Geoff Petty - Mastery is no mystery

Geoff Petty demonstrates he’s a master of mastery, although it’s possibly not the first time he’s encountered it. Geoff is the author of Teaching Today and Evidence-Based Teaching.

Have you noticed that ‘mastery learning’ is back in fashion? You know you’re old when it comes back for a third time. A recent study found that Singapore-style maths mastery boosted pupils’ progress in the UK. It’s thought it helped Singapore become the world’s No 1 in maths education. But that’s not all.

A review of research on the best revision techniques by Dunlosky et al. has found that self-testing in a mastery way is perhaps the best revision method.


What is mastery learning?

Mastery goes back to Aristotle and it’s an embarrassingly obvious idea, but when you’re spinning all the other plates, it’s easy to drop this one. The basic idea is that every student can learn the important basics of a topic given enough practice.

So we need to diagnose the basics that students know, and don’t know, and then ensure they plug the gaps you’ve found. These improvements are done in the students’ own time and are checked with another test.

Mastery only works for discrete basic facts and simple skills (e.g. learning low on Bloom’s taxonomy.) The driving test is an example of mastery learning.


There are five stages in mastery learning:

  1. You define precisely what students must know and be able to do. Only essential learning low on Bloom’s taxonomy is considered, for example, the ability to explain the meaning of new technical terms and to complete simple routine tasks or calculations (reproductive learning). For example, you could give students a ‘must know’ list for each topic.
  2. You teach a topic, say, five hours of tuition, give plenty of learning activities, including corrected practice of the learning in ‘1’ above. Tell your students to prepare for a ‘must know’ test on this topic, ask if they are ready.
  3. When they’re ready, give them your test, which is very short, three to five minutes long, on the basics in ‘1’, above. The students mark the test themselves from a mark scheme with either model answers, or worked solutions provided by you. The good news for the students is that the questions are easy and predictably based on vital material they were given in advance, and the learning has already been practised. The bad news is that the pass mark is very high for this material, at 80 or 85%.
  4. The students who did not pass do a retest. First, they look at what they got wrong and work on this for a day or two in their own time, perhaps with a helpmate preparing for a retest, also done in their own time. They keep doing remedial work followed by retests until they get a pass. The retests are very similar but not the same as the original test. If the topic splits neatly into subtopics, then the student only retakes the subtopic they did not pass. The teacher does not wait for completion of this remedial work, they teach the next topic.
  5. Students get a ‘P’ for a pass, but their percentage is not recorded. If they do not pass then the space in your mark book is left blank until they do pass. Students enjoy the confirmation of passing their tests so much that, even though they retake tests in their own time, they usually don’t cheat. Most teachers make their mastery tests far too hard at first. The purpose is not to stretch students but to check they know the very basics. When I first used mastery tests I thought the tests were so easy that the students would laugh. Yet to my surprise, quite a few did not pass (the others were cock-a-hoop!).

I remember one student saying ‘I thought I knew that until I tried to write it down’. So, teach students to prepare for mastery tests with the study-cover-recall-check-repeat approach described in my earlier piece ‘Help! They forget faster than I teach’. As I continued with mastery learning their revision improved.

The educational researcher and theorist John Biggs thought there was a danger that mastery learning might encourage learning without understanding. Arguably this could be overcome if other tasks and assessments require a deeper approach. It might help if your ‘must know’ questions include ‘why’, and not just ‘what’ questions.


Making mastery fun

There is a game students can play that is less rigorous than mastery testing, but much more fun. This version is for level 2 learners, but it can easily be adapted for more advanced learners. The first step is that you (or your students) create cards, each with a ‘must know’ question and its answer. Students work in pairs, preferably with question cards on every subtopic.

Alternatively, card-sets on subtopics can move from group to group. In their pairs, they take it in turns to ask each other a question. If the other student gets it right, they move their counter up one square on a game board with a mountain drawn on it. Ensure that there are at least as many question cards as there are squares to the top of the mountain – or they won’t get to the top!

If a student does not get their question right, they keep their ‘wrong card’ and can study the correct answer during the game. One square before the summit of the mountain is a ‘base camp’ where students must pass their ‘wrong cards’ over and make a second attempt at answering correctly.

The object of the game is not to race to the summit first, but for the team of two ‘climbers’ to both get to the top of the mountain. Another option is to ask students to create the cards. Appoint teams and give each team a subtopic from the past few weeks of teaching.

For their subtopic, each team writes three or four simple questions (low on Bloom’s taxonomy) with answers. You check these questions and answers, making sure they are on vital material, are very simple questions and have good answers. The questions and answers can be typed into a table. You can then print sets on thin card with a different colour for each sub-topic if necessary and cut them into question cards. Make sure you, or they, print off enough sets.

Don’t worry, this game is twice as much fun as it sounds yet it has a very serious purpose – checking and correcting students’ learning of vital material. Mastery games can be used to prepare for mastery tests. It would be great if some technological wizard could make an electronic version of this game which teachers could download.


Mastery marking with peers

This method can sometimes be used on a summative assignment, or for coursework in draft form.

  1. Students complete an exercise, quiz or test.
  2. Students’ work is marked by you (though you could use self or peer assessment instead).
  3. Students correct or redo any question they got wrong working in groups or in pairs.
  4. Students explain the right answer, to any question they got wrong, to another student, not the one(s) they worked with in 3, above.

This strategy, like most teaching strategies, can be overused. Students may find it too dispiriting if you ask them to correct all their work, and they may well not be able to keep up!

However, the method can also be underused. Students sometimes need to have another go at something if they are really to understand how to do it properly. If groups are supportive this can be greatly enjoyed.


Mastery marking by teacher

This is the same as above – you ask students to redo parts of their work that are not up to scratch, for example:

  • Re-do questions 1 and 2.
  • Rewrite any paragraphs I’ve starred, adding evidence to justify your views.


Marking key

This method is commonly used by teachers of languages. The teacher marks written work by writing codes in the margin to show that an error has been made on that line somewhere. However the exact point where the error occurred is not shown.

A typical code might be:

  • S for a spelling mistake
  • T for a mistake with tenses
  • SVA for a subject verb agreement issue
  • P for a punctuation error

The student looks at the marking and then corrects their work using the code. Why is the student not told the details of their error and where it took place? Because the teacher hopes to develop in the student an understanding of what they did wrong, and this is best achieved by making the student hunt carefully for their error and think about what they have written. This will develop the ability to proof-read errors. Could you adapt this approach?