From a measurement prospective, traditional grading has some huge issues. It has the major advantage of ubiquity and being easy to understand, usually on a scale from 0-100, but the disadvantages are substantial and often overlooked. As mathematics and statistics teachers, it perhaps would be incumbent to use valid and reliable measurements for our grades and assessments, for if we – the experts in the uses and manipulations of numbers – are not practicing the best way to help our students, how can we expect everyone else?

What are the problems with traditional grades? They are too numerous to fully go over here, but I highly recommend checking out Dr. Robert Marzano’s book Formative Assessments and Standards-Based Grading , where he discusses it at length. Much of this post draws from this book, as it has fundamentally changed the way I look at assessment in the classroom.

For one, the grading scales teachers usually employ are very poorly designed and have arbitrary and capricious subjectivity. The classic “10-point” scale shows A’s from 90-100, B’s from 80-89, C’s from 70-79, D’s from 60-69, and F’s from 0-59. Ignoring the slightly annoying issue that an A actually covers 11 points, the ranges here are essentially chosen on whim and fancy, based on tradition and convention. What makes an 89 fundamentally so different from a 90 so as to call one an A and the other a B? Why not use a 6-point scale with A’s from 95-100, B’s from 89-94, etc. Or a 15-point scale? There really is no solid reason why not. It usually boils down to tradition and convention.

One might argue what is wrong with that, but that raises the fundamental question of this post: **What does a grade mean?**

*I posit that a grade should be the evaluation of a student’s mastery of the standards taught.*

If we take this notion as our basis, it is no longer valid to arbitrarily assign grades on a 100-point scale. It is absurd to claim that any assessor can judge the difference between an 89 and a 90. Just by chance alone, that student may score a 94 on a similar text on a different day, so it is invalid to assign them a B simply because of chance. Likewise, should a 0 truly be given for a student not doing the work? Does that mean the student doesn’t know the material? On a traditional 100-point scale, this can bring their grade down significantly, but it falsely portrays their true level of mastery. The same can be said with the F-range. An F ranges from 0-59, nearly a super-majority of the 100-point scale. How can we know a failing student’s mastery level so specifically as to assign them a grade of 55 versus 25? Don’t both mean “failing”? Is it truly necessary to have such a range to say essentially the same thing?

Enter standards-based grading. Different schemes can be employed, but the template * employed by Marzano and his team use the numbers from 0-4 in their scale, which has been empirically proven to be very reliable among teachers assigning mastery levels. The scale ranges from “0” (no mastery demonstrated at all) to a “4” (in-depth inferences and applications that go above and beyond the standard’s material), and decimals such as .5 can be employed to more specifically assign a score. But instead of 100 points to choose from, this eliminates it down to 5-10 scores to choose from, each with a rubric for each standard to easily select the current level of mastery.

Teachers can easily fill in the rubric and samples of each score level for each standard as they teach them and attach to assessments and lesson plans. The new scale takes some time for students to learn, but when I used it with high school seniors and first-year college students, they picked up on it very easily and often learned to like it more than traditional grades from 1-100. One of the biggest pieces of feedback I received on multiple occasions was that the rubric of the SB (standards-based) scale made it easier to see what was expected and why they received the grade they did.

In a 100-point grading system, test questions often have different weights (this question worth 5 points, this one worth 10, etc.) due to their importance and level of assessment, but this makes grades extremely unreliable since different teachers assign different weights. One student may make a C where another makes an F simply because an essay question was worth 15 points versus 40. In an SB scale, this is no longer an issue. A student demonstrating “mastery” makes a 3.0, regardless.

The above link shows an example for a common statistical standard, the normal distribution. This is often taught in an Algebra II, Pre-Cal, or Statistics class in high school, and it easily shows students what is expected to make a certain grade. No longer do students have to worry about “get 2 questions wrong, I make a B”, but instead they think about “I need to show I can rise to this mastery and prove I know it”.

(By the way, my school system made me record grades in the electronic gradebook on a 100-point scale, so I just came up with a transformation that made sense. So a 4.0 was a 100, a 3.5 was a 90, a 3.0 was an 85, etc. It is easy to play around and do this if you need to.)

The best part? The vast majority of the secondary (and some collegiate) mathematical standards you will ever go over have already been done by teachers across the country! Visit the Proficiency Scale Bank* on the Marzano team’s website to search scales of essentially any topic you can imagine. (They are not limited to math, by the way, so tell your other teacher friends, also.) The best part is that you can tweak and edit these as you need to fit your needs. It really is an fantastic resource.

I do not claim that SB grading is without its own flaws and difficulties, but I do feel it is an important improvement over what we have traditionally done. Give it a look, give it some thought, and do what you feel is best for your students’ learning mastery.

Until next time!

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