Long assessments can waste precious class time unless there is much material to be assessed, but shorter assessments (with few questions) can cause small errors to have too big an impact on a student’s grade.

For example, consider the following assessment lengths where each question is worth 4 points, and the student has a total of two points subtracted from their score for errors:

# Questions | Points | % | % Grade |

1 | 2 / 4 | 50% | F / F |

2 | 6 / 8 | 75% | D / C |

3 | 10 / 12 | 83% | C+/ B |

4 | 14 / 16 | 88% | B / B+ |

5 | 18 / 20 | 90% | B+/ A- |

The “% Grade” in the table above reflects a 7-point / 10-point per letter grade approach. A one question quiz is risky for students: they could get a failing grade for losing two points on the only question. Two question quizzes are only slightly less risky. Only with three or more questions does this scenario start to minimize the risk of actively discouraging a student who loses several points.

Should quizzes therefore only have three or more questions? What if I don’t want the class to spend that much time on an assessment, or don’t have that much material I wish to assess?

### A Solution

Instead of using a 0-100 grading scheme based on the sum of all question scores, assign letter grades to each question (or their 4.0 scale equivalent), then average them. Doing so produces less extreme results for the above scenarios (see the Avg Grade column below), and reduces grade risk for students:

# Questions | Points | Avg | Avg Grade | % Grade |

1 | 2 / 4 | 2.0 | C |
F / F |

2 | 6 / 8 | 3.0 | B |
D / C |

3 | 10 / 12 | 3.3 | B+ |
C+/ B |

4 | 14 / 16 | 3.5 | A- ? |
B / B+ |

5 | 18 / 20 | 3.6 | A- |
B+/ A- |

Losing two points (two whole letter grades in this scenario) on a 2 question quiz would result in a grade of “B” (compared to a “D / C” for a percentage approach), or on a 3 question quiz a “B+” (instead of a C+ / B for a percentage approach). By making a quiz less risky to a student’s grade, the fear factor for quizzes should decrease, allowing quizzes to be used in a more formative manner. Don’t we all learn best from our mistakes? If we want students to embrace their errors and learn from them, we should not penalize them overly harshly.

Furthermore, time saved by giving shorter quizzes can be either used to give more short (and timely) formative quizzes, or reclaimed for other purposes.

### Average Occasionally or Always?

Should I grade all assessments this way? What if I graded shorter/formative assessments by averaging, and longer/summative ones using a percent approach?

A potential advantage of this could be to make quizzes less risky, but retain the high stakes incentive provided by “chapter tests”. A potential disadvantage is that students and/or parents could perceive grading to be inconsistent, which is generally not helpful.

What might some downsides to grading all assessments this way be? Grading each student response using a 4.0 Rubric instead of subtracting points for errors will probably improve grading consistency slightly, but could add to grading time until it becomes familiar. Once all questions are graded, the time needed to calculate a student’s overall grade should be about the same using either approach.

The major downside risk might be perceived grade inflation when compared to more traditional grading schemes. While the mean and median grades are likely to rise (depending on the rubric used) because weaker students are not being penalized as heavily, a perfect 4.0 is just as difficult to get under either grading approach. The overall pattern of the grade distribution should not change.

Such an approach could also make perfect scores harder to obtain by including something like “*a demonstrated understanding of the concepts involved*” as part of the grading rubric.

### Who Benefits?

Students who make a number of small errors on mathematics assessments often receive discouraging letter grades. Even among students who understand the underlying concepts well, some students (often with ADD) have difficulty consistently executing procedures flawlessly, particularly on longer problems. Expecting such students to focus more is not as effective as finding ways of increasing their engagement in the class and the subject. Averaging scores provides such students with less active discouragement (bad grades for small errors) without watering down the meaning of the higher grades.

If we can recognize students, math students in particular, for what they understand and do correctly without penalizing them too harshly (something that will always be in the eye of the beholder) for smaller mistakes made along the way, perhaps this can help to reduce the number of students who gradually come to dread math or science courses despite their love of the subjects when they were younger.

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