Bending the Numbers: Standards-based Grading in the Traditional Grade Scale

Jonathan Corbett
13 March 2016
I happen to work at a school that requires traditional percentage grades to be assigned for nearly all assignments. While this method has its advantages -- namely, students and parents nearly universally understand what a 65% means -- I prefer to take a standards-based approach to assessment. Thus, the math question was:
How do I assess my students using a standards-based rubric, but still compute a numerical grade in Gradebook?
I do not claim to have the only answer, or even the best answer. But what I have come up with is a (simple-ish) way of assigning the numbers of a standards-based rubric to a numerical grading system. This page is really meant as an invitation for other teachers to check my methods and my math, and help provide the most meaningful assessment criteria and scores to students.

The philosophy of grades

Assessment should be the process of gathering evidence of student understanding. This evidence should then drive instruction, and provide students feedback as to how to increase understanding (or ability, as with a skills-based subject). It is important to keep this last step in mind: the goal is always to increase understanding. How does a failing grade help increase student understanding? How does a score of 100% on a test do the same?

The problem with failing

There seems to be a current mindset in academia that failing students is not what is best for kids. I have examined enough of the research to be in agreement with this idea, but with a few caveats. Namely, students should have the right to fail. I believe that a student should fail a class if he or she has not made attempts to complete the work or learn the material. It is my strong view that these are completely separate things.
In my class, the only way to receive a "zero" in the grade book is to not attempt or complete an assignment. Mathematically, there is no reason for 59 of the 100 percentage points available be reserved for failure, while only 10 points remain in each other category (A, B, C, or D). If a student fails an assignment, the assignment is failed. But a 59% in the grade book is a much more recoverable failure than a 29% or a 19%. Is it a sensical statement to say that a student has "failed less" or "failed more" than another student?  The 19% failure has a far greater impact, however, on the student's overall performance in the class. Students have a sense for when they are mathematically incapable of passing a class, and this will bring nothing but problems to the classroom.
 I do describe the reasons listed above to my students, but I also share with them that (as much as I wish it were false), in real life, you do get half credit just for showing up. ​​For this reason, any score falling below 50% in the grade book earns a 50%. I explain to my students that the rubric may state a lower score, but the grade book will reflect 50%.

The problem with "A students"

The problem with "A students" is that they expect to get As. To be sure, many students are A students because they have developed successful study habits and work diligently to be "good students". Unfortunately, the drive to be an "A student" has muddled the definition of the term. Per my district's school handbook, grade letters describe students of the following calibers:
Superior
Above Average
Average
Below Average
​Failure
90 - 100
80 - 89
70 - 79
60 - 69
​0 - 59
Students (and parents, and teachers?) have lost the sense of what it means to be Average. Average does not mean struggling, does not reflect poorly, and does not imply a lack of academic prowess. Average grades should be the "norm", as in the most common or most frequent grade. As a science teacher, I expect that many of my young poets, musicians, writers, bakers, and businesspeople will demonstrate "average" ability in science class. Put another way, I hope their scores (and therefore their efforts and abilities) in the courses of their interest will exceed those in my course. Likewise, I expect that the budding young scientists in my class will demonstrate a higher degree of ability in science. 
My grade book needs room for both. As it is, my poets, musicians and writers will still be evaluated by their future prospects based on their ability in my class. It is not prudent, then, to say that students should expect to earn a "C" in my class just because science is not their interest. If they are willing to do the work and construct an understanding of the Natural world in a scientific way, then they deserve a good mark. A good mark. But not an A.
An "A" should be reserved for my students who grin when I confide in them that I am not teaching them the whole truth about the nature of the electron, and that they will  have to wait until they get to college to learn all of the strange things that electrons do. An "A" should be reserved for the student sending me articles on the first ever discovery of gravitational waves, or asking about the criteria for differentiating Homo from Australopithecus. The "A" should be reserved from those students who go above-and-beyond, who really reflect the "Superior" category handed to me by my school. These students need a way to Exceed Expectations.

Standards-based Assessment

The term "Standards-based" has many facets, and I will not go into them here. The short form is this: Standards-based grading aims to provide a more holistic indicator of a student's level of proficiency with specific material or a specific skill. Deduction of a point here or a point there is not necessary, and it is understood that small errors are part of the learning process and are a necessary consequence of encouraging students to take risks. The term "failing" is not irrelevant, but the student either "Meets the Standard", or does not. The recurring message is that the goal for all students is to meet the standard. Some will do this on their first assessment, others will not.

Bending the Numbers

Balancing all of the factors described above, my take is this:
Students who Meet the Standard should get an 89, the highest possible B
This is a debatable point, and more a reflection of pressures unique to my own education and my current school climate. It also stems from frustration grading lab reports and giving the same "A" score to students who robotically checked off each requirement on the assignment handout and those who spent time reviewing scientific sources and synthesized the assignment into the bigger pictures of both the course and the Natural world. Out of this philosophy, rubrics something like the following were born:
​Figure 1.
An early version of my Standards-Based rubric for a modeling assessment. This was used with freshmen students who are (a) still learning to produce models, and (b) likely unfamiliar with this type of grading
Each category is assigned a weight (percentage) on the entire assignment, and students can earn up to 4 points (including half points) in each one. As I grade the assignment, I check off which description best fits the student work. Whichever column contains the most checkboxes ends up being the student's score, or a half score is assigned in between.
I then determine a value called MOD. Instead of making the maximum category value a 4, where 3/4 = 75%, the maximum category is the MOD value, or 3/MOD = 89%. Thus,
MOD = 3/0.89
Note that the MOD value can change depending on how many categories include an "Exceeds Standard" column. I use a spreadsheet to calculate each student's grade according to the following algorithm:
Final Grade = (category 1 score/MOD*category 1 weight)+(category 2 score/MOD*category 2 weight) ...
Figure 2.
Screenshot of a sample grade calculation spreadsheet. The MOD value for this assignment was 3.45, which correlates to a score of 4 on the rubric; thus, a score of 3.5 is entered into the calculation as a 3.22 (roughly). Note that the TEST student (row 3) demonstrates how a score of all threes on the rubric.