This is not a blog post on investing. Take a break from portfolio updates and if you are science or math teacher, take notice as this is a somewhat unique method for evaluating exams. Before getting into the grading system, a brief explanation of the Celebration Bell pictured above. This bell hung in my classroom for most of my teaching career. It is actually a fire alarm bell that was in the trash bin when my original high school was remodeled. I asked permission to rescue it and was granted ownership. My wife had it refinished with new brass. That is why it looks so great. This bell was rung when a student came up with an interesting idea, I pulled a faux pas, or something important happened in the classroom. It was not used frequently, but just often enough to provide great mirth in the classroom.

Now on to the grading model. The first change is to move away from the standard percentages that range from a perfect 100% down to some failing level. Instead of 100%, select a prime number such as 137 or 137%. Set this prime number as a perfect score. This throws students off a bit and requires them to kick in their ratio calculation abilities. But this is not the main thrust of this unique grading model.

The following idea is not new with me, but originated with a physics teacher I learned to know back in the early to mid-1980s. Here we go.

Assume you are giving an exam of seven problems to be solved in a 50 to 60 minute period. The number of problems and the level of difficulty can be adjusted depending on the length of the exam period.

At the core of this model is not which problems are solved correctly, but how many are solved. This point needs to be remembered.

The first four problems cover the basic material and if all are solved properly, the student passes the exam. Problems five and six are more difficult and are designed to separate the average from the very good students. The last problem is quite difficult and only a few members of a very bright class are expected to solve this problem.

When I first began grading tests, the first four problems were granted fewer points and the last problem quite a few points, based on the zero to 100% system. As a result it was not unusual to find good students ending up with a much lower grade for want of solving that last difficult problem. That system did not seem fair as I did not grade on the curve. My classes were too small to use curve grading.

Enter the new grading system. Assume each problem receives one (1) point if solved correctly. Further, assume failing to include units or miss-use of significant figures results in two (2 minor points) points subtracted for each of these potential errors. Alert: The points for significant figures and failure to include units are not the same points as those assigned for correct problem solution. This will be explained in the example below.

Here is the basic grading system.

- The first four basic problems are each worth 20 points for a total of 80 points if all are solved correctly.
- Problem #5 is given a value of 25 points. If five problems are solved, it moves the student very close to the B or B¯ level.
- Problem #6 is given a value of 20 points.
- Problem #7 is given a value of 12 points. This totals to 137 points.

I would expect the teacher to set up their own evaluation system and I varied these point assignments from test to test, depending on how I rated the level of problem difficulty.

A few example are required to understand how this works. First we take a very simple situation.

**Student #1:** This student solves all of the first four problems and makes not additional errors such as forgetting to attach units. Therefore, the score is 80/137 or 58%. This is considered a passing grade of C in this class. The student understands the basic material as that is what the first four problems are designed to test.

**Student #2:** This student solves problems 1, 2, 3, and 5 correctly and forgets units on one problem. Now pay close attention as this is where the system varies from your experience. Since the student solved only four problems, they receive 4 x 20 = 80 and then we subtract two “small” points for forgetting units. The final total is 78%. It is the number of problems solved, not which problems are solved.

**Student #3: ** This student solves six problems correctly, They are: 1, 3, 4, 5, 6, and 7. This student missed one of the “easy” questions, either for not showing their work, setting the problem up incorrectly, or just making awful calculations. Since six problems were solved correctly, they receive (4 x 20) + (1 x 25) + (1 x 20) = 125 or 125/137 = 91% Call that an A minus.

**Student #4:** This example is closer to what frequently happened in my classes. Assume the student solved five problems correctly and showed all their work on those five problems. It matters not one wit which of the five out of seven are solved correctly. Assume the sixth problem was set up correctly, but there was a calculation error to such a degree that I took of 5 points. Further assume this student did not include units on one problem (minus 2 minor points) and wrote down too many significant figures as they took the numbers off their calculator thus losing two more minor points. Here is how the grading works.

4 x 20 = 80 point for the first four problems solved correctly.

1 x 25 = 25 points for the fifth problem solved correctly. Again, it does not matter which problem this is.

The last problem worked on is considered #6 and the sixth correctly solved problem normally receives 20 points. However, five points were removed for the calculation error so this problem only counts for 15 points.

Total Score: 80 + 25 + 15 = 120. However, four (4) minor points are remove for units and significant figure errors giving the student a total score of 120 – 4 = 116. 116/137 = 85% or a very good score.

When I moved to this new grading system vs. the old traditional system, to my recollection, I never received one complaint about grading. Once explained to the students, they loved this system because they were not “dinged” such a huge percentage for not being able to solve that last problem in the limited time period.

Lowell Herr

Dennis Ryan says

I am a teacher and like your system. With your permission, I would like to “re-post” this information to other teachers.

Thanks

Lowell Herr says

Dennis,

Absolutely. Use and adapt however you wish and do share with other teachers. That was my intent.

There is a lot of flexibility in the model so go at it. If you have questions, just ask.

Lowell

Robert Warasila says

Lowell,

I used a system that is somewhat different. I never let my students use a “cheat” sheet. Instead I would put four questions up front that were derivations and they had to choose one of the 4. In the questions asking for a derivation I would give the harder equations so they didn’t need a cheat sheet and it gave them an incentive to understand where the equations come from. Then I would have about 5 text book based problems which they should be able to complete if they did the homework. The derivation plus the these 5 served as 100%. Yes significant figures and units were 1 point dings. Then I would put a last question that was much more challenging. I always graded all questions with partial credit depending on how much of the problems they could solve correctly. I always had classes of 24 or less and never curved, I always believed I could right a fair test. Generally no more than 2 or 3 people would tackle the bonus question. I could usually allow 90 minutes for a test.

In my own educational coursework as a college student ’59 to ’68, I did encounter courses where you either got the problem done correctly or it was totally wrong, different time different place:^ )

Bob Warasila

Lowell Herr says

Bob,

Partial credit was also in my evaluation bag. I was interested in how the students set up problems. There were a few times when I gave problems that had multiple solutions. I think such problems are called “over drawn or over described.” There might be another term. The explanation is much too long to describe here, but in one case it led to what I called the “Million Dollar Problem” as it not only had one solution, but it had an infinite number. And if one worked hard enough, the geometric shape of all the solutions ended up as a circle. It was a combination of momentum and kinetic energy. Great fun. I still remember the student bounding into my classroom pronouncing that the problem did not have a solution. She was right. If one removed one variable, the problem had an infinite number of solutions.

As for “cheat sheets,” my students were permitted a 3 x 5 card of any information. Those cards became very valuable and well worn by the end of the year.

Lowell

Jim Hotvedt says

Lowell,

I wish that I had been this creative. I told my students that my grade book didn’t have enough space for three digits (100%). I was up-front with them, to a fault, that exams were designed to challenge the best students. I assured them and established a track record that I would grade accordingly. I rarely received complaints about the rigor of the exams, but I suspect your approach would have reduced potential stress going into the exams for the “average” student.

~jim