Different grading systems

Hello everyone!

 

Today’s post will deviate from the usual blogposts on the website, as it’ll be targeted at teachers and fellow tutors. I’m sure students can still benefit from this, but this post is written with teachers in mind.

 

We’ll discuss two main systems – numerical (raw) marks vs marking at the question level as a whole.

This may sound confusing but it’ll make sense when you finish reading the post.

 

A brief rundown of the two systems

 

Numerical marks converted to final grade

This is the most common method.

A-level, IB, Scottish qualifications, it’s not hard to list systems that opt for this option.

 

Each exam has a fixed number of raw marks.

Students take the exam, teachers mark each question and tally up the final raw mark.

 

The overall performance is not determined until the awarding process takes place.

 

Marking at the question level

The biggest example of this is New Zealand’s NCEA system, first introduced in 2002.

We’ll focus solely on the external exams which take place in November each year.

 

Each question has several parts and each part is associated with a grade – a, m or e.

Partial credits are rarely awarded as each question is marked as a whole.

Minor errors are usually ignored EXCEPT excellence-level questions.

 

Here’s an example, because I know this is getting quite confusing!

The following questions are taken from Level 2 Maths and Stats 2023: Apply algebraic methods in solving problems.

 

Notice how each question part has no grade associated.

 

Notice how each question part has low to no partial credits.

The grades awarded for each question is then converted to a numerical grade for the question.

The numerical grade for each of the three questions are then added up to give the final judgement.

You might have noticed that there’s no numerical grade attached to each question part.

This is because each part is associated with their own grade – a, m or e – as seen in the answers.

 

If a student answers part ONE (a) correctly, or if they make a numerical slip, they’ll be awarded with an “a” in this part. If they make a CONCEPTUAL error though, they’ll not be awarded any grade (“n” for “not sufficient”).

 

Similarly, if a student answers part ONE (b)(i) correctly, they will be awarded with a “m” for this part.

Because this is slightly harder, students can get partial credits – but the partial credits here is only associated with a complete skill, such as partial factorisation, not just any attempt.

 

These pieces of evidence are then compiled at the end of the question to give a numerical mark representing the overall performance.

 

 

What are the implications for teachers?

Firstly, let’s look at the students sitting at either end of the spectrum.

 

At the top end we’re talking those aiming for As and A*s: in the numerical mark system, students could get an A or A* without being able to answer a question pitched at A/A*.

 

At the lower end it’s even more concerning. You don’t need to get that many marks for a C, so a student could still “pass” A-level without demonstrating sufficient evidence at every topic. For example, one could choose to ignore all trig equations in A-level and still able to come out with a C.

 

June 2022 Edexcel A-level maths grade boundaries for A* and C are in 70-75 and 31% per paper, respectively. Knowing that one only needs to get 31% of the marks to get a (decent) pass at A-level is honestly disappointing.

 

In the NZ system, students have to answer at least the excellence-level questions correct to get Excellence for the standard, and more importantly, they need to answer at least 5-6 achieved questions to pass. And each topic is tested separately; a Level 3 Calculus (comparable to AS) student will normally take 4-5 standards – Algebra and complex numbers, Conics, Differentiation, Integration and (sometimes) Linear programming. A pass in conics does NOT imply a pass in differentiation.

 

A perfectly appropriate argument here is the NZ does not allow opportunities for synoptic assessments. For those who are not familiar with the term, this means questions testing several topics, like the new GCSE questions. This is true, and I’ve noticed they tried to avoid mixing topics from different standards, but as teachers we can go beyond what’s expected.

 

Scholarship Calculus is an exciting course that covers a LOT of content – we’re saying the entire A-level, if not more – in a more manageable form than STEP or MAT or AEA. If you’re looking for some fun questions with your class, it is definitely a solid option.

Here's the Scholarship Calculus paper last year: Scholarship Calculus 2022.

Secondly, for classroom assessments: I think students shouldn’t get away with accumulating partial credits and call this a pass, as we’re not sure where the marks come from. A superb suggestion from Chris McGrane that I’ve heard on a podcast: his end-of-term tests are split up into sections and students must obtain a certain number of marks per section to pass. This is very similar to the days of National Assessment Bank in Scotland (wouldn’t be too surprised to know Chris’s school is influenced by this hehe, but I don’t want to put words into his mouth) – a student must pass unit tests for each of the three units to be allowed to take the external exams, each unit test has several sections and students must pass each section with an appropriate grade (around 70%).

 

So there you go, that’s my quick rundown of the grading systems I’m aware of that could be implemented in schools without undergoing a massive renovation. I hope this could make you revisit your school assessments and perhaps considering implementing any changes. Chris’s suggestion is a great starting point, but personally I’d still develop a list of skills that students have to be able to perform to completion to call it a pass.

 

If you have any comments please don’t hesitate to let me know!

 

Andrew