asking for, and worked it out. Then, in the subsequent problems, which required the answer from the first problem, I just continued with the alternate scenario. The problem set was worth 25 points. He took off 3 points total. No, I did not do the problem he asked, but I showed him that I understood the concept. From that point on, I never considered NOT giving partial credit.
     
  15. mopar

    mopar Multitudinous

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    Since the point of the assessment is to see what the students know, it is important to give them credit for what they do know even if they make a mistake!
     
  16. Aliceacc

    Aliceacc Multitudinous

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    mm, I like your style. (And his as well!)

    I always tell my kids: if you need to, FAKE a step in the middle of the problem. You can even write "Faked this number." But FINISH THE PROBLEM!!!

    I'll take off for whatever caused you to fake the number. But I'll give you credit for the rest. I'm not testing to find the right answer, I already know the right answer. I'm testing so you can show me that you know the process.

    And, for me at least, multiple choice doesn't enable my kids to show that.
     
  17. Joyful!

    Joyful! Habitué

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    My school has a set curriculum with set tests that are required to be used. The tests for each chapter are not MC. However, the Cumulative Review given at the end of every chapter beginning with the 2nd is MC. I like the combination very much. When I "debrief" them after the test, I go over the MC test showing them the correct way to do each problem. We discuss why someone might have chosen a different answer. This has been effective for my groups.
    I don't think one single method of assessment is innately better than another. As has been stated, it is what the teacher does with the information the assessment reveals that makes a test an effective one (or not).
     
  18. runsw/scissors

    runsw/scissors Phenom

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    Oct 3, 2010

    I don't teach math. I'll preface with that.

    I do remember all through high school the math tests were always multiple choice because the school used the Scantron test strips. We were required to show all work on the test itself though and did have points deducted if we did not show work that was evidence of actually trying to solve the problems (so no guessing and no random addition with numbers of our choosing.) If I did teach math I might use sum (hehehe!) multiple choice so they kids could get the practice for standardized testing, but I would also have some problems that required them to solve for the answer or interpret the data on their own. Work must always be shown.
     
  19. ACardAttack

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    Oct 3, 2010

    I dislike them big time; my Alg 2 classes have to be given multiple choice tests; this time Im gonna tell them to show their work so they can get partial credit.

    No multiple choice in my college algebra class since its not state dictated, I do throw a couple on the test just to give them practice with ACT type questions
     
  20. Aliceacc

    Aliceacc Multitudinous

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    Yeah, I do an SAT prep question or two at the start of all my high school classes. When I hit a mixed number, I also go over changing it to either an improper fraction or a decimal for those SAT fill-in questions. (But the kids know that, unlike the SAT, I'll take any form of the correct answer, as long as it's been simplified.)
     

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