1. Bloom's 2 sigma problem

We're going to start off with a bit of stats. Brace for impact:

A picture is worth a thousand words. So, I drew one for you:

Let's say you have a perfectly normal classroom full of perfectly normal students - butts in chairs. And you have a perfectly normal teacher doing perfectly normal information-transfer type teaching.

You'll have a bunch of learners who are capable of moving at different paces. Some learners will be capable of moving quickly through the coursework, and some will not be. This can be for a variety of reasons, not just because of differences in aptitude.

Now, if the course difficulty and pace was tuned so that it perfectly matched the capabilities of the average student, then half the learners would pass the course and half the learners would fail.

What bloom's 2 sigma problem says is that if you teach the same content to the same people and change the delivery mechanism to one-on-one tutoring, using mastery-based techniques then the pass rate will be more like this:

So we can change the success rate of learners dramatically by changing the delivery mechanism of the course. This does not mean lowering the standards of the course and giving everyone a participation award. This means maintaining quality and changing how instruction is given.

What dark magic is this?

This seems magical. How does it work?

There are 2 things Bloom refers to:

• Mastery-based learning techniques
• one-on-one tutoring

I'll dig into both of these next.

Mastery-based learning

If you have been following me for a while, you'll know that Mastery-based learning (MBL) makes my heart go boom.

The TLDR goes a little something like this:

1. Learners learn a thing
2. Learners get assessed on that thing
3. If a learner fails the thing-assessment then they get support on that thing until they nail it
4. If a learner passes the thing-assessment, they move on to the next thing

So this means that if a learner is able to move quickly through a syllabus, they can just do that, and if learners need more support, they are not forced to move forward before they are ready to do so.

Now, we know that skills build on top of other skills.

Let's say, for example, that a learner is tasked with writing a recursive function that scans through a directory hierarchy in order to find pictures of adorable kittens.

In order to get that task right the learner would need to know about kittens. And also recursion, and the filesystem. To understand recursion they would need to understand functions and arguments, therefore variables. It would also be useful to know about loops.

To access the filesystem they would need to know about how to import the right functionality.

They would also need to know about if statements...

It goes on and on...

Now, let's say you have a learner who is struggling to keep up in a cohort-paced course. Let's call her Alice.

If you start by teaching the whole class about loops and then move on to functions before Alice has mastered loops, then move on to importing code before Alice has mastered functions, and so on, then Alice will not master very much at all.

Now, think about how Alice might feel - feelings matter a lot in education.

If you followed a mastery-based structure instead, then Alice would have the chance to master some things. She might still struggle, but she will have the opportunity to stay on task and overcome those struggles. Even if she did not manage to get through everything, she would still have mastered something.

One on one tutoring

The other thing that Bloom's 2 sigma problem refers to is one-on-one tutoring. Of course, this is prohibitively expensive to pull off in many situations. But it is still worth looking at.

In a one-on-one tutoring situation:

• the learner is engaged at all times
• the educator is able to pay close attention to the learner and is able to adapt to what the learner needs
• there is more social pressure for the learner to do their part, they cannot hide in the crowd

But it's hard!

One-to-one tutoring using mastery learning techniques is hard to implement. It's expensive and operationally challenging.

Bloom and others did some work to figure out if there are other ways to get a class of students to perform well. There are other ways. But nothing is quite as effective as meeting the learner where they are and giving them your full attention.

The real trick is in figuring out how to layer different types of teaching interventions, this will be the subject of a future post.

Want to know more?

Give this a read if you are interested in the finer details:

The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring (original paper)