Criterion-referenced assessment, anytime, anywhere
A discussion on Twitter recently made me nostalgic for Graduated Assessment.
Graduated Assessment was the last large-scale attempt at an assessment structure suitable for mastery learning in the UK. Rather than a Higher and Foundation GCSE paper, pupils could sit papers at different levels, securing the grade, then move on to study the next level.
This is exactly what mastery learning requires.
I would love to see the UK exam system include an offering for those of us who wish to implement a mastery approach to learning. So, here’s a short description of what I think we should do…
Firstly, we must define the whole of school level mathematics as a series of increasingly complex maturation stages. This is entirely possible to do when we think of mathematics as interconnected webs of ideas that mature over time to form a complete schema of knowledge.
For each stage, design an exam consisting of questions that require a pupil to work with the stage ideas in their full range of complexities. The exam can only be passed by demonstrating elite performance. A typical mastery threshold of 80-90% must be achieved to secure a pass.
Allow pupils to take a stage examination at any time in the calendar year. A pupil must secure a pass on a stage before being permitted to take the next stage. There are no limits on how many times a pupil may sit the examination.
There are good examples of mastery assessment systems already in use, such as securing a grade in piano or learning how to drive.
If an individual does not pass their grade 5 piano, we do not assume that they have hit their limit and must always remain grade 4. We know with additional practice and focus, they’ll be able to pass at some point.
Imagine if we said to an adult who failed to pass their driving test, ‘I’m sorry, you’re just not a driver.’ This is clearly ridiculous. Instead, we recognise anyone can learn to drive given the right amount of practice. When they feel ready again, they take a new test.
Being able to take the mathematics stage examinations at any time of their choosing, pupils can focus determinedly on learning and practising the necessary knowledge and skills for the stage at hand and then choose to enter the exam when the time is right.
Requiring the passing of one stage to unlock the next, means pupils are always attending to mathematics on the horizon of their comfort zone. The mastery threshold to pass an examination at one stage means new learning is always based on firm foundations.
The examinations can be taken at any age. This means pupils can collect a portfolio of evidence of their achievements across their time at school rather than the cliff edge, high stakes school leaver exams they currently face.
By collecting the grades throughout their childhood – just like the child ascending in their piano grades – the pupil is engaged in an honest conversation about the impact of their own effort. This is motivating and gives a much higher chance of success.
This would remove the far too common situation of 15-year-olds suddenly realising they haven’t learnt enough & can’t get a grade they need. Too many pupils leave school mathematically illiterate because the curriculum moves on like a conveyor belt whether or not they grip ideas.
Mathematics can be treated in this way. We can take a proper mastery learning approach. It really is a process of maturation. There is no right or wrong answer to how many stages there should be, but I think 15-20 would be about right.
I'm aware many will throw up their arms and cry this would be an administrative nightmare. They are wrong. Yes, there are complexities to implementing such a system, but just because a thing is difficult does not mean we should not do it.