Tag Archives: 100 point scale

Hacking the 100-Point Scale - Part 2

My previous post focused on the main weakness of the 100-point scale which is the imprecision with which it is defined. Is it percentage of material mastered? Homework percentage completion? Total points earned? It might be all of these things, or none of them, depending on the details of one person's grade book.

Individual departments or schools might try to define uniformity in grading policies, give common final assessments, or spread grading of final exams amongst all teachers to ensure fairness. This might make it easier to compare two students across a course, but still does not clearly define what the grade means. What, however, does it signify that a student in an AP course has an 80 while a student in a regular section of the same course has a 90?

Part of the answer here is based in curriculum. Understanding what students are learning and in what order defines what is being learned, and would add some needed information to compare the AP and regular students just mentioned. The other part is assessment: a well crafted assessment policy based in learning objectives and communicated to a student helps with understanding his or her progress during the school year. I hope it goes without saying that these two components must be present for a teacher to be able to craft and communicate a measure of the student's learning that students, teachers, parents, and administrators can understand.

At this point, I think the elementary teachers have the right idea. I've been in two different school systems now that use a 1 - 4 scale for different skills, with clear descriptors that signify the meaning of each level. Together with detailed written comments, these can paint a picture of what knowledge, skills, and understanding a student has developed during a block of the school year. These levels might describe the understanding of grade level benchmarks using labels such as limited, basic, good, and thorough understanding. These might classify a student using the state of their progress with terms like novice/beginner/intermediate/advanced. The point is that these descriptors are attached to a student and ideally are assigned after reviewing the learning that the student has done over a period of time. I grant that the language can be vague, but this also demands that a teacher must put time into understanding the criteria at his or her school in order to assign grades to a particular student.

When it comes to the 100 point scale, it's all too easy to avoid this deliberate process. I can report assignments as a series of total point values, and then report a student's grade as a percentage of the total using grade book software. Why is a student failing? He didn't earn enough points. How can he do better? Earn more points. How can he do that? Bonus assignments, improving test scores, or by developing better work habits. The ease of generating grades cheapens the deliberate process that may (or may not) have been involved in generating them. Some of the imprecision of the meaning of this grade comes, ironically, from an assumption that the precision of a numerical grade makes it a better indicator. It actually requires more on the part of the teacher to define components of the grade clearly using numerical indicators, and defining these in a way that avoids unintended consequences requires a lot of work to get right.

Numerical grades inform a student's progress, but don't tell the whole story. The A-B-C-D-F grading system hasn't been in use in any of the schools where I've taught, but it escapes some of the baggage of the numerical grade in that it requires that the school report somehow what each letter grade represents. An A might be mapped from a 90-100% average in the class, or 85-100 depending on the school. As with a verbal description, there needs to be some deliberate conversation and communication about the meaning of those grades, and this process opens the door for descriptors for what grades might represent. Numerical grades on the 100 point scale lack this specificity because grades on this scale can be generated with nothing more than a calculation. That isn't to say that a teacher can't put in the time to make that calculation meaningful, but it does mean it's easy to give the impression of precision that isn't there.

Compounding the challenge of its imprecision is the reality that we use this scale for many purposes. Honor roll or merit roll are often based in having a minimum average over courses taken in a given semester. Students on probation, often measured by having a grade below a cut-off score, might not be able to participate in sports or activities. Students with a given GPA have automatic admission to some universities.

I'm not proposing breaking away from grading, and I don't think the 100 point scale is going away. I want to hack the 100 point scale to do a better job of what it is supposed to do. While technology makes it easier to generate a grade than it used to be, I believe it also provides opportunity to do some things that weren't feasible for a teacher to do in the past. We can improve the process of generating the grade to be a measure of learning, and in communicating that measure to all stakeholders.

Some ideas on this have been brewing as I've started grading finals and packing for the end of the year. Summer is a great time to reflect on what we do, isn't it?

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.