Grading Students with the Gap System and a Gradebook

Grading students is about evaluating how much each student has learnt in a course. While it is possible to debate the merits of measuring and grading student performance and how this should be done, it is an important part of a teacher’s role in a schooling system. The focus of this article is explaining one system for converting numerical results into alphabetical grades.

In a typical school course the papers, assignments and exams that make up the assessable tasks, i.e. those tasks that directly contribute to each students final result and grade, are given a numerical score that is a measure of how well the task was completed. These numerical results may be converted to letter grades for each task, or are finally combined into a single total that is then converted to a grade.

Different grading systems

Going back a few decades this combining of results needed to be done by hand or with an electronic calculator. Now using a spreadsheet or gradebook program on your PC is a faster and more accurate way to do this sort of work with student results. But independently of the tool that you use to add results and assign grades, you still need to have a system, i.e. a method, to follow in deciding who gets an A or a B and so on. Generally, there are two broad approaches that you can follow. One is a norm based system and the other is criterion based.

A norm based system assumes that in a group of typical students, the results will tend to follow a normal distribution. What this means is that most of the student results will tend to be grouped around some middle point with the number of students getting higher and lower scores being much less. You may have heard of the "bell shaped curve" which is what you see if you plot a chart with a set of results that follow a normal distribution. With a norm based system the grade for each student is affected by the performance of all the other students in the course.

Whereas a criterion based system assumes that there is an objective measure of the content in a course, and the grade assigned to each student is based on how much of that content has been learned. With this type of system each student grade is independent of all the other students in the course and instead based on a measure of how competent the students are in the knowledge and skills that they are expected to learn.

Which type of system is best? There is no right answer to that question and both systems have strengths which vary depending on the type of course and the students being graded. For example, a norm based system is harder to apply and justify if the number of students in a course is small. This is because with a small number of students the results may be less likely to follow the classic bell shaped curve. But that doesn't mean that a norm based system should always be avoided - it all depends. The grading system that you are comfortable using may depend on your philosophy of teaching and learning. Sometimes you may not have a choice as the grading methods may be dictated by your faculty, school, or education department.

The gap system

In the remainder of this article you will be introduced to the gap system that is neither norm based nor criterion based. Like the norm based system, grades are assigned based on the relative performance of the students, but the gap system does not assume a normal distribution or a bell shaped curve if the results were plotted on a chart. The gap system can also be successfully used with a small number of students. One other advantage of the gap system is that it is simple to understand and does not require seemingly arbitrary statistical methods that can be difficult to explain.

To apply the gap system all the scores for the students are sorted from top to bottom and you then examine the list looking for gaps in the results. Then based on the gaps and your judgment you can set the cut-off point for each grade. In other words, where there is a gap the cut-off mark is set in that gap. Because the minimum result needed for each grade is distinct and separated from the next group of students you do not get the situation where students who may differ by a single point get different grades.

With a gradebook

Using a gradebook program to assign grades with the gap system should be straightforward and easy to apply. Using The Gradebook Program as an example, the process below assumes that you have a column that has the final student results. If you are using a different gradebook program then you will need to translate the actions done here into your program. The sample gradebook data included with The Gradebook Program includes columns with results in case you want to experiment with the gap system without having to type in results yourself.

Once you have a gradebook open with results that need to be converted to grades, the first step is to have some way of examining the results so the gaps are made obvious. One way to do this, which can be done in any gradebook program, or in a spreadsheet such as MS Excel or Open Office Calc is to sort the cells in the column of results. In The Gradebook Program put the cursor in the column of results and choose the Numerically by column command in the Tools, Sort students menu. In a spreadsheet you could highlight the column and choose the Sort command, which will vary depending on the program you are using.

With the sorted results you then need to start looking for gaps. Depending on your grading philosophy you may already have an idea of how many of each grade can be given. This may guide you as to where to look for gaps, or you may not have pre-determined requirements and the number of each grade will be influenced by which the gaps you think fairly discriminate between different levels of performance.

While avoiding a printout to save paper is good for the environment, you may find that using the print command of your gradebook and having the results in front of you makes analyzing the results easier. Being able to draw lines and make notes as you figure out the groupings can be easier with pen and paper than scrolling up and down on screen.

If you are using The Gradebook Program there is an easier way of discovering the gaps than a sorted list of results. By graphing the result distribution with the Distribution command in the Print, Graphs menu what you are looking for are gaps in the chart - which are made more obvious by the white space in the graph.

Professional judgment required

Regardless of the method you use to discover the gaps, once you have the cut-off point for each of the grades you can then use them when assigning the grades, either by hand or with your preferred grading tool. Before finishing there is one unanswered question: how does the gap system work if there are no clear gaps in the results?

In that case the gap system may not be the most appropriate way of assigning the grades. If there are gaps, but not enough for the number of different grades, then you can use the gaps that do exist and look for points where there may only be a single student and that point can then be used in lieu of a clear gap. It is important to remember as mentioned at the beginning that there is no single "best" grading system and as a teacher there will be times when you need to use your professional judgment as to what the final grades will be.

References:
Testing and Grading: Evaluating and Grading Students by Marilla D. Svinicki, The University of Texas at Austin.