Hacking The 100-Point Scale - Part 1

One highlight of teaching at an international school is the intersection of many different philosophies in one place. As you might expect, the most striking of these is that of students comparing their experiences. It's impressive how the experienced students that have moved around quickly learn the system of the school they are currently attending and adjust accordingly. What unites these particularly successful students is their awareness that they must understand the system they are in if they are to thrive there. 

This is the case with teachers, as we share with each other just as much. We discuss different school systems and school structures, traditions, and assessment methods. Identifying the similarities and differences in general is an engaging exercise. In general, these conversations lead to a better understanding of why we do what we do in the classroom. Also, in general, these conversations end with specific ideas for what we might do differently on the next meeting with students.

There is one important exception. No single conversation topic has caused more argument, debate, and unresolved conflict at the end of a staff meeting than the use of the 100-point scale.

The reason it's so prevalent is  that it's easy to use. Multiply the total points earned by 100, and then divide by the total possible points. What could go wrong with this system that has been used for so long by so many?

There a number of conversation threads that have been particularly troublesome in our international context, and I'd like to share one here.

"A 75 isn't a bad score."

For a course that is difficult, this might be true. Depending on the Advanced Placement course, you can earn the top score of 5 on the exam by earning anywhere between around 65% and 100% of the possible points. The International Baccalaureate exams work the same way. I took a modern physics exam during university on which I earned a 75 right on the nose. The professor said that considering the content, that was excellent, and that I would probably end up with an A in the course. 

The difference between these courses and typical school report cards is that the International Baccalaureate Organization (IBO), College Board, and college professor all did some sort of scaling to map their raw percentages to what shows up on the report card. They have specific criteria for setting up the scaling that goes from a raw score to the 1 - 5 or 1 - 7 scores for AP or IB grades respectively.

What are these criteria? The IBO, to its credit, has a document that describes what each score indicates about a student with remarkable specificity. Here is their description of a student that receives score of 3 in mathematics:

Demonstrates some knowledge and understanding of the subject; a basic sense of structure that is not sustained throughout the answers; a basic use of terminology appropriate to the subject; some ability to establish links between facts or ideas; some ability to comprehend data or to solve problems.

Compare this to their description of a score of 7:

Demonstrates conceptual awareness, insight, and knowledge and understanding which are evident in the skills of critical thinking; a high level of ability to provide answers which are fully developed, structured in a logical and coherent manner and illustrated with appropriate examples; a precise use of terminology which is specific to the subject; familiarity with the literature of the subject; the ability to analyse and evaluate evidence and to synthesize knowledge and concepts; awareness of alternative points of view and subjective and ideological biases, and the ability to come to reasonable, albeit tentative, conclusions; consistent evidence of critical reflective thinking; a high level of proficiency in analysing and evaluating data or problem solving.

I believe the IBO uses statistical and norm referenced methods to determine the cut scores between certain score bands. I'm also reasonably sure the College Board has a similar process. The point, however, is that these bands are determined so that a given score matches

The college professor used his professional judgement (or a bell curve, I don't actually know) to make his scaling. This connects the raw score to the 'A' on my report card that indicated I knew what I was doing in physics.

The reason this causes trouble in discussions of grades in our school, and I imagine in other schools as well, is the much more ill-defined definition of what percentage grades mean on the report card. Put quite simply, does a 90% on the report card mean the student has mastered 90% of the material? Completed 90% of the assignments? Behaved appropriately 90% of the time? If there are different weights assigned to categories of assignments in the grade book, what does an average of 90% mean?

This is obviously an important discussion for a school to have. Understanding the meaning of the individual percentage grades and what they indicate about student learning should be clear to administrators, teachers, parents, and most importantly, the students themselves. These is a tough conversation.

Who decided that 60% is the percentage of the knowledge I need to get credit? On a quiz on tool safety in the maker space, is 60% an appropriate cut score for someone to know enough? I say no. On the report card, I'd indicate that a student has a 50 as their grade until they demonstrate he or she can get 100% of the safety questions correct. Here, I've redefined the grade in the grade book as being different from the percentage of points earned, however. In other words, I've done the work of relating a performance measure to a grade indicator. These should not be assumed to be the same thing, but being explicit about this requires a conversation defining this to be the case, and communication of this definition to students and teachers sharing sections of the same course.

Most of this time, I don't think there is time for this conversation to happen, which is the first reason I believe this issue exists. The second is the fact that a percentage calculation is mathematically simple and understood as a concept by students, teachers, and parents alike. Grades have been done this way for so long that a grade on the 100-point scale is generally assumed to be this percentage mastered or completed concept.

This is too important to be left to assumption. I'll share more about the dangers of this assumption in a future post.

5 thoughts on “Hacking The 100-Point Scale - Part 1

  1. I struggle with this. The meaning I place on grades is mastery. My school sets the standards that are to be mastered. Mathematically, averaging scores where Zero is a possibility (anything below 50 actually) is so incorrect, my gut screams against it. There is a better way. Looking forward to your next post.

    1. The struggle is widespread, for sure. Part of what I'm exploring in this series is a way to make things better, given that schools likely aren't changing their reporting away from a 100 point scale any time soon. Some simple guidelines behind assessment design, scaling, and conversations about what grades should mean at any particular school are required for moving forward.

  2. Perhaps you would be interested in my post: http://somenxavier.xyz/posts/My-next-assessment-function/ Another topic is what we need to grade. I think that we should pass from mean function which mesures the average of the knowledge to knowledge based grading: does he know simplify algebraic expressions? (yes or no), does she know....?

    The grading function is an oversimplification. And with that we lost the meaning of grading: knowing what our students know. The secondary school should not be divided by courses. They should be divided be skills. And in the report card should appear only the skills. Nothing more. But the systems does not match the "it-should-be-this-way".

    I hope you publish your next post soon

    1. I completely agree that deciding what to grade, and how to grade it to indicate learning, is the defining question here. Your idea of abandoning the mean is interesting, as that calculation certainly obfuscates learning in some cases, or at least blurs the details enough to reduce the grade as an indication of what has been learned.

      In your post, you suggest adding points as a way to get away from the average. I agree that this might be a better measure than the average, but I think there still needs to be an indication of what that number means. Is a 72 an indication of making good progress, or does it show that a student is behind the mark? Some process of normalization is required. This is what I'm thinking can be solved using some creative use of technology.

      1. First of all, Evan, thanks for sharing my thoughts. It encorages me a lot.

        On the topic about what 72 means... I think it's a no solution problem. A number is just that a number. So we just could summarize the state of the learning of one particular problem. But the learning is a process: so we need the start (what a student knew), the end (what a student knows right now) and the road (how much and how the student have learned in all the time).

        How do you solve that? With a sequence of numbers? With a sequence of grading meaning the skills she knew in every time?

        If you have an answer, say to us.

        With all of my admiration,
        Xavier

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