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I want to know if there is any research on whether students' learn better by answering selected response (multiple choice) questions than constructed response (written) questions.

My gut feeling is no. Well-structured written questions bring out much more reflection and learning than multiple choice. There are written questions that cannot be converted to decent multiple choice questions, such as proofs.

However, I may be wrong. Is there any evidence on this?

Daniel R. Collins
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Mark Fantini
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  • Imagine the following. Essay question: "What is the definition of a polynomial?" Multiple choice question: "Choose the answer with the correct definition of a polynomial. A) ... B) ..." Which one is better for teaching? Usually we don't ask questions like this using multiple choice. If we did, would it be as effective? Does the student learn more when we force them to write down their thoughts? – Mark Fantini Jul 29 '16 at 13:50
  • Pick a computational problem. Solve x^2 -4=0. Do students learn better if we force them to show the computations and write effective sentences explaining their reasoning or can they learn better if we just let them pick one answer out of five or four? They can guess the answer, not know anything and still get it right. – Mark Fantini Jul 29 '16 at 13:58
  • Not exactly a duplicate, but the following seems relevant: http://matheducators.stackexchange.com/q/2457/6891 . Some of the answers provide links to research. – John Coleman Jul 29 '16 at 14:22
  • I would not consider "what is the definition of a polynomial?" an essay question. To me the word 'essay' implies at least a page. – Jessica B Jul 29 '16 at 16:47
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    I think the terms you are looking for are "constructed response" vs. "selected response". – mweiss Jul 29 '16 at 17:35
  • @JessicaB I was using 'essay' in a very broad way.@mweiss Thank you. That's a better fit, I suppose. – Mark Fantini Jul 29 '16 at 21:11
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    I think that the change to the title is actively harmful to reader understanding. Everyone understands what "multiple-choice" is. The opposite of that is probably best called "short answer" or maybe "open response". E.g., "Problem-solving and higher-order reasoning skills are better assessed through short-answer and essay tests." https://en.wikipedia.org/wiki/Multiple_choice#Disadvantages – Daniel R. Collins Jul 29 '16 at 22:17
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    Another example, from instructions to NYS Common Core math testing, grades 6-8: "For all three grades, the tests consist of multiple-choice and short- (2-credit) and extended- (3-credit) response questions." -- http://www.p12.nysed.gov/assessment/sam/ei/td-68math16.pdf – Daniel R. Collins Jul 29 '16 at 22:21
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    I'd suggest that SOME multiple choice questions can be written in a way that assesses understanding and successfully exposes common misconceptions, for instance, in the AP curriculum. I have students who can do all the procedural questions get completely tripped up on questions that ask them to pick between five similar, but not identical answers with subtle but important differences. – Opal E Jul 30 '16 at 00:00
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    I like the question better now. However, you ask about how much students learn, but as if they will only see one of the two. Do you mean to ask about the effect of the assessment style on learning? I would say teaching benefits from both types in different situations. As well as @OpalE 's point about checking subtle points at the end of teaching a subject, multiple choice is good when a topic is first introduced to give the students the confidence to have a go at all. ... – Jessica B Jul 30 '16 at 07:40
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    Also, the main advantage of MCQs is the ease of automation. Being practically able to administer assessment (formative or summative) is better than not being able to. But this advantage holds within teaching too. While it is possible to display group answers to written questions, a bar chart of group responses to a clicker MCQ is far more meaningful. Clicker questions can also be used to trigger debate, but I think it's much rarer for that to be applicable in maths than most other subjects. – Jessica B Jul 30 '16 at 07:45
  • @OpalE: And that's because procedural questions are just routines that any machine can do, not because there's any inherent advantage to MCQs except for ease of grading. – user21820 Jul 31 '16 at 02:59
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    Coming back in late, but: @DanielR.Collins the reason I suggested "selected response" instead of "Multiple Choice" is that the former also includes True/False, "matching" problems (i.e. "match each of the following four equations to the correct graph") and other formats, and I suspect that the OP would appreciate info on those, as well. Likewise "constructed response" includes both short answer (definitions) and "essays" (e.g. longer proofs). – mweiss Jul 31 '16 at 12:56
  • While "any machine" may be able to do procedural questions, many students still struggle with these and it's important to assess procedures. Multiple choice is a poor chioce to assess procedures unless you're also including multiple common missteps as distractors. – Opal E Jul 31 '16 at 21:53
  • There is another type of question and that is the multiple choice question which allows multiple answers. For example given such and such which of the following will be true. In my opinion and as a test writer and teacher, these are the most challenging of all. Furthermore, these can be graded by machine. – Amy B Aug 02 '16 at 05:15
  • There are actually three main types of test (with variations of each): multiple choice(varies with # options and construction of the options), short answer (no partial credit, answer must be 100% correct), constructed response (work is examined with possible partial credit). All have advantages and disadvantages. If time permits, constructed response allows assessors to follow the student's work and estimate where the student is on the continuum of "no idea" to "knows it, but made a small mistake". – todd w. May 12 '19 at 16:27

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In most fields, I think the research indicates the opposite, though I don't know of any research that is directly on point.

One of the weaknesses of multiple choice tests is that they allow the student to write the answer when they recognize it among the choices. This is easier than retrieving it without answer cues, and so the well-established benefits of retrieval practice (a.k.a. the testing effect) for retaining information aren't gained. However, in math, even multiple choice questions typically require some calculation rather than mere recognition, so this is likely less of an issue in math.

While I don't know of research directly on point here either, I also suspect that multiple choice tests give students an excuse to guess on a problem and stop thinking earlier than they might if they had to come up with something rather than leave a free response question blank. Since even unsuccessful initial struggles with a problem promote retention (assuming appropriate feedback is soon provided), I would imagine that this would be a problem even in math.

Also, while very skilled test writers can find ways to write test questions to test a wide range of thinking processes in math, it isn't easy. Even some government or commercial sources often produce multiple choice questions in math whose intent can be evaded by a clever student. (A blatant example: figuring out which choice is the solution to an equation by plugging each choice in turn into the equation rather than solving the equation.)

As for anything that indicates superiority of multiple choice questions in some respect, I don't know of any. They're really used more for convenience than because they're better at promoting learning.

DLH
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