This seems relevant: https://en.wikipedia.org/wiki/Bloom%27s_2_Sigma_Problem

I haven't read the paper myself and don't vouch for it, but I've heard two-sigma mentioned a lot.

The paper's here: http://web.mit.edu/5.95/readings/bloom-two-sigma.pdf

It's not relevant to my specific question, as the three groups in the test had student:teacher ratios of (1) 30:1, (2) 30:1, (3) between 1:1 and 3:1

I'm interested in variation between the students within group 3, not the difference between the three groups.

I think a mix of 1:1 tutoring and student collaboration is the best deal. No data, but when I worked in a primary school with high % of school meal children, the literacy rate was noticeably higher when there were more literacy specialists doing 1:1 tutoring. The sessions are often 5-10 minutes but occur daily. They also have classroom literacy where they get a chance to do lots of partner work.

I worked in a high school for 5 years teaching English as a foreign language. I was not a great teacher because being a teacher is really hard, but I learned a lot in those 5 years. I will let you in on a secret.

Education is not what the teacher does: it's what the student does. Most people think that the job of a teacher is to organise information and explain it to students to make it "easy to understand". This is just plain wrong. In fact, by doing so you cheat your students because you steal their opportunity to organise information and discover how to understand it.

1:1, 1:2, 1:20, or 1:40 doesn't actually matter from a perspective of teaching material. If we make the teacher the font of all information, then we also make the teacher the bottleneck of learning. I was teaching language and if you want native level fluency and proficiency, then you might need to spend up to native level time acquiring the language. In other words, to get to a 10 year old's ability, it might take you up to 10 years of nearly full time practice. Sorry, but I'm not going to teach you 58,400 hours (10 years, 16 hours a day) unless you have Bill Gates level money to spend.

So, you're going to spend something like 3 hours a week in my class, and only something like 30 of those weeks are going to be productive in a year (if I'm lucky). So that's a pidly 90 hours of instruction per year. I'm going to teach you practically nothing in that time.

This is what is wrong with education.

But getting back to 1:1 vs 1:40. In a 1 hour class, if I have 40 students I can spend just over a minute paying attention to each student. In other words, I'm going to present my pidly amount of information and hope like hell that you're going to do something useful with it -- because I do not have enough time to interact with even one person in the class. If you assume that 1 in 40 students have a behaviour problem (just 2.5%!) you will see that I will expect to be interrupted in every single one of my classes. So probably I won't even be able to present my pidly amount of information. Probably I will just babysit and the students who know how to study will do well, while the others do poorly.

As we reduce the ratio, I have more time to interact with the students. But it's really important to realise that if I waste that time trying to teach the material, I will do no good. So in fact, what I want to do is let the students study and then watch them so that I can can correct their behaviour. By doing that, they can become good students and succeed in studying.

How many students I can handle depends a lot on my class management skills and also on the students. Some students require no intervention. They just need a friendly, welcoming, and engaging environment in which to study. Some students need considerable attention. 1:1 might be amazing for some students, but even 1:10 or 1:20 could be amazing for others (depending on the teacher). Some students like to study alone, some like to study in pairs, some like to study in groups. You have to be flexible.

My first day with my new violin teacher, he asked me who my teacher was. I gave the normal answer, and he said 'Wrong! You are your own teacher. I am just here to help you teach yourself.' Have never forgotten those words.

We need teachers who will enable their students to learn for themselves. Only then can the teacher no longer be the bottleneck.

I'm making a low-cost multilingual audioplayer, that students can take home to get more exposure to a language. Programmable in JS. Just in case anyone is interested. https://photos.app.goo.gl/gLvng2La37aWIADE3

I feel good online classes fit this scenario. Often all the material required for the course is presented and allows students to work at their own pace. Homework/papers are due every week to allow teachers to understand if students are learning the material properly. If not, the teachers will spend time with those students via video conference and other means to sheppard their performance. Of course, I've taken several bad online courses too where the teachers simply do not interact with students hardly at all.

> So that's a pidly 90 hours of instruction per year. I'm going to teach you practically nothing in that time.

Well, there’s always not enough time to teach something properly :) I don’t think that teachers need to be so idealistic, just as long as they tick-box the curriculum (sadly exams do matter a lot) and plant plenty of seeds which, we hope, would set root soon if not later in their lives.

By that I mean spending significant classroom time on interaction and the “fun stuff”. For example if it’s ESL and the students are into pop music, okay let’s decipher some Beyoncé or let’s try and mimic some funky singer’s accent. Do some immersive stuff, make it real. I’m a big fan of flipped classrooms, where students study most of the formal stuff for homework - this will also help them construct the knowledge in their own way - and then present it in class and have more meaningful discussions.

But I would say that if the students are beginners, then yes you do need to organise information to make it as easy as possible. The initial learning curve is always the hardest! When they become more comfortable and confident, they can always go back and revise their mental models.

Edit: Sorry, I didn’t take into account that you might be a private tutor. If you were, then I can absolutely relate to the frustration! Parents’ (totally unrealistic) expectations also do not help at all

I agree that:

- For language learning, total study time should be a multiple of classroom time. (From personal experience, I've found 10:3 to work pretty well.)

- Teaching can be very effective in groups of 1:10 or 1:20

- Classroom time should not be spent on introducing new material

However:

- For language learning in particular, I don't believe that 'let the students study and then watch them...' approach is best. If you're doing 1:1 or 1:2, you can actively manage the learning process by asking the student questions in the target language, and (for example) making them reply using newly-acquired grammatical structures.

- You've made the point that teacher:student ratio isn't the only important factor (agreed!) but haven't made a strong case that it's insignificant, or addressed my question about whether 1:1 is better (assuming money no object) than all other ratios.

As an ESL teacher myself I sympathize with you. For real, it's frustrating how people [more like parents] just expect to send their kid to a private academy after school [more like 3-4 academies] 2x/3x a week and just expect them to know English. Even if the kids are actually interested, that's a paltry amount of time actually spent practicing English. Very few people understand this so private academies continue to be a big industry.

This is really insightful. Thanks.

> I'd be interested to see some data to support or refute this.

https://www.amazon.com/Equality-Achievement-Introduction-Soc...

Interesting as a dyslexic I was lucky enough to have a 1:1 tutor provided as well as a typewriter for some of my junior school years (late 60's in UK)

This was well before dyslexia was a mainstream issue in schools - needles to say this did not go down well with the headmaster

You are correct that course sizes matter to educational outcomes for a variety of reasons. If the groups are too small, it is possible that nobody has enough of what is needed for the class and everybody flounders, requiring intensive instructor led tutoring and learning. This brings us back to the 1:1 situation.

If we are interested in how many students are required to support peer to peer learning, you might enjoy the following articles (popular and academic) about how Harvard physics professor, Dr. Eric Mazur has embraced and studied peer-to-peer instruction. This should provide a partial answer to your questions.

1) Eric's Harvard Profile https://www.physics.harvard.edu/people/facpages/mazur) 2) A good story/video about the development of his peer-to-peer, active learning methods (https://www.youtube.com/watch?v=WwslBPj8GgI). 3) One of Harvard's articles about his educational work. (https://www.harvardmagazine.com/2012/03/twilight-of-the-lect... 4) A list of Dr. Mazur's publications (https://academictree.org/physics/publications.php?pid=66072) 5) Eric's 2015 papers on peer learning a) 2015 - Dowd JE, Araujo I, Mazur E. Making sense of confusion: Relating performance, confidence, and self-efficacy to expressions of confusion in an introductory physics class. Physical Review Special Topics - Physics Education Research. 11. DOI: 10.1103/PhysRevSTPER.11.010107

b) 2015 - Miller K, Schell J, Ho A, Lukoff B, Mazur E. Response switching and self-efficacy in Peer Instruction classrooms Physical Review Special Topics - Physics Education Research. 11. DOI: 10.1103/PhysRevSTPER.11.010104

Googling for "ideal group size for peer to peer learning physics" brings up articles from Vanderbilt University and those mention groups of 2-4 or 5-7.

As there are many different models of peer learning, this article does a nice job of discussing practice and the theory behind peer to peer instruction (https://www.ncbi.nlm.nih.gov/pubmed/29128431)

My personal beliefs and experience is that people tend to like groups of 6 or fewer and the groups which speak the most among themselves range from 2-5 people. The limitations are that at least 1 person in the group must be advanced enough to help the others learn.

Last, if we look at apprenticeship models of learning, we are back to the 1:1 ratio (expert : learner). However, any single student can also have multiple 1:1 "teachers" and apprenticeships/internships usually include a peer group which engages after the 1:1 instruction. We see this in music and sports with individual sessions with a variety of experts followed by group work or performances with varied sized groups.

I hope you enjoy!

Thanks for these links. They are exactly the types of things I had hoped someone would post! And they'll be helpful to me as a newish parent.

I don’t know whether there has been large-scale empirical testing of this, but anecdotally it sounds plausible. I can typically have a deeper and more efficient knowledge-sharing conversation about some technical topic 1:1 than 1:4 (e.g. in a professional context).

In a 1:1 interaction, it is possible to efficiently figure out where the two interlocutors’ common premises are, and then explain concepts in whatever amount of detail is necessary for understanding, skipping over any parts that are known, with frequent checks that the other party is following along (not just pretending, and not suffering some misconception).

In a 5-way interaction, it is typical for each participant to be coming from slightly different background / preparation, and have difficulty with different parts of the new material, which makes it necessary to take time for (sometimes extended) digressions to fill in whatever details are missing for anyone. It’s easy to accidentally not notice that 1 or more participants is missing crucial background, because it is time consuming to verify that each separate participant has a solid understanding of every idea. A problem that is too hard for one student will be too easy for another.

Things might be better if you had the same 4 students to 1 tutor for, say, 3–4 years at a stretch. Then you could assume a lot of shared history, and amortize digressions to fill knowledge gaps for particular students. Better hope the students learn at a similar pace.

When actively trying to solve a set of problems, with the students working independently with minimal guidance/help from an instructor, and if the only goal is problem-solving efficiency, then having more people is helpful, because different students will have trouble with one problem or another, and they can then confer and fill in the other answers at the end. Often the weaker students don’t fully understand everything to the extent they could solve a similar problem independently, but that’s often an acceptable standard. [Same story if you are trying to build some work project with many parts, etc.]

But if the goal is to get everyone to understand every answer deeply and accurately, then in a 1:1 tutorial setting the expert tutor can ask leading questions, give appropriate hints, or just outright explain the answer if the problem gets to be too big a time suck. And the student can get more direct personal experience with trying to solve all of the problems with a fast feedback loop and without getting bogged down, and hopefully feel like they personally figured out most of the main breakthroughs.

One issue is that often tutors (probably more than other types of teachers) are amateurs rather than experts in the subject or in teaching. For instance the tutor might be a slightly older student, a family member, a retired person volunteering, or the like. In that case 1:1 tutorial is still helpful vs. the student working alone, but obviously pales in comparison to highly skilled tutoring.