Humanizing the multiple-choice test with partial credit

We describe an innovative method for machine-grading precalculus students: the partial-credit, multiple-choice test (PCMCT). Our scheme is to assign partial credit to any wrong multiple-choice answer for which we can ascribe partially correct reasoning. This permits us to accumulate additional information about the extent of a student's incomplete understanding. We add the assigned partial credit to arrive at our final measure of a student's total knowledge-the student's grade. In comparison with the standard multiple-choice test (MCT), the PCMCT judiciously avoids the necessity to scale scores-an educationally unsound but common practice with MCTs. In addition, the PCMCT turns out to be better at distinguishing uneducated guessing than the MCT. We conducted student surveys in our pre-calculus classes and found that most students believed the PCMCT is a more accurate measure of their knowledge than the MCT. We also uncovered the remarkable result that most students are less math-anxious when taking the PCMCT than when taking either the MCT or a standard essay test.