Challenging the Grading Paradigm, Part 3 (Alternatives to the 100-Point Scale)

Ben Mainka's picture

A little over a month ago, I posted the first part of a series entitled, “Challenging the Grading Paradigm.” The goal of this series is to build awareness of a very important curricular issue in public education today – grading that promotes learning. I previously discussed the basic dilemmas that educators face with regard to this topic, and then in the last article, I discussed removing behaviors from the academic grade. In part three, I will discuss alternatives to the 100-point grade scale and the statistical problems with the 100-point scale. This article is sure to drum up lots of controversy as this is the most common scale still being used in most schools, but please give the next few paragraphs an objective look. Before we can really have any type of meaningful discussion on this topic, we need to first agree to some common assumptions. First, I still believe that most people in our field want to do what is best for children. I do not think there are many people out there that want to intentionally harm students emotionally or academically. Therefore, regardless of your feelings on this topic, we all want what is best for students. The final assumption that is very important is that we agree on a typology of evidence. Basically, we understand that there are several different levels of informational evidence. Doug Reeves does a really nice job explaining the five levels of evidence: 1. Opinion – “This is what I believe, and I believe it sincerely.” 2. Experience – “This is what I have seen based on my personal observation.” 3. Local Evidence – “This is what I have learned based upon the evidence that includes not only my own experience but the experiences of my friends and colleagues.” 4. Preponderance of Evidence – “This is what we know as a profession based upon the systematic observations of many of our colleagues in many different circumstances in many different locations and at many different times.” 5. Mathematical Certainty – “Two plus two is four, and we really don’t need to vote on whether that statement is agreeable to everyone.” It is almost impossible to reach mathematical certainty in most conversations that we have in our field, and very rarely do we find it in our discussions as we try to influence positive change. Most of the time, the best thing we can do is get to level four, a preponderance of evidence, which is very good. However, with regards to some elements of these grading discussions, mathematical certainty should play a strong role in the examination of policy. At this point, hopefully we can agree that we all want what is best for students, and that there are clearly different levels of informational evidence that can be considered when evaluating issues. Let us start with looking at our commonly held practice of using the 100-point scale. For as long as I can remember, it has just been assumed that teachers use the 100-point scale for all of their grading efforts. For example, if you received a 78% on a test, that would be 78 out of 100 points and result in a C+. Another way that the 100-point scale manifests itself is when teachers set their classes up by points such as: Project A = 25 points, and Lab B=50 points, Notebook/Journal=10 points, etc. At the end of the marking period or semester, the teacher tallies up all of the points earned and divides that number by the points possible and if you received 60% of the points, you receive a D-. Most of you should be nodding your head at this point recognizing the use of this type of system. If you have not seen this as a professional educator or used this type of system, you are in a very rare group of people. The ugly truth behind this practice is that it is statistically ridiculous and incredibly inaccurate. Mathematical and statistical evidence can prove that a 100-point scale is incredibly flawed; unfortunately, this has not stopped the use of this system on an alarmingly broad scale. I believe that this is mainly due to the fact that opinion and personal experience are the main sources of evidence that we use. This is very ironic for our field where we lay claim to being progressive, looking at facts and data, and objectively looking where evidence takes us. However, no matter how overwhelming the evidence is, personal experience and opinion in education remain the most powerful force in discussions on policy. The prominent use of the 100-point scale is evidence of this. What is the real problem with the 100-point scale you ask? The issue is that when you assign a student anything lower than a 50 on a 100-point scale you violate the basic principle of ratios. In Michigan, part of the fifth grade GLCE is teaching students about the principles of ratios, i.e. A is to B as 4 is to 3; D is to F as 1 is to zero. The ramification of using the 100-point scale is that you will almost certainly get a statistically inaccurate score when grades are calculated. Most schools have a variation of the following scale: A= 90-100 B= 80-89 C= 70-79 D= 60-69 E= 0-59 If you look at this closely, each grade range is roughly ten points with the exception of the E which is sixty. This means that anything less than fifty points would be in violation of the principle of ratios. Obviously the most damaging effects are seen when a zero is awarded on this scale, but anything less than fifty is inaccurate none the less. For example, if a student has received a zero on the 100-point scale, their score would be six times lower than the next grading interval. The only way you could make this scale accurate is to have a label for each mark below 50 points like this: E= 50-59 F= 40-49 G= 30-39 H= 20-29 I= 10-19 J= 0-9 I cannot imagine many schools educating their parents on awarding a “J” on a report card so this is probably not going to be happening. Hopefully you can see how using the 100-point scale defies mathematical logic and accuracy. In fact, if we go back to our typology of evidence, we know that using this scale and the calculations that occur go against mathematically certain evidence. There does not need to be a lot of discussion on this, because it is a fact, which is the catalyst for this conversation. Understanding that using the 100-point scale is not a best practice, I would like to propose several alternatives that you could use in your building. Also, I will share the scale that we will be using here at Fowlerville Junior HS. Each of the following scales has pros and cons, which I will briefly discuss, but the one thing that they all share is reliability and accuracy from a number-crunching standpoint. 50-point Floor Scale The first scale I would propose is a 100-point scale with a 50-point floor. What this means is that you would still use points or percentages like it has been done traditionally, however 50-points would be the lowest grade that you could assign. Again, each grade range interval would be roughly ten points and would like this: A= 90-100 B= 80-89 C= 70-79 D= 60-69 E= 50-59 You can obviously see the difference here, and that is that teachers would not be able to assign scores lower than fifty points. The benefit of using this scale is that you do not really need to change your mindset very much to the new system. Most teachers would be comfortable using this scale from a familiarity standpoint, but this system has one extremely large hurdle – the emotional attachment to the zero. In my opinion, this scale is almost impossible to sell to teachers because of the fanatical attachment that people have to the mighty zero. I guarantee that you will hear things like, “I refuse to give something for nothing!”, “This is falsifying grades!”, “How can I “give” 50 points to a student who does nothing!” Actually, I challenge you to find many other topics that bring up more emotion than this type of a system. That being said, these attachments are based on opinion and personal experience and not a preponderance of evidence or mathematical evidence. You are essentially “correcting” the scale by putting the floor at 50 points. You are not “giving” anyone 50 points, but 50 points is the lowest score on your scale. Essentially, 50 points is an E, just like a zero is an E on the traditional 100-point scale. This scale has merit and is a much improved first step from the traditional 100-point system, but I would caution you to the staff response. The 4-Point Scale The second scale that I would suggest is the 4-point scale. One of the great things about this scale is the simplicity that exists within it. The basic premise to this scale is that teachers would use rubrics with various indicator levels (depending on the assignment) with the highest level work being four and the lowest level being worth zero. There are a couple big advantages here, and the first is probably the biggest for moving this change forward. First, teachers can assign a zero on this scale without causing statistical inaccuracy. This can occur because zero is the lowest score which is only one interval below the next lowest score just like all the others. In essence, the principal of ratios remains in-tact. The next advantage to this scale is that it really works nicely with colleges as most universities are already on this scale. The only real flaw with moving to this type of a scale is that you would need to invest some time coming up with well-crafted rubrics to score the assessments that you are using. Overall, the ties to GPA and the college level coupled with simplistic accuracy make the 4-point scale a great option to consider. For a very complete and thorough look at the 4-point scale, I would recommend you pick up the book “Formative Assessment & Standards-Based Grading” by Robert Marzano. 12-Point Scale The third scale is one that we are moving towards utilizing here at FJHS; the 12-point scale. The first thing that needs to be clear about this scale is that it is not actually a point system at all. Really the 12-point scale is a way to provide a numerical representation of a letter grade. The scale looks like this: 12= A 11= A- 10= B+ 9= B 8= B- 7= C+ 6= C 5= C- 4= D+ 3= D 2= D- 1= E 0= No Attempt The 12-point scale shares some of the advantages of the other options such as the statistical accuracy, and also the ability to assign a zero. However, one advantage to this type of scale (you could also do this with the 4-point) is that you can use any type of scoring method that you want. For example, as a teacher, I could use rubrics, points, percentages, or any other method to score individual assignments. Then, I would take that score and convert it to the 12-point scale. That may seem confusing, but it is actually quite easy because the bottom line is this: what letter grade should the student receive on their assignment? If I gave a test, and a student scored a 40%, their grade would be an “E.” An “E” would be a “1” on the 12-point scale and therefore a “1” is what would be entered into the grade book. The disadvantage to the 12-point scale is the learning-curve at the beginning as teachers try to memorize the conversions. However, it will not take very long before people start to realize that a “C” is a “6”, or a “D” is a “3”. Soon, people will not even need to look at the scale because it will be memorized. In my opinion the 12-point scale is a great scale that is very well-rounded. I think that this scale has the most upside which is why we have decided to implement it. Presented here are three examples here of alternatives to the 100-point scale, but there are even more out there. The key is that we address the misuse of the 100-point scale in almost all of our schools. As I discussed earlier, most all of us truly want what is best for students. However, even the most well-intentioned grading systems can be riddled with inaccuracy. My hope is that you dive deeper into this area and continue to challenge outdated paradigms. Always remember, you have the highest level of evidence (mathematical certainty) on your side, and any other evidence for the accuracy of the 100-point scale will come from opinion and personal experience. Thank you for taking the time to read these articles, and I hope you find them mildly informative. There are many others who have done much more extensive work in these areas. Please do not hesitate to contact me for resources or for contacts of others who can really help you engage in these conversations. In a couple weeks look for part four of this series which will address alternatives to assigning zeros.