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Early on in my teaching career I grew frustrated with the deciding the exact grade boundaries for internal exams. So I created two tools.

IGCSE Calculator

IB Calculator

## The issue

British schools subscribe to externally provided exams. In my case the IB and the Cambridge IGCSE. Every year these boundaries are normalised based on the performance of the students of that year.

Rarely do we give a full past test papers. That would require the students to know the full course and creatively carving out the full 90 or more minutes allotted on a time table made of 55 minute lessons. So when assessing the students grade we are unable to use the exact grade boundaries associated with the exact paper.

Typically teachers would craft a paper by combining questions from different years and scale the number of marks to match the time available.

I was told to base the grade boundaries based on past test boundaries. Due to different timezone international papers have several version of the same paper and the boundaries between these papers can vary by more than 10% of the marks. In the example below an “A” could be 43, 51 or 49 marks. This variance exists across years as well.

If you have 3 A/B borderline students with and 47,48 & 49 marks, how do you decide what is the fair hard boundary. Since questions were drawn from several papers I could not use only one set of boundaries for my own purposes. Taking a simple mean would also be unfair since it would be set too high or too low 50% of the time.

I did not like arbitrarily deciding who gets to be above or below the borderline, so I set out to make a tool to resolve the following problem. How can I make judgements on a student’s grade that respects their efforts but does not give them a false sense of security?

The issues I was trying to solve now before the solution.

• Subject are tested by 3 separate exams. So we needed a way to assess the overall score of the the three papers which each have their own weightings. Paper 1 may normally be 20% of the overall mark and 30% of the exam time, however, a dictat may have been made where I had to now grant Paper 1 40% of the exam time. This will skew all 3 papers’ contribution to the total mark.
• It became far too easy to be swayed by favouritism and “this person DESERVES an A”
• Students have access to the past exam papers so it is far too easy for student to encounter some of the questions during revision. In fact I explicitly include at least 1 question that was covered extensively in class to encourage students to study the materials and homework in the hopes of an assured 100% on 1 question.
• The topic covered is narrow and was covered very recently compared to the final exam which can occur 18 months after it was covered in class.

## The hack

Of course the tool would not be perfect So I decided to alter my goals. I decided to set the boundaries higher than the historical average by 1.25 standard deviations. That would mean that for each numerical mark, 90% of the time, a student who got that mark would get at least the grade I set. This has the effect of pushing borderlines student below the threshold thereby undoing over confidence. This 90% threshold seems rather high but it is countered by the fact that students have access to the bank of questions from which the exam problems are drawn and are being immediately assessed on a narrow slice of the syllabus. Luckily the effect of this raised boundary affect the higher grade more than the lower grades and thus does not unduly punish less able students.

This is a hack. Grade boundaries are not actually normally distributed. Due to small sample size if the number calculated is higher than the historical highest it will take the historical highest. It also assumes that the teacher has selected question of a range of difficulties that are distributed similarly to the real paper

For combined tests, these thresholds are then converted to percentages and scaled to the marks per minutes for each individual paper and recombined with paper weightings. Simply put the total marks in the white box and you will have a set do grade boundaries for the individual papers and the exam season. Sadly as you can see in the image below it become nonsensical if the paper is scaled too much. Paper 6 normally has 40 marks.

I have used this to inform my judgements rather than an absolute system but at the end I felt more comfortable making the decisions of who should lose out when a single mark could be the difference between pass or fail.