# How much credit for a single arithmetic mistake?

A question related to this one, on an equivalent problem on a community-college College Algebra exam. In the prior question most readers observed the error as a critical conceptual issue. Now consider this example of student work:

In this case, the distribution has been done correctly, and two of the three combinations of like terms. But in the very last term, a signed-arithmetic error has been made; the student replaced $-3-14$ with an incorrect $-11$.

On a percentage basis, what is the most appropriate amount of credit to award in a case like this? Assume that the problem is worth an appropriately granular number of points (not necessarily 10).

• Again, just a comment: I cannot tell, contextually, whether this is a simple arithmetic error as opposed to another critical conceptual issue. I have seen students mistakenly transfer the notion of "two negatives makes a positive" from multiplication to addition. If cornered, I would give it a 75% by [roughly] following the ideas in the earlier answer here to your previous question. – Benjamin Dickman Jun 30 '17 at 5:45
• As per my comment: matheducators.stackexchange.com/questions/12516/… I would look at the whole exam and see what type of mistake this is. Looking at problems individually and independently of other problems on the exam can lead to a death by a thousand red marks for what could be one single conceptual mistake. If this is the only mistake they've made of this type, I'd nick a minimal amount. If it is chronic, I would deduct a hefty amount from one problem only and circle the error on other problems. – Math Misery Jun 30 '17 at 21:37

The correct realization of the operations prior to the error indicates that the student does understand how to take sums and differences of negative numbers, how to negate a negative numbers, and how to realize more complicated operations, such as the distribution of the negative sign over a sum, and this suggests that the mistake in the final step is due to carelessness. If one accepts this reasoning, only a minor deduction should be made. Exactly what it should be depends on the context. Were this a final step in the solution of a problem in a university differential equations class, I might not even deduct points (were everything else perfect), but in a class dedicated to teaching precisely this sort of operation, some deduction is in order, on the order of $1/8$ of total value (depending on how one counts there are $6-10$ operations that have to performed, and one of them has been performed incorrectly, and the evidence supports the conclusion that the student understands what to do, simply has made a careless mistake).
• RE: "suggests that the mistake in the final step is due to carelessness" If other items in the same student's paper suggested a conceptual error instead -- e.g., $-5 - 3$ calculated elsewhere as $-5 + 3$ -- would this have an effect on your proposed deduction of points? – Benjamin Dickman Jun 30 '17 at 5:51