When people see the year 1984 most think of George Orwell’s book about a dystopian future, but a few other things happened that year. Dynasty and Dallas were the most popular TV programs and one of my favorite movies, Amadeus won best picture at the Oscars. You can be excused for missing the publication of what has become known as the two Sigma problem by Benjamin Bloom, of Blooms taxonomy fame. He provided the answer to a question that both teachers and students have been asking for some time – how can you significantly improve student performance?  

One of the reasons this is still being talked about nearly 40 years later is because Bloom demonstrated that most students have the potential to achieve mastery of a given topic. The implication is that it’s the teaching at fault rather than the students inherent lack of ability. It’s worth adding that this might equally apply to the method of learning, it’s not you but the way you’re studying.

The two-sigma problem
Two of Bloom’s doctoral students (J. Anania and A.J. Burke) compared how people learned in three different situations:

1. A conventional lecture with 30 students and one teacher. The students listened to the lectures and were periodically tested on the material.
2. Mastery learning – this was the conventional lecture with the same testing however students were given formative style feedback and guidance, effectively correcting misunderstandings before re-testing to find out the extent of the mastery.
3. Tutoring – this was the same as for mastery learning but with one teacher per student.

The results were significant and showed that mastery learning increased student performance by approximately one standard deviation/sigma, the equivalent of an increase in grading from a B to an A. However, if this was combined with one-to-one teaching, the performance improved by two standard deviations, the equivalent of moving from a C to an A. Interestingly the need to correct students work was relatively small.

Bloom then set up the challenge that became known as the two-sigma problem.

“Can researchers and teachers devise teaching/learning conditions that will enable the majority of students under group instruction to attain levels of achievement that can at present be reached only under good tutoring conditions?”

In other words, how can you do this in the “real world” at scale where it’s not possible to provide this type of formative feedback and one to one tuition because it would be too expensive.

Mastery learning – To answer this question you probably need to understand a little more about mastery learning. Firstly, content has to be broken down into small chunks, each with a specific learning outcome. The process is very similar to direct instruction that I have written about before. The next stage is important, learners have to demonstrate mastery of each chunk of content, normally by passing a test scoring around 80% before moving onto new material. If not, the student is given extra support, perhaps in the form of additional teaching or homework. Learners then continue the cycle of studying and testing until the mastery criteria are met.

Why does it work?
Bloom was of the opinion that the results were so strong because of the corrective feedback which was targeted at the very area the student didn’t understand. The one to one also helped because the teacher had time to explain in a different way and encourage the student to participate in their own learning which in turn helped with motivation. As you might imagine mastery is particularly effective in situations where one subject builds on another, for example, introduction to economics is followed by economics in business.

Of course, there are always problems, students may have mastered something to the desired level but forget what they have learned due to lack of use. It’s easy to set a test but relatively difficult to assess mastery, for example do you have sufficient coverage at the right level, is 80% the right cut score? And finally, how long should you allow someone to study in order to reach the mastery level and what happens in practice when time runs out and they don’t?

The Artificial Intelligence (AI) solution
When Bloom set the challenge, he was right, it was far too expensive to offer personalised tuition, however it is almost as if AI was invented to solve the problem. AI can offer an adaptive pathway tracking the student’s progression and harnessing what it gleans to serve up a learning experience designed specifically for the individual. Add to this instructionally designed online content that can be watched by the student at their own pace until mastery is achieved and you are getting close to what Bloom envisaged. However, although much of this is technically possible, questions remain. For example, was the improvement in performance the result of the ‘personal relationship’ between the teacher and student and the advise given or the clarity in explaining the topic. Can this really be replicated by a machine?

In the meantime, how does this help?
What Bloom identified was that in most situations it’s not the learner who is at fault but the method of learning or instruction. Be careful however, this cannot be used as an excuse for lack of effort, “its not my fault, it’s because the teacher isn’t doing it right”.

How to use Blooms principles.

• Change the instruction/content – if you are finding a particular topic difficult to understand, ask questions such as, do I need to look at this differently, maybe watching a video or studying from another book. Providing yourself with an alternative way of exploring the problem.
• Mastery of questions – at the end of most text books there are a number of different questions, don’t ignore them, test yourself and even if you get them wrong spend some time understanding why before moving on. You might also use the 80% rule, the point being you don’t need to get everything right

In conclusion – It’s interesting that in 1985 Bloom came up with a solution to a problem we are still struggling to implement. What we can say is that personalisation is now high on the agenda for many organisations because they recognise that one size does not fit all. Although AI provides a glimmer of hope, for now at least Blooms 2 Sigma problem remains unsolved.

Listen to Sal Khan on TED – Let’s teach for mastery, not test scores