# On what total do you grade your exams?

Let's say that a given course has $3$ exams that are worth $25\%, 35\%$ and $40\%$ each. When building and correcting the exam, do you give/take out points so that the total sums to $25,35$ or $40$ respectively, or do you score all of them on $100$?

Reasons for a $25,35$ and $40$ scoring system that I can think of:

• Students know right away how much points they have cumulated;
• They know how much points each mistake is worth;
• If the teacher judges that some mistake should be penalized for $1\%$ of the grade each time, then it is always $1$ point out of your total, whatever that total might be.

Reasons for a all on $100\%$ scoring system that I can think of:

• A minus $2$ points might have less chance to get contested than a minus $0.5$.
• Students are more used to $100\%$ scale, and thus can better compare.
• This gives you the opportunity to give variable weights to your exams, should you need it for some reason, or allows for dynamic weighting (Say the best exam of the class or individually is worth more)

What do you guys use and why?

• "If the teacher judges that some mistake should be penalized for 1% of the grade each time, then it is always 1 point out of your total, whatever that total might be." To me, this sentence states 1 / total = 1%, for all values of total, which just isn't true. What are you trying to say here? – Thanatos May 20 '14 at 22:51
• If your students can't figure out what a 60 on an exam worth 35% means... – vonbrand May 20 '14 at 23:05
• I'm not saying these are valid reasons, just some things that came to mind. The core of the question asks whether you grade on 100 each exams or on what they are worth. – Jean-Sébastien May 20 '14 at 23:14
• @Thanatos I mean that 1 point over total is worth 1% of the semester, if you grade with weigths – Jean-Sébastien May 21 '14 at 0:40
• I'm fond of the second grading scheme that I outlined here: matheducators.stackexchange.com/a/2119/262 It lets students know where they stand and encourages them to work hard on the pre-final tasks, but also gives everyone a chance to do well in the course by acing the final. – Benjamin Dickman May 21 '14 at 3:44

## 4 Answers

You should not design your exams, tests, whatever to have a special number of total points in each exam, test, whatever. Reasons:

• It is mathematically totally irrelevant (as long as it isn't 0).
• We're talking about math courses:
• The students should be aware, that it's totally irrelevant.
• The students should be able to calculate their current standing on their own.
• It disturbs the evaluating in an exam, test, whatever.

Let me explan the last point:

Assume, that there are 23 items of equal importance in the exam. If you want to give 50 points in total, then each item will be worth approximately 2.17 points. If a task consists of 5 of these items and a student has got 3 of them, then his performance in this task is worth approximately 6.52 out of 10.87. This is just disturbing.

The most natural way of assigning points is to give each item, that the student should produce according to your expected solution, 1 point. If an item should be worth more or less than a standard item, use natural or easy fraction (0.5,0.25) weights.

Then the total number of points is 23 and the student got 3 out of 5 points in task (A). At the end, you can weigh the total number of points according to your plan for the whole course.

That way, you support the didactic value of your exams, tests, whatever rather than their selective value.

My friend has a course design she likes. She knows the course will be worth 200 points total, and she knows exactly how many points to give to the two quizzes (10 ea), the midterm (50), the final (90), the clickers (10), and the homework (30). This works well for her, except she has to have an exact number of questions on every exam and homework, and she can't adjust assignments on a whim.

I teach the same course, and I like to keep things nimble. I have three midterms (10%, 25%, 10%) and a final (40%). I have regular online quizzes (10%) and random in-class assignments (5%). If I find my students are slow readers, I can reduce the number of questions on the next exam. If I suddenly want to have students turn in an index card with their group answer during a class, I can collect another assignment without worry. I can add a quiz retake whenever I want. I can make a quiz long or short. This works well for me, and I rarely get students asking me to figure out their grade for them. I will say that our course management system does the math for both me and the students, which helps the students track their progress. You may wish to stick to simple points if you don't have a good gradebook system.

To summarize, do whichever suits your style, but always be happy to talk to your students about their grades.

• I used to keep it flexible like this also. Additionally, I always told the students what each question was worth. For example, on a 2nd or 3rd test in first semester calculus, some easy "find the derivative using short-cut rules" problems might be 5 points each, whereas a real-world max/min problem might be 20 or 25 points. If I didn't get a chance to write the point values on the tests before I had to make copies of them, I'd put the point values on the board. On major tests I had the totals be 100, and on short quizzes the totals were 10 (partially to avoid "nickel and diming" of points). – Dave L Renfro May 21 '14 at 14:54

I find it easier to asign points when the maximal grade is the same all around, be it an exam, quiz, or homework. It makes grades directly comparable too. To see what it means in terms of the final grade is just a simple proportion away (or stick into the appropiate formula, whatever).

It sounds like this is a grade weight question. When weighing grades, like saying a test is worth 25%, it doesn't matter how many questions you put on the test/exam. There are two ways that I know of the weigh grades, points and percents. They are basically the same method, just represented differently. With points, you have a total number of points that you allot per assignment and the total points earned is divided by the total points available is the average. The percent method is a method in which you do not necessarily know the total number of points that will be allotted by the end of the course, however, you do know how many assignments you will give and what percentage you think they should be worth. Then you take the scores of the assignments in that category, average them, and then multiply them by the percent. Then you add up all the averages*percents and get the overall grade for the course. This will prevent the need for determining how many questions are needed to make sure you have the same number as your desired percent. It sounds like you are trying to combine the two methods. If you want to do a point method with 100 points total, then you need to be careful with how many points each question are worth. You can give fractions of points for questions if you feel the need to give more questions than a 1 point system will allow, also.