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I refer only to academic PhDs, not doctorates in education. Many swanky fee-paying schools in England and the US hire PhDs as teachers. So what qualities are likely unique to PhDs and may not be mastered (pun intended) by teachers whose highest degree is a Masters?

Charterhouse's PhDs in math include:

Dr Graham Kemp, MSc, MMath, PhD
Dr Philip Langman, PhD
Dr Stephen Marshall, MMath, DPhil

Phillips Exeter Academy:

Zuming Feng, "Ph.D. from Johns Hopkins University with an emphasis on algebraic number theory and elliptic curves."
Panama C. Geer, M.S., Ph.D.
Filip Djordjije Sain, PhD Applied Math

St Paul's Girls' School (in London):

Damon Vosper Singleton (Head of Department) — MMath (Oxon), PhD (London)
Pip Bennett BSc, MA (Durham), PhD (Bristol)
Alexandra Randolph MMath (Oxon), PhD (Nottingham), MIMA

Tonbridge:

Head of Department
Dr Ian Jackson

MA (Hons) Mathematics : Trinity Hall, Cambridge
MMath : University of Cambridge
PhD (Radial Basis Function Methods for Multivariable Approximation) : University of Cambridge

Dr Jeremy King MA (Hons) Mathematics : St. John's College, Cambridge
PhD (Finite presentability of Lie algebras and pro- groups) : University of Cambridge

Dr Zi Wang MA (Hons) Mathematics and Statistics: Christ Church, Oxford
MMATH: Christ Church, Oxford
PhD (Sparse multivariate models for pattern detection in high-dimensional biological data): Imperial College London

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    Prestige, of course. If you want parents to spring up the moolah, then you need a little flash.
    – user9646
    Feb 20, 2018 at 9:04
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    Well, as someone who taught 3 years at such a school after getting my Ph.D. in math (in the U.S., a math/science academy; but public, not private), the answer is simply because they can. But the Ph.D. is by no means a free ticket, and from my experience in job searches for such positions, a much higher percentage of Ph.D. applicants than Masters applicants do not make it very far in the application process due to a lack of evidence offered in their applications for how/why they would be successful in teaching adolescents in a high-pressure environment. Feb 20, 2018 at 12:31
  • @NajibIdrissi Thanks. I agree. But any other substantive reasons?
    – user13306
    Feb 20, 2018 at 17:26
  • @NNOXApps PhDs are usually forced to teach or teach-assistant multiple courses. Many PhDs also teach the college summer school (where many high school students also participate). So PhD usually has more teaching experience than MS. Moreover, the high schools uses the number of PhD holders to convince the parents to pay.
    – High GPA
    Apr 24, 2021 at 4:23
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    To add to the comment about prestige, it's worth pointing out that not only do the letters "PhD" look impressive, but it also gives these schools the opportunity to put "University of Cambridge", "Oxford"/"Oxon", "Durham", "Imperial College London" and so on in these teachers' bios. Rich parents want their kids to go to these universities, so they will prefer schools where the teachers themselves qualified at those universities (and by implication, have experience with the admissions process).
    – kaya3
    May 1 at 4:10

6 Answers 6

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Having studied in one of these schools and been taught by two of the teachers mentioned, I would say the benefits are:

  • Having better understanding of the subject as a whole and ability to answer deeper questions, as well as how different parts connect and fit together during lessons. Some of the topics covered in more advanced modules (e.g. M4, S4, FP3 in Maths) are pretty complex and students ask questions even beyond that. "Not on the curriculum" would have been a disappointing answer, especially when the parents a paying £40k+/year for tuition.
  • Ability to answer questions of what the academic track looks like beyond BA/MA. In the hindsight, probably not very relevant at school level, but can still be beneficial when discussing future prospects with students.
  • Finally, probably most importantly: having real interest and passion for the subject. Comparing teaching from people with BA/MA and PhDs, I would say that I definitely prefer the latter. This applies both in the classroom and in the after school activities. Again, when you are paying money for school, you would prefer that there is a club/society for each subject where non-standard topics can be explored by your kids. Such activities are usually much more interesting when people organising it also enjoy it. Most people in the academia tell me that you should do a PhD because you like the subject, not just for career benefit. So while you don't need to do a PhD if you like the subject, many people choose to do so.

EDIT: Forgot to mention other non-syllabus activities such as IMO or STEP exam for Oxbridge (as mentioned by @kaya3). These are very hard and there is probably a large overlap between people who can help prepare for them and people who have done a PhD.

EDIT2: M4, S4, FP3 are (or used to be) most-advanced modules in UK syllabus for A-Level Maths (16-18 y/o) - for Mechanics, Statistics and Further Pure respectively. (As requested in comments, based on @kaya3's answer).

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    What are M4, S4, and MP3? May 1 at 1:11
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    @AzorAhai-him- In the UK syllabus for A Level mathematics (taken at ages 16-18), these are some of the most advanced modules ─ Mechanics 4, Statistics 4, and Further Pure 3. When I was in sixth form, the school brought in a PhD student from a nearby university to teach me FP3 among other modules.
    – kaya3
    May 1 at 3:59
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    To add to this, many teachers also wouldn't be confident helping their students study for STEP exams (additional entrance exams to study mathematics at Oxford and Cambridge) ─ mine directly told me, that if I had any queries about STEP practice questions then I shouldn't ask her because she wouldn't be able to help. The same would apply for helping students prepare for interview questions at those universities.
    – kaya3
    May 1 at 4:04
  • Can you please edit in you answer to AzorAhi'him's question into your answer? Comments can be ephemeral on this site. (Nice answer BTW and welcome to the site). May 1 at 12:00
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    Do recall most people aren’t British mathematicians. May 1 at 14:03
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While the PhD is explicitly geared toward research and secondary education is not, many people earn a doctorate for the explicit reason of becoming teachers, not researchers. That was my own driving force, though I had/have an intense interest in mathematics for its own sake, teaching was what drove me to earn a doctorate.

But, getting a doctorate in some field also gives you (or should) a lot of insight in to how that field works and how ideas fit together. That insight is hard to convey, but it is an important part of anyone's development, even, or maybe especially, for young learners. While someone with a masters can also have and convey such insights, a doctorate may provide an extra measure that has value.

My very first positive educational experience was in high school; plane geometry. I didn't have especially good instruction, but learned, through endless problem solving sessions to get a feel for it and to begin the drive toward a deep education in maths. And, had I had better guides at the time, I might have developed confidence earlier than I did.

A PhD, alone, however, isn't the answer. It needs to come with a desire to excel at teaching that provides they synergy to make it work effectively.

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  • "geared toward research... secondary education is not" Mostly right, although the secondary National Curriculum in England and Wales these days does contain some bits and pieces about the scientific method, research ethics, and peer-reviewed publication that weren't there in my schooldays. (Not that that's helpful with OP's specific question: private schools don't have to follow the National Curriculum.) May 1 at 15:52
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So, one simple answer is that often when they are hiring someone with a PhD, that candidate is simply the most qualified candidate and would be even if they did not have the PhD.

But some PhDs are also doing work with high school students that does involve research projects or does involve working with extremely gifted or advanced students on topics. This is likely a small fraction of PhDs in question, but they do exist. I know, because I am one of them. I do regular math teaching at a high school, but I also run what we call our "Honors Seminar" for students who have gone through the most advanced standard topics (multivarible calculus and linear algebra). The first semester of the Seminar is an advanced topic (often graph theory or number theory) and then the second semester we spend on a research project in that area. So far, of the five years I've taught the seminar, 2 out of the 5 have lead to published research projects. Now, the vast majority of that work is due to the students, but finding appropriate problems that they can reasonably tackle is not at all easy. I would strongly suspect that the vast majority of people with a Masters do not have the relevant expertise. (Although I would also suspect that most people who have a PhD also don't. Finding the right sort of problems is tough.)

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Turning the question round: there are some people with PhDs who decide to go into teaching. These people are likely to look for schools with a lot of strong students who will take advanced mathematics options, whereas for many mathematics teachers in the UK this is either not a priority or something they prefer to avoid. The PhDs are probably already comfortable teaching strong students (having done some undergraduate teaching), and certainly have sufficient subject knowledge. So I would expect these schools attract many more job applications from people with PhDs than typical schools do. Unsurprisingly, some of these people will be good enough to appoint.

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To some extent this is a matter of marketing.

These schools are ultimately commercial (although non-profit) enterprises - they are in competition with eachother and with the state school sector for parents' cash. Rightly or wrongly, many people assume that people with PhDs must be somehow 'better' at their subject than those without, and so a school with many Drs on the teaching staff will provide a 'better' education than a school staffed by teachers who are mere Mr/Mrs. Whether this is true or not is immaterial; it's the impression that counts.

In addition, many of these schools (claim to) pursue a more avowedly 'academic' atmosphere, modelling their traditions and teaching structures on those of Oxbridge colleges. Again, recruiting PhDs contributes to this (or at least to the impression of this). It may also work in the opposite direction: the kind of teachers who are attracted to these jobs are also the kind of people who are likely to have pursued PhDs.

Edited to add: To get a teaching job in the state sector in the UK one typically needs some kind of school-teaching qualification, such as a PGCE. Private schools are not subject to the same regulations as state schools, and are (or at least, have been) willing to treat a PhD as an acceptable alternative. Thus, a PhD graduate who is considering a career in teaching will likely find the private sector more attractive than undertaking an additional year of study. Of course, one could argue that this is 'effect' rather than 'cause' - the schools may be setting their policy with the aim of attracting more PhD-educated teachers.

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  • Private schools simply don't (or at least didn't) require a PGCE, even without a PhD. I suspect one reason for this policy is that there is some effort from the PGCE side to avoid admitting people who are going to disappear into the private sector. May 1 at 10:47
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Some things not mentioned yet:

Most of the time, the competition for the PhD is not people with Masters degrees, but rather those with Bachelor degrees. Compared to those with BS degrees, there's a noticeable knowledge gap. Rizhiy mentions this in point 1 of their answer, and although there is also a knowledge gap compared to those with MS degrees, it's more apparent when compared to those with BS degrees. To go a bit further, sometimes a question will be deep enough that even a PhD teacher will not be able to answer it, but they can be expected to figure it out. This is not easy, since it can involve reading through advanced material, but people with PhD degrees can be expected to do it. This means strong students especially love the PhD teacher, especially since you can ask them things that aren't in the syllabus and expect a useful answer.

To go even further, the school will likely want to send its best students to Olympiads or other competitions (example), and the PhD teacher has a clear advantage in mentoring these students.

Another thing is that the PhD teacher can write recommendation letters that carry more weight, because they've been through more of the academic system. This matters for getting the school's graduates into university (a competitive metric that most schools care about).

Finally, what is likely the most important reason is the prestige value. It pays to be able to advertise your program as being led by Dr. Big Name with a PhD in the field. Parents probably don't know what exactly Dr. Big Name can do that non-PhDs can't, but they do know (or at least think they know) that whenever something unexpected shows up, Dr. Big Name will be able to adapt better than non-PhDs.

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