Test Corrections Calculator
Do you allow your students to do test corrections for partial credit? Here is an online calculator to make it easier.
Why test corrections?
Allowing students to do test corrections for half credit serves two purposes.
First, it means tests can be a bit more difficult while still giving students the opportunity to get relatively good grades. They may not get as high a grade, but they still do decently well.
Second, for the students who do the corrections, it gives them another pass at learning the material — instead of just accepting their grade, they go back and look at their mistakes. In a perfect world students would do this anyway, but that rarely happens if there aren't points attached.
Test Correction Calculator
Enter the max score (typically 100) in the first box. The second box is what percentage of missed points you want to give back — 50 is a common choice. The third is how many decimals you want in the corrected grades. Enter all of the grades in any order in the large box; duplicates and ordering don't matter, results are sorted and de-duplicated automatically.
The Math
Here is the math behind the calculator. Let's assume a student scores a 75%, a perfect score is 100%, and we want to give half credit back.
\[\begin{align} grade + ((max - grade) \times (percentage \div 100)) &= \\ 75 + ((100 - 75) \times (50 \div 100)) &= \\ 75 + (25 \times 0.5) &= \\ 75 + 12.5 &= 87.5\% \end{align}\]That gets tedious once you've got a stack of grades to adjust, so you might as well use the calculator above.
Other Options
Aside from returning partial credit for test corrections, a linear grade redistribution is worth a look for tests where the grades just don't quite line up where they should.