Sunday, August 3, 2008

Grading Systems Part 1 - Logic and Percentages

This is part one of a series of posts on grading students. Last year during a professional development seminar my former principal starting discussing perceived inequities in grading systems. He rambled on about an F being worth 50% and 5 point grading scales. I attempted to follow what he was talking about, but failed to understand its relevance to my(or any) classroom. Recently, I ran into an article describing exactly what he was talking about. I finally am starting to grasp the issue that lead to the faulty conclusions discussed in that article and by my principal.

The general problem is when teachers arbitrarily assign a letter grade to an assignment and then try to convert it to a percentage. Thus what happens is a D is worth 60% and an F a 0%. The article is correct, this does not make sense. The problem is the use of a letter grade as the initial grading system and then trying to convert this into a number. This problem does not include the more common practice of converting a numerical grading system to a letter grade. Thus for most math classrooms this article should not apply. Math lends itself to figure all grades in terms of percentages. Then when grades are reported letter grades are assigned to those percentages. Here is the statement I am referencing from the article.
Their argument: Other letter grades — A, B, C and D — are broken down in increments of 10 from 60 to 100, but there is a 59-point spread between D and F, a gap that can often make it mathematically impossible for some failing students to ever catch up.

The problem with this is they are incorrectly viewing the problem. There are two sets, passing and failing. Failing is from 0-60 and passing is from 60-100. Now the other letter grades give the student, parent, school and college exactly how well they are passing. Now if they want to make an argument that failing should be 0-50 and passing from 50-100 that is fine, but the argument that 50% should be a minimum failing number is weird and doesn't make sense. If you want to do that then work off of a 4 point grading system.

However, I am not sure I logically agree with a 0 to 4 scale. My problem is that it doesn't distinguish well between a student that is almost passing and one that isn't close. This is an important distinction to make. Not because it matters on their report card, but from a teaching perspective. When I grade something I need to be able to quickly determine the skill level of each student. I am digressing though because, as I said before, this doesn't apply to a math classroom. Math lends itself to total points and percentages.

As you can tell I disagree with the ideas put forth in this article. They are born out of a desire to pass more students and are disguised as a self esteem booster. It always amuses me when schools attempt to dictate grading systems to their teachers. In a classroom it is always possible to manipulate the system so the grades look like you think they should. I think in general schools spend way to much time looking a the grading and numbers involved with failing students. At my last school our failure numbers were monitored. If they were too high then you were going to here about it. Accordingly many teachers lowered standards.

In my mind the best way to grade a student is using point totals and percentages. Letter grades are only useful as communication tools to parents, students and colleges. All assignments should have number values associated with them. A much more difficult question is, how do I determine what number represents a minimum competency in my classroom? This question is not asked nearly often enough.


Maria H. Andersen said...

And there's a great example of a function that is NOT one-to-one (and why it is important, in the real world, for most of our relations to be functions).

Relation: {Numerical grade, Letter Grade}

95 --> A
90 --> A
85 --> B
80 --> B
75 --> C
70 --> C
65 --> D
60 --> D
55 --> F
50 --> F
45 --> F
40 --> F
35 --> F
30 --> F

The forward mapping shows that for every x maps to only one y. But a y-value maps to multiple x-values.

This is a function, but not one-to-one.

Trent Tormoehlen said...

Never thought of it that way. You are correct. The teacher I work with when I student taught would actually create a function to determine the percentage grades. It was his means of curving the students grades. How do you determine what is considered passing and what isn't?

Becky Davis said...

I am an Algebra teacher in Oklahoma, and I actually use the 50% as the lowest F. Here's how it works for me, homework grading is from 0 to 10 points. Since I see homework as practice, students can re-do problems that they got incorrect for full credit. Tests and quizzes are graded from 50-100%. I was wary of this at first, but students who don't deserve to pass generally don't pass, but others who are really trying to learn and pass the class aren't devastated by a single low grade. This has been VERY effective in my class. I would suggest reading Grading that Works by Robert Marzano. It takes a look at grading for mastery. Grades under today's system are often based off completion, compliance, attendance, good behavior, etc. Anything but truly learning.

Trent Tormoehlen said...

I would love it if you would give me more information on how your grading scale works. What earns a 50%? Do you use a point system? For example would a 10/50 and a 25/50 earn the same score?

I have dealt with Marzano a little, and I agree with what you are saying about completion, effort, etc. However, I believe teaching responsibility, hard work and consistent effort or more important than the math. Thus I think they should play a part in the grade. My next blog post will deal with weighting. But in general I think the majority of the grade should be based on what a student knows.

Becky Davis said...

I'd love to give you any information I can about my grading. I use weighted grades. Homework is 25%--enough to make it worthwhile, but not enough to boost a kid's grade if his parent is doing is homework. Each assignment is 10 points. I do let kids redo their homework, so I don't use the 50% on homework.

Quizzes are 30%. I use quizzes based on mastery of single skills, so basically I give a mini-quiz on each skill I teach. I grade these from 5-10 points.

Tests are worth 30%, too. I create my own chapter tests. Even students who make a 25% on the test will receive a score in the gradebook of a 50%. Same with my final which is worth 15% of their grade.

Please let me know if there is anything else you want to know. My quizzes on mastery are the most powerful grading tool I have because it lets me know what skills my students have attained and which ones they still need to master.

Trent Tormoehlen said...

Thanks for the information. Do you give a minimum of 50% on the quizzes as well?

Da5e said...

Thanks for your thoughts; however, your credibility is seriously undermined by numerous typos and by failing to recognize the difference between "here" and "hear."