[Random Musings] More on grading systems: compensatory model vs mastery model

Assessment Theory 101: Compensatory vs Mastery Model

Hi everyone,

This post is more targeted at fellow teachers, tutors and assessment enthusiasts, but of course students are welcome to learn more about the various grading systems.

Today's post is on compensatory model vs mastery model. For simplicity, compensatory model is often used in external assessments in many countries, but there's nothing stopping us from adopting the mastery model on end-of-unit assessments in class.

To keep it simple, let's consider a short end-of-unit test on logarithms consisting of three topics:

1. use properties of logarithms to simplify expressions
2. solve exponential and logarithmic equations
3. solve modelling problems involving exponential and logarithmic functions

Each topic is worth 10 marks, giving a total of 30 marks for the whole paper.

The pass mark is 50%, so 15/30 marks.

Notice that there's a LOT of paths that would get students to 15/30. To illustrate my point later on, we'll consider two students.

Student A gets 5 marks on each standard, so 5 + 5 + 5 = 15.

Student B gets 10 marks on one standard, 5 marks on another and 0 marks on the last one, so 10 + 5 + 0 = 15. 

This has massive implications as we'll discuss later.

Compensatory model

The compensatory model does not care about the marks breakdown; as long as the total is 15 or above the student passes the test.

Student A has demonstrated that they knew the basics of each of the three standards to deserve a pass. This is what we usually think of - a student getting 50% has demonstrated they could handle 50% of the content presented in front of them in each topic.

Student B, on the other hand, used their strength in one topic (10 marks) to offset/compensate for a lack of achievement in another one (0/10). This is the tricky case - does this student deserve a pass? According to the model, we don't care about the breakdown; as long as there's a total of 15 it is considered a pass.

In public examinations, this model is usually adopted, perhaps thanks to its simplicity. However, in the classroom, I think we can raise the bar and expect more from our students.

Mastery model

A mastery model requires students to reach some level of achievement in each standard to obtain a pass. In this case, instead of making an aggregate score of 15/30 as a pass, we can set the pass mark to 5/10 per standard. 

This is inherently more challenging than 15/30 total, as they definitely cannot use their strong suit to compensate for their slightly weaker performance. But what we can say is a student who achieves a pass on the test has successfully demonstrated the minimum competence on each of the three standards.

Of course, a more balanced approach can also be adopted. This is my favourite. Why do we have to choose one or another?

"Halfway house"

Using the same example, I'd like to make the passing criterion as follows:

• a total of at least 15/30
• a minimum mark of 4/10 per standard

This way we can kind of achieve the best of both worlds - you have some confidence that your students show some achievement in each standard, yet allowing some flexibility in how they achieve the minimum passing mark.

Going to the extremes

Of course, one of the most interesting ways to destroy a model is to consider the extreme cases. If the pass mark is 80-90%, there's isn't much room for error or for compensation in the first place, so both methods should probably give the same outcome.

Example: pass mark 24/30, the absolute worst you can do is 10/10/4, demonstrating a minimal achievement in the weakest standard.

On the other end, if a student can barely demonstrate any achievement, both methods would also make zero difference. 

Has the mastery model been implemented at a large scale? Yes!

Consider Scottish qualifications in the back old days with the NAB. Each course consists of three units and schools usually require students to achieve a pass in each of the three unit tests to be eligible for the final external exam. The questions on the NAB were really easy as they are not intended to be discriminatory.

This is a quick rundown of the compensatory and the mastery models. If you're interested in posts like these, let me know and I'd love to write more!

Peace!

Andrew