In a yes/no question, a student gives the right answer and an unnecessary but wrong explanation. How to grade?

Question

Example:

Q: Does Venus exhibit retrograde motion? (1 mark)

A: No. This is because Venus orbits the Sun and not the Earth.

The first part is correct: Venus does not exhibit retrograde motion. But the explanation is incorrect: the reason Venus doesn't exhibit retrograde motion is because it's closer to the Sun than we are. Mars for example also orbits the Sun and not the Earth but does exhibit retrograde motion.

Do I award 1 mark or 0? On the one hand, for obvious reasons, the grading scheme only covers whether the student said "yes" or "no". Based on that, I should award 1 mark. Further, if the student hadn't written the incorrect explanation, then the answer is perfect, and it feels wrong to penalize the student for going beyond what the question asks for.

On the other hand, the explanation is clearly incorrect and the student should've known the correct explanation (it's part of the curriculum). It also feels wrong to award full marks for semi-incorrect answers. For example, if the student had written something silly such as "This is because Venus is made of Swiss cheese", do I still award 1 mark?!

Ideally, I'd award 0.5 marks, but for various reasons, fractional scores aren't permissible.

Answer 1

You asked for a yes/no answer (which, as you've discovered, has its disadvantages) and got one plus some other stuff. You should grade the yes/no answer and ignore the other stuff. If you like, you could add a note like "You got lucky! This is actually because..."

The whole point of yes/no or MC questions is that you grade only the answer, and assume that type-1 and type-2 errors cancel out or are normalized out. That paradigm doesn't work if you don't uniformly ignore everything other than the answer.

More concretely: other students likely got this question right using the same incorrect reasoning, but didn't write their reasoning down. There is no way to identify these students; so, you need to make sure they get the same score as this student.

Answer 2

I think that if you would allow full marks for just yes/no without an explanation at all, then you should allow it here. Otherwise the question is flawed and can't be properly and fairly graded. But a note to the student would be good, also.

To be more precise, if it is possible to answer a question with inconsistent parts it isn't a valid question for examination. It should be clear and clean.

But your job is to educate, not to grade. Give the marks and write the note. And think harder about the questions you ask and how they are presented.

If the explanation is required, it is a different situation. In that case, and if you weight the explanation heavily for other students, then probably 0 marks is better than any other alternative.

Answer 3

This is a discretionary matter, and different lecturers will treat it differently, depending on their own educational preferences. However, I disagree strongly with some other commentators on this thread. In my view, there is nothing unfair in marking a student down for unsolicited and incorrect information. Indeed, I would say that this is generally a good practice, since it ensures that the student is held responsible for the correctness of their assertions, even in cases where they offer unsolicited information. This implicitly gives the student some broader training in the importance of ensuring that they give correct information even when they choose to advance information that is unsolicited --- something that is a broader life-skill of importance.

In my personal practice, if a student gives me more information than was requested, and that additional information is wrong, this incurs a marking penalty just as if that information was part of the question. I warn my students in advance that this is my practice, but it is a justifiable practice even without giving a warning. In this particular case, if I were marking the question, I would not give the student full marks.

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What kind of graduates do we want? We are training students to become professionals in difficult fields. So, in considering this issue, I think it is important to consider the implicit lessons we give students by what we penalise and what we don't. Imagine that this student graduates and practices in your field. Would it be okay if this practitioner gives unsolicited information to people on the subject area, and that information is wrong? Would you be comfortable working with a colleague who gives information to you or others that is sloppy and incorrect, but then he faces no penalty just because that information was not requested by others? Is that the lesson you would like to impart to your students? Is that what you want to teach them about the world?

Answer 4

Give him the point. If you want, mark on the paper "wrong reason" in red.

If you wanted to evaluate reasons, you would have made it more points and required an explanation. But you didn't. So treat it like a normal true false or multiple choice problem. Reason not graded, just getting the right answer. Luck allowed. Etc. Similarly right reason but wrong result gets hammered.

If providing an answer was required then I guess you could mark wrong any case where both answer and reason were right.

P.s. This is if you are the teacher. If you are the student, don't debate 1 point. Get it all perfect next time.

Answer 5

There are a few schools of thought here, and it really depends on your teaching style.

From a fairness perspective, you shouldn't mark this student down. I'm quite sure that there are a few other students in your class who could not explain why they got the right answer (a good number of them probably just guessed at random). Unless you have a system to find out who those students were and penalize them, I think you'll have a hard time justifying why this student gets marked down and all those other students are not.

From an instructional perspective, there is some merit to marking this student down. Students have a tendency to write down random stuff with the hope that something sticks. If you incentivize your students to write less bulls**t and more to the point, you are teaching them a valuable lesson. You will be signalling to this student that you care about how they reason about answers, and not just the final product. I know of some lecturers who give their students 1 point in essay questions if they write nothing, just to provide an incentive to not write nonsense.

I would lean towards a fair verdict, but this is really because your question was very limited in answer scope.

Answer 6

The cause of the problem would seem to be the lack of instructions on how to answer the questions.

If the exam paper clearly said "answer the questions with either yes or no," the answer given is wrong because the candidate did not follow the instructions. That might sound harsh, but that's the way the real world works, unfortunately.

If candidates were expected to explain their reasoning, the answer is also clearly wrong.

This is no different in principle from the converse situation where candidates are expected to show their working, and someone simply writes down the correct answer. If they really were smart enough to see the answer immediately rather than do the expected half-page of calculations, they need to learn to be smart enough to also explain why their answer is correct, in real life!

Answer 7

It depends on the actual title above the questions (if there is one). For example:

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"Are these statements true?" (or synonyms):

In this case, the actual answer is only "Yes" or "No". There are two options: marking it as incorrect since it's not fully complying with the title (writing further information was not asked), or marking it as correct since its actually complying part ("No") is indeed correct (and potentially crossing out the non-compliant part).

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"Are these statements true? Justify your answer." (or synonyms):

The answer would be it as a whole. In this case, I'd mark it as incorrect since it does not answer all the title's parts correctly and thus it's not fully correct.

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In case there is no title, it becomes a difficult situation since the mark turns out to be subjective. Besides, the student would be in their right to complain about what they get.

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Conclusion: always make your exams with clarity in mind, clearing all technicality loopholes for justifying wrong answers, and no one will be harmed.

Answer 8

I would usually give no credit for a correct answer supported by incorrect argumentation, particulary when the argumentation contradicts the putative answer, is irrelevant, or is absurd. However, given the grade-seeking, formalist/legalist behavior of many students, it is imperative to indicate in the exercise statement that answers will be regarded as correct only if adequately justified. In the current case I would not give full credit, but would not give the 0 I would like to give, unless this had been my practice throughout the course and was known as such to students, because the problem or exam formulation should indicate what sort of answer is required.

It seems to me educationally irresponsible and entirely unfair to award points for an incorrectly reasoned "correct" answer. Such an answer reflects a lack of understanding, and should be graded accordingly.

Here is a concrete example, understandable to some. One asks a student if a given matrix is diagonalizable. One student makes calculations, indicative of conceptual confusion and poorly performed, that would clearly indicate that the matrix has nontrivial Jordan form, but answers that the matrix is diagonalizable anyway. A second student makes a minor arithmetical error that leads via otherwise correct argumentation to the erroneous conclusion that the matrix has nontrivial Jordan form and answers accordingly that it is not diagonalizable. Some seem to think that the first student should be given more credit than the second, when the second student has clearly demonstrated a high level of mastery of material and understanding. (Neither answer should receive full credit).

This isn't a hypothetical example. In mathematics and engineering exams this sort of situation occurs fairly frequently.

Grading serves to indicate whether certain standards have been met. Guessing, or obtaining accidentally, a factually correct answer does not meet reasonable standards for demonstrating understanding of content.

Answer 9

It seems you were giving a point (a) to students answering "yes" for the correct reason, (b) to students answering "yes" and wasting their time by writing down the correct reason, (c) to students throwing a coin and answering "yes" because they were lucky, (d) to students answering "yes" for the wrong reason, and you ask whether you should give a point (e) to students answering "yes" and writing down the wrong reason.

Since you are willing to give a point to groups (c) and (d), it seems unfair to me not to give a point to group (e). (But if papers are returned to the students, the wrong answer should be marked as wrong).

Of course, asking for an answer and giving reasons would make more sense.

Answer 10

Is this a standardized exam? Will the score acquired by the student affect his chances of getting into college? Will it be carried onto the future? If so, award full marks. You were not testing the mechanics behind it. There is a good chance that other students didn't know the right explanation either, and thus, on account of fairness, you should give the student full marks.

The question only asked the student to answer Yes/No to the statement presented. Consider this: on any given test, there are going to be a number of people who answered "Yes", but didn't give an explanation. What if they didn't know the explanation either? What if they just guessed it? What if they tossed a coin? There are lots of facts that we know without knowing why they are true. Plenty of students in your class would not have known the explanation.

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If this test is not for some standardized exam and if it'll not have any bearing on the student's feature, we can throw the fairness criterion out the window entirely, and concentrate on the more important aspect of testing: to see if the student has gained the required knowledge. In this case, whether or not you award 1 mark will not matter. You have two options:

• Award full marks, but leave a note.
• Award zero marks and leave a note.

What you choose is entirely your preference. Ideally, you'd want to award 0.5 marks; but since fractional scores are not permitted, I'll make a case for (2). Students are most likely to review questions for which they are marked wrong. If something is correct, it's correct and most students wouldn't want to bother with it. If they're marked wrong on a question, they'd want to know why. A student might review the whole paper, in which case your comments would be noted in both cases; but this is less likely to happen. It'll also encourage a student to not go beyond what's asked in a question. You don't have to present everything you know to the examiner in a test. While "sticking to instructions" may not always bode you well in life, in a test, it will certainly help you very much.

Answer 11

If you want to be absolutely right, treat the answer as wrong.

The purpose of marks is to accurately reflect the level of student's learning. If there is clear evidence that the student hasn’t learned the correct concept, marks should not be awarded.. unless you are grading their luck. (The student is clearly lucky here.)

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But, really... marks are secondary. Won’t hurt if you give them the marks and make sure that they get the concept too. That’s your job as an instructor.

So, give them the points and explain the correct concept to them. Win-win for everyone.

Answer 12

Whatever you do, you need to do it consistently for all students. For this reason we have a marking scheme. Presumably, you are not the only person responsible for the course? Are you working with a professor or colleagues? Ask them what they would do and do the same.

If there is no marking scheme and each marker makes an independent decision — discuss and work out a marking scheme that everyone can accept. Then write it down and ideally incorporate into the questions to make students aware, e.g. You need to explain your answer - correct answer with incorrect or absent explanation is worth 0 marks. Then simply stick to it.

Answer 13

Where does this "grading scheme" come from?

If you made it yourself, cross it out and make a better one that gives zero marks for both "yes" and "no" and only gives marks for an answer with a correct explanation. Students should by this point know that an unexplained answer is worthless, unless the question specifies otherwise, and your example does not.

If you received it from somewhere else, don't ask strangers on the internet to adjudicate, go back to the person or organisation that gave you the grading scheme and ask them for a ruling. This is the only way that the grading can be fair between different graders.

Answer 14

I personally would award the point (but disclaimer: I'm not a professor), but probably implement other answers' solutions (like write on the test an explanation). I'd like to point out that if this one question or a similar one were worth a huge amount of points on a test, of course it would be necessary to award points because the question never asked for reasoning. That question could simply ask for an explanation to avoid this whole issue.

Answer 15

There are two methods to use in this situation, and it really comes down to the environment you have made in your classroom.

Let's start with method one. Disregarding the response, giving the question full marks, and leaving a note for the student describing what was wrong with their explanation. There is nothing wrong with this method, and it educates, not punishes the student, because at least they gave effort. However, do cross it out and make sure the note explicitly states that the answer is wrong.

Method 2: Mark it wrong, and leave a note. While this doesn't "punish" the students, per se, though it does help them learn something and prepare for the field that they want to go into. Many of these students will want to go into fields that involve specific (correct!) answers. In this case, you would mark it wrong in the hopes that they may review it. If this seems a bit harsh, maybe invite him to do a correction of sorts.

Inviting him to do a correction seems like a compromise without resorting to fractional grades. It also allows him to make up the question while preparing him for the workplace, and making sure he learns and reviews the material, which will be beneficial later in life. If this isn't allowed, then it is more of a personal preference and a moral compass type situation, in which case you should look at both of the methods above and decide which one most supports the atmosphere that you have created in your class.

Answer 16

A recommendation I usually give when someone has an analysis paralysis:

1. Grab a coin. Head for 1, tail for 0.
2. Toss it high, so that it will spins as long as possible on the floor
3. During the spinning, your expectation will show up most. Which side do you DON'T want most?

After you have know what you want, you can know why you don't want it.

Answer 17

Ask them to give a confidence score (1 to 5 say) for their explanation. A high confidence but wrong explanation suggests a real lack of understanding for example.