How Bloom’s Two Sigma Problem Applies to Learning English--and Teaching It.

Published on
September 1, 2020
Updated on
April 24, 2023
min read
This article may contain affiliate links
Written by
Ramsay Lewis

Bloom found that one-on-one tutoring leads to significantly better learning than traditional teaching methods. Here’s what that means for learning English.

How Bloom’s Two Sigma Problem Applies to Learning English--and Teaching It.
Table of contents

If you've taken one-on-one private lessons at some point of your life, you may have noticed that they were much more effective than a typical classroom for learning. 

Research has consistently found that one-on-one (1:1) tutoring is a more effective teaching method than traditional classrooms. This revolutionary discovery was made in the early 1980s by renowned educational psychologist Benjamin Bloom, who examined teaching and learning techniques and found a way to considerably improve student performance. 

It has now been named Bloom's two sigma problem and it has important implications for learning English.

What is the two sigma problem?

In 1984, Benjamin Bloom authored his seminal article The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring.

In the article, Bloom used a series of experiments to demonstrate that one-on-one tutoring that included regular testing and constant feedback greatly improved students’ performance compared to students in a regular classroom. The difference in performance was two standard deviations (in statistics, “standard deviation” is represented by the Greek letter “sigma”, which is where the name “two sigma problem” comes from). 

Standard deviation, if you can remember your maths class, tells us about the spread of scores… how different they tend to be from the average. A high standard deviation means that there is a wide range of numbers, a low standard deviation means there is a small range.

Two standard deviations is a massive improvement; it’s like the difference between a “C” and an “A” on an assignment. 

Bloom’s studies showed that most of the poor performance of students in a conventional classroom comes from the teaching method and not to a lack of their knowledge or skills. This finding was important because it suggests all students have the potential to achieve mastery of a subject—as long as they have the right teaching method.

So what is the “problem”?

The reason the “two sigma problem” is a “problem” is because Bloom knew that, although it is the ideal teaching model, individual or small group tutoring is not scalable.

An education model in which a single student is taught by a single tutor is incredibly expensive, and requires one teacher for every student.  It is not practical for most education systems to have 1:1 tutoring for everyone. 

So what other approaches could create the same kinds of benefits that Bloom saw with 1:1 tuition in larger classes? Is it possible to create a system with one teacher for several students that is as efficient as one teacher for one student?

The search for this new approach that could be as effective as 1:1 tutoring, but could be scalable, became known as the two sigma problem. 

What is mastery learning?

One of the problems with traditional teaching methods is that sometimes the class moves on before you’ve finished learning the current material. You might have experienced this: a feeling of frustration when, even without understanding a math concept, the teacher had already moved on to the next one. This is a common problem with English classes.

Mastery learning was proposed by Bloom in 1968. It refers to a type of learning where a student must master a topic (achieving at least 90% on a knowledge test) before moving on to learn subsequent information. 

This means that the learner needs to study the topic until he or she has complete mastery of it, even if it means taking more time on that topic than the other learners. This type of learning recognises that students learn at different speeds. This “mastery learning” model is quite different from the traditional methods observed in schools, where a certain amount of time is spent on a subject, regardless of whether all students in a class master it or not.

Bloom found that mastery learning is more effective than traditional teaching methods - specifically, it led to an improvement in performance of one standard deviation over conventional teaching. However, he found that it still wasn’t as effective as 1:1 tutoring.  

Why is 1:1 tutoring so effective? 

Why does the average student taught under the 1:1 tuition model achieve better outcomes than 98% of students in a traditional classroom? 

Bloom suggested that the best explanation for the success of students who had a private tutor came from the constant feedback they got, as well as the application of mastery learning. 

Bloom argued that, while traditional students don’t get much feedback in a common classroom environment, 1:1 tuition offers a more frequent corrective process. This means they have more opportunity to improve on their weaknesses than traditional students. As a result, every part of the material can be reviewed and re-learned until the student masters that particular subject. 

How does Bloom’s two sigma problem apply to learning English?

When we think about how we study English Bloom’s two sigma problem may tell us why we feel that we are not making any progress when studying English in a classroom. Perhaps we’re lacking appropriate feedback or the content is moving too quickly.

What can you do? 

Well, one option is to hire a tutor. But that can be expensive. For those of us learning English on our own without a tutor, what can we do to ensure our learning is effective? 

Here are some steps to take to build your English learning programme in such a way that you build in the benefits of 1:1 tutoring.

1. Be clear on your goals

The first thing I do when I tutor a new client is find out what their goals are. Then I build a programme aimed at achieving those goals. 

Do you want to become fluent in English, like Daniel? Do you just want to be able to converse easily when you visit your family in Australia? Are you looking to write academic papers in English? Do you want to be able to teach English, like Kristian? Do you want to participate in English conferences in your field, like Coté?

Define your goals clearly. Then, break down your goals into components, and figure out how you can complete them. Being clear on what you’re trying to achieve will allow you to adapt your learning and focus your study appropriately.

2. Take a test

Take an online test to find out your English level. In my experience, many learners of English actually underestimate their ability. Then they choose activities that are too easy for them. 

Find activities that are right for your level. They should challenge you, but not too much. Like a good 1:1 tutor, adapt your materials as you progress. 

3. Choose activities that you like

A good 1:1 tutor will work with the interests of their client. You should do the same with your own choice of activities. 

Find activities that you like

By incorporating your passions and interests into your English learning programme, you’ll make it much easier to stick with it over the long term. Choosing boring activities is one of the most common mistakes English learners make

4. Choose activities for each skill

A good English tutor builds all four skills into your class: listening, speaking, writing, and reading. You should do the same, even if you’re a beginner. 

Need some help? Here’s some guidance on activities to choose. 

5. Aim for mastery

Try to build in mastery learning. This is especially relevant if you’re doing grammar drills, vocabulary exercises, or something very specific. That means don't move on to the next topic until you have mastered the previous topic. You don’t need to master 100% of every little aspect of the English language... but try to get to a point where you are very comfortable before moving on.

Again, this is really just for very specific activities. It’s okay to listen to a podcast and not understand everything. 

It’s the same with reading, you don’t need to know every word. But if you’re trying to master the past perfect tense, say, don’t move on to another tense until you feel comfortable with it. 

… and how will you measure that?

6. Test yourself 

Part of what is so useful about 1:1 tutoring is that your tutor will constantly adapt the material to your level. In order to do this for yourself, you’re going to need to continuously assess your learning. 

So make regular testing part of your process. When you study a new concept or grammar structure, look for tests and exercises online to test yourself. That way, you can see if you really learned what you studied—and if you mastered it. Try to measure your progress

7. Find a conversation partner

Part of the benefit of a 1:1 tutoring session is the opportunity to practise speaking. In a 1:1 setting, your partner can adapt their speech so that you understand it and can correct your mistakes.

While an English tutor is trained to do this, you can get a lot of the same benefits from simply having a conversation with a native speaker.

8. Ask for help

When questions start popping into your head, ask someone. Look around and make use of your resources—your teacher (if you have one), your friends, and the internet. There are tonnes of online forums and people from all over the world who are struggling with the same things as you.

If you’re a member of Leonardo English, you can even bring your questions to our monthly Q&A, or email us anytime. We’d be happy to help you out!

How Leonardo English can help

Bloom's two sigma problem makes it clear that each student learns at their own pace. The best education is one that adapts to that student’s learning.

So how can Leonardo English help?

Our podcasts are easily adaptable to your level

Research on podcasting pedagogy suggests that podcasts can significantly help learners develop several English language skills—not just listening. For example, this research review found that podcasts don’t just improve listening skills, but also speaking fluency, grammar, pronunciation, and vocabulary.

The English Learning for Curious Minds podcast allows you to study English through varied subjects in your own time and at your own pace. You can listen to the episodes as many times as you like, and members can use the transcripts and key vocabulary as a learning resource to help follow along with the audio. You can even slow them down or speed them up according to your level.

Last thoughts: My advice as a teacher

Bloom's two sigma problem helps us understand what teaching methods lead to the best learning outcomes. The most effective methods are those that are adapted to the level of the student and that provide feedback.

You can build these into your own language learning programme by following the steps above. Think about your goals, find your level, and then adapt your activities. Build in a variety of activities that you enjoy. Work at mastering grammar, little by little. Test yourself, and adapt your activities regularly. Speak. And ask for help when you need to.

If you do those things consistently, over time, you’ll get closer to fluency. Who knows, one day you might even be an English tutor. 

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