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Exeter Mathematics Program and Problem-Based Learning

Discussion in 'Mathematics' started by Karvol, Jul 10, 2015.

  1. Karvol

    Karvol Occasional commenter

    Hi Everybody,

    A couple of weeks ago I spent just over a week at Phillips Exeter Academy, having a look at their Mathematics program and the Harkness Method of learning/teaching.

    Here is a link to their material:


    Has anybody put any of these ideas - no matter how loosely - into place? If so, what have your experiences been?


  2. primenumbers

    primenumbers New commenter

    Just read through the Wikipedia page about the school.

    I learnt Maths in a model similar to what was described in the Wiki page. We did problem sets every lesson. Demonstrated our solutions on the board or handed to teachers to mark individually. We only did around 2-3 problems per 45 minutes lesson.

    I was doing something similar with 2 groups of more able pupils in my schol this year. we met every 2 weeks to discuss the set of problems sent by UKMT mentoring.

    The intermediate group was more succesful. When they came up against something that they couldn't do, I gave them some direction and they normally were able to search the internet, learnt something new then came to me with the solution. Only 4-5 students in the group so they were able to demonstrate most of their answers on the board.

    The junior group was more difficult to manage as they were a mixture of 10 year 8 and 9.

    I am planning to extend it much further next year but only have limited time on my hand.
  3. Shatnerbassoon

    Shatnerbassoon New commenter

    Hi Karvol I have sent a PM,

    but in general I am very keen on trying this approach, and our classrooms are well set out for it, but the real problem comes I think with rewriting the materials in order to fit in with a strict curriculum and external assessments, which are not a feature at Exeter. I really like the strong geometric approach to maths, and the early emphasis on parametrics, but realistically that is not so relevant for how our pupils will be assessed, and the task of writing the questions themselves seems rather enormous.

    From what I have seen on here I believe that you are in an MYP school? If so I guess there is more space to adapt the curriculum and assessment for this model.
  4. David Getling

    David Getling Lead commenter

    Don't know if it's still the case, but the school in Leysin was using it a few years ago.

    For those who don't know, Phillips Exeter Academy has an awesome reputation for it's involvement with the IMO. If memory serves me right, some of their teachers have been mentors, and some of their students have made it onto the American team.
  5. kyle21b

    kyle21b New commenter

    Hi all,

    At Wellington College, we are into our second year of teaching in this style - indeed we had guys over from Exeter in the Summer to deliver a course on how to teach the Harkness style. I have to say that it is brilliant and early signs are that there is an absolute definite increase in resilience and knowledge retention.

    Please message me if you would like more info or to come and see it in action. We are running another course in July next year, too.
  6. Vince_Ulam

    Vince_Ulam Star commenter

    Any school which can identify a group sufficiently small, able and well-behaved to learn via this 'method' should have no difficulty teaching them to equivalent or higher levels without supplementing the income of another school.
  7. Karvol

    Karvol Occasional commenter

    That is true, Vince, but the aim is to try this method with all the students in the school, starting with the weakest. The strongest students will learn irrespective of the teacher, it is the weakest that I am most concerned with.

    Traditional methods of teaching have only gone on to reinforce the idea that they are not very good at maths. So the idea is to try something different, starting with the premise that they are all capable of learning something, and see how far it gets us. If it fails, it is no worse off than where they were anyway.
  8. Vince_Ulam

    Vince_Ulam Star commenter

    The first four words of the first sentence of your reply are sufficient and answer your own question of whether this thing will work with the 'weakest' i.e. in general it will work about as well as an anvil functions as a parachute.

    It will work with lower ability groups:

    1. That are sufficiently small.
    2. That are sufficiently able.
    3. That are sufficiently well-behaved.

    These things are to say that it will work with lower ability groups:

    1. That are in selective schools.

    Over the past forty years or so "traditional methods of teaching" have either been slowly phased out or rendered impotent by the population explosion. If heritage is inversely proportional to value & efficacy then why anyone feels the Socratic method is the way to go is as clear as mud.

    For the right groups the tutorial system will work very well indeed but for the vast majority of schools this is just another expensive and time-wasting foreign fad.
    Last edited: Sep 28, 2015
  9. kyle21b

    kyle21b New commenter

    It certainly works better with small, well-motivated groups but it can be done in a "group-work" format too for more pupils. There are key principles that you can take from the Harkness ideal without doing the full thing (ie. you may not get everyone to come in and puts solutions up, sits in a circle and talks about the solutions).

    For example, you can expect everyone to do work pre-lesson and bring work with them to class. You can test children regularly (every two weeks) and you get them to critique each other's work. The nature of bigger groups Is that those who don't do the work have more chance of "getting away with it" but that's the same whether it is traditional classwork or homework. One of the biggest benefits is that the children are now doing 5-10 hours of maths per week which is considerably more than usual even if you have 6 lessons and 2 homeworks they are not doing 10 hours in total.

    The other ideal that you can definitely implement is teaching by problem and not by topic. Why teach straight lines and then stop and teach statistics and then stop and teach circle theorems? You can produce resources which do all of this simultaneously and get to the same end point in the time constraint.

    The "Harkness" thing is more about the idea of flipping what we do on its head - learn outside of lesson and embed within.
  10. Vince_Ulam

    Vince_Ulam Star commenter

    If any of your colleagues do not believe their students are capable of learning something then you might wish to have a private word in their ear. Meanwhile, the difference between students' culture at the fee-paying, selective prep schools selling Harkness and that found in most British schools to whom they wish to sell is such that Harkness will not translate. An anvil is different to a parachute but I would not swap their roles for the sake of novelty.
  11. David Getling

    David Getling Lead commenter

    For those who haven't bothered to go to the link, it's worth pointing out that Phillips Exeter Academy makes the Harkness material freely available.

    Also, don't be put off by the word Academy. Unlike in the UK, this isn't a euphemism for **** School.
  12. Vince_Ulam

    Vince_Ulam Star commenter

    Unless Phillips Exeter Academy are giving away large polished oak tables then the value of whatever materials they offer gratis is negligible. PEA charge $1,100.00 per person for registration on their Harkness CPD programmes for Humanities and Diversity. They do not appear to have a mathematics CPD programme dedicated to Harkness.

    In partnership with PEC, Wellington College charges up to £200.00 per person for registration on their Harkness mathematics CPD programme.

    I am not saying that these rates are not good value nor am I dismissing the tutorial system out of hand. As I have said, for the right groups it will work very well as it has worked for a very long time.

    Certainly it isn't. PEA and its intake are about as far removed from their average American and British counterparts as Heaven is wide.

    This CPD will look great on a C.V., make for super school promotional material but in the end it's just unsuitable for most British schools and its experimental implementation is a waste of student and teacher time.
  13. kyle21b

    kyle21b New commenter

    This is currently under review - we are trying to subsidise this cost.

    The course is fantastic and I think it goes some way to squashing the many "reasons this will not work" (which I believed 6 months ago).
  14. Vince_Ulam

    Vince_Ulam Star commenter

    This is beginning to look like commercial advertising, @kyle21b. This is not allowed under the terms of membership.

    The tutorial system, whether it's packaged as Harkness or 'flipped-classroom' or whatever, just will not work in the vast majority of schools in the UK for reasons previously given. No matter how 'fantastic' your commercial product, you cannot replicate the conditions obtaining at Wellington in these schools.
  15. Karvol

    Karvol Occasional commenter

    They have one for mathematics, which takes place in June. It was the one I attended.

    This conversation seems to be heading towards a state school/private school divide. My initial question did not ask as to what type of school an individual taught in. It asked if anybody out there had used any aspect of the program.

    The Exeter maths program has been taken up by a fair number of public schools in the US and, while the initial process of adapting to the program was painful, the short terms results appear to be quite positive, although I haven't seen any long term results of the program (outside of PEA).

    Also, PEA were quite selective on which aspects of the program that they revealed. While they were quite happy to give solutions to the questions on their program, what they didn't reveal was the commentary to the questions (apparently much more interesting and useful - although I'll have to take their word for it, as there was no material to judge).
  16. kyle21b

    kyle21b New commenter

    Apologies, I am not using this as advertising at all.

    It doesn't need a certain set of conditions, it is a philosophy that can work if done in the right way. The two main things being you come to class with work done and you learn maths as opposed to learning topics.

    I think it can and does work in promoting independence, resilience and it is accessible for all. Very rarely will there be a question that someone can't start. It takes some buy-in from the students, admittedly, but in general they want to succeed and they learn very soon that the way for that to happen is for them to have a go and contribute.
  17. Karvol

    Karvol Occasional commenter

    Some questions for you, kyle21b.

    Do you continue with this method during the Diploma program?

    Is method applied with mixed ability groups?

    Is the method applied to other subjects?

  18. kyle21b

    kyle21b New commenter

    We only use this in full with A-Level at the moment. Creating the resource is the most time-consuming part.

    Personally, I have just taught vectors to my Standard Level groups in this format for two weeks (work pre-lesson). Others have taught various parts of the other courses (GCSE or IB) with these ideals in mind. They haven't seen a single exam question so it will be interesting when I test them this week to see how they cope.

    In terms of mixed ability, with a-level mathematicians, you are given quite a mix! There are students who have struggled through the first month but they are hopefully feeling a little more successful now. No doubt this is the biggest challenge, the tests are the only real way of gauging how pupils are coping as well as monitoring the class discussion.

    Other subjects that use it wholly are English, Economics and Business studies. The language department are also trialling various parts of this, too.
  19. Vince_Ulam

    Vince_Ulam Star commenter

    This one? It barely mentions Harkness so I was not sure. If not then please link, thanks.

    This may be your preferred direction but I have not pushed this discussion there. I have referred only to selective schools. I am fairly pointing out that Harkness is far more likely to work with groups which meet certain criteria. These groups occur more frequently in selective schools.

    I am more than willing to look at any evidence you are able to provide. I am not intractable in the face of evidence; I am all for what works. Until you can provide this evidence so I am justified in arguing that Harkness is unsuitable for most schools in the UK.

    I've noticed in several documents that PEA are cringingly coy about the status of their school as integral to their success with Harkness. This topic is broached in the following video at timestamp 18:02. In response, PEA Principal Thomas Hassan walks quite wide of the question. Apparently the success of Harkness is all about having 'a lovely oval table' in classes and having discussions around tables in administrative meetings because, you know, no other organisation has discussions around tables.

    The question of PEA's status and its apparent Harkness-success is answered more in the exterior and interior shots of PEA and Hassan's other responses, particularly that immediately following this fudge.

    I think an important question is whether prep schools so wealthy as PEA or Wellington would not have equal or greater success without the use of Harness. I suspect they would, but USPs are USPs.
  20. Vince_Ulam

    Vince_Ulam Star commenter

    You work at Wellington and you're promting a commercial product offered by Wellington. It looks like you're advertising.

    Then you are telling us that Harkness will work with a group of 30+ KS3 students?

    1. Students who won't do homework after class will not do it before class where, in most cases, it would need to be taught to them before they could possibly gather around a lovely oval table.
    2. Maths rather than 'topics'? Are you telling this forum of maths teachers that you think most maths teachers do not teach maths?

    The student culture in most British schools is such that most students will not, to use your significant phrase, 'buy-in' to your philosophy. This is not because of the philosophical position of their teachers but because of the mandated and circumstantial structures in which we must work due to funding, population and government diktat. Even were these things not an issue then anyone may adopt a philosophy without having to buy it from one of the wealthiest prep schools in the UK.

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