Notch 7: Ed Barbeau on Gifted Education

A very pleasing irony of writing this thoughtless and classless, “We’re all doomed” blog is that it has resulted in my being introduced to thoughtful and classy heroes like Tony Gardiner, mathematical stars who have been working tirelessly for decades that we not be doomed. The most recent introduction is to Edward Barbeau, a star of Canadian mathematics education. Tony Guttmann, AKA Mr. Very Big, alerted me to a long comment Ed contributed to a maths-ed discussion, on gifted education. Ed has kindly permitted me to reproduce his great comment here.


I do not see how anyone who has much dealing with children can deny that
there are essential differences in abilities that make some of them
superlative in their capacity to learn, understand and perform. However,
it is also the case that a large number of students can learn and perform
to a high level if the circumstances permit, and our schools should become
equipped to draw out this potential.

To be sure, for some students, the best approach may be to have separate
schools or at least special classes. In a very few cases it seems to me
that the gift that a child exhibits may be so entrenched in the
personality of that child that it is inconceivable for it to imagine any
other kind of life; this is what I pick up from some interviews with
leaders in certain fields such as sports, dance, arts. In this case, then
extraordinary and idiosyncratic approaches are needed.

But I do not think that this applied to all gifted students, however
interested they may be. Some may not realize that they have a gift for
mathematics until they have an exposure to the subject and find that
something clicks. Others could excel in different ways.

There are many possibilities for nurturing talented students, especially
these days when there is ready access to the net.

First of all, the ordinary syllabus should have some value added that
keeps students on board who may otherwise be bored by the standard fare
and approach. In the traditional curriculum, the Euclidean geometry served
this purpose. The deductions that students were called upon to solve
varied from the routine to quite challenging, and many deductions had
alternative arguments of varying elegance. I do not know how much mental
arithmetic occurs in the modern school (I suspect very little) but this is
another area where children can perform with more or less efficiency and

Even in basic algebra, word problems can vary from routine to challenging,
and some allow for different ways to set up and solve an equation.
Trigonometry is a dream topic for the secondary syllabus because it
touches on so many essentials of mathematical formulation and technique.
One test of a curriculum might be how often it calls upon students to make

So the first place I would look is to see how we can get teachers in front
of the children who have the mathematical experience to understand the
nature of what they are teaching, to assess where the kids are at and to
exploit the possibilities inherent in the syllabus. This is a political
question: how we allocate resources, recruit teachers who might otherwise
go into other fields, and foster and respect (especially when it comes to
salary and working conditions) the professionalism of teachers.

Another thing we need to look at is the range of extracurricular
activities in a school; a lot of the real learning (and setting students
on fire) comes from the activities they pursue after school. If the school
has a mathematics club, participates in mathematics competitions or math
fairs, this can go a long way to keeping good students interested and
progressing in mathematics. Of course, this is another thing that comes
down to the teaching corps who have to have the willingness and space to
be involved in such things. (Not if they have to find a second job to make
ends meet or not afford to live in easy commuting distance to the school.)

Then there are things that cut across schools that might be district wide.
One of the Toronto suburban boards was very good at this about forty years
ago. The school math heads met regularly during the year, they set up an
annual competition for schools in the board and had an annual weekend
“math camp” at a country property that the board opened. Politics again —
this particular board had a politically astute math coordinator that was
quite adept at squeezing the necessary fund from the trustees.

Then there is the outreach from universities. Back in the 1960s, Israel
Halperin at the University of Toronto established a correspondenc program
(the Gelfand Club) and started the Metro Math Club, a series of monthly
lectures. The University of Waterloo has a continuing programme of school
visitations, workshops for teachers and competitions. The Fields Institute
established Saturday morning sessions for secondary students.

Finally, we come to the net, where talented mathematics students all over
the world can make contact. More old-fashionedly, there are also a lot of
very good books that students can read, in particular, those by our
colleague Tony Gardiner.

My own predilection is to nurture students in their neighbourhood schools
while giving them access to resources and contacts of the outside world,
and our first job is allowing students to make these connections.

In my experience, most students who are good at mathematics are
multidimensional — they also excel in other areas and have a wide array
of interests.

I find it hard to put my finger exactly on what has gone haywire in our
system of public education; there is a kind of desperation to improve it,
but somehow things do not quite work out. Twenty years ago, I would say
that the bulk of the students who rose to the top in competitions were in
the public system and I knew the teachers who made that possible. Now many
of them come from private schools.

The problem with the private or separate school option is first that it
can be ruinously expensive and secondly is can be a “caveat emptor”
situation; the parents are often not in a position to make a judgment and
you are not quite sure what you are getting. The other somewhat intangible
cost is that of taking students out of their home environment and into a
culture that may not be particularly copecetic.

The most persuasive example I have of the value of the public system is in
the field of music. The high school I went to had a sort of working
orchestra; we had a weekly assembly of the whole school which including
entry and exit numbers by the orchestra, which was also available for
school shows. My daughter went to a school that had an exceptionally fine
orchestra with a long tradition and among other things, I heard them give
a fine performance of a Shostakovitch symphony. She gained sufficient
proficiency on the cello that many years later, she decided to join her
community orchestra. Both her sons went to a middle school where virtually
every student was part of the music programme somewhere; one learned the
saxophone and other other the trumpet. The music director was
uncompromising on discipline, but his students gave a solid annual concert
and when he was recognized by the principal the cheering of the students
brought down the house — quite moving actually.

There was nothing special about this. I am sure that the kids involved
could have come from anywhere. What made the difference were the teachers
who were willing to invest their time and expertise to supporting these
kids. Again — the solution rests in politics and the insights and
priorities of the community at large.

Mathematical examples are rarer, but an outstanding situation is that of
Bruce While at Vincent Massey School in Windsor who ran several
mathematics clubs and produced a few team members for the International
Mathematical Olympiad.

Robin Pemantle pointed to the SEED program, which was a remarkable
undertaking. But it does beg the question as to whether this can be built
into public education.

18 Replies to “Notch 7: Ed Barbeau on Gifted Education”

  1. The ‘gifted’ label is often abused in schools. Schools, usually encouraged by pushy parents, all too often equate ‘gifted’ with slightly above average. Genuinely gifted students are rare, but go to almost any school and you’ll be told it has dozens of them … You only have to look at these Select Entry Accelerated Learning (SEAL) programs to see how the gifted label gets misused as just another marketing gimmick. And when a school is blessed with a genuinely gifted student, there aren’t too many that know what to with that student, except to ‘accelerate’ them (along with all the wannabe gifted students).

    In more than 25 years I’ve maybe encountered no more than a dozen of what I would consider genuinely gifted students.

    1. Often parents will angle to get their child in a gifted program because they have lost confidence in the regular program. Some years ago, our government encouraged schools to have French immersion programs and many parents felt that as these programs were unlikely to attract weak students, they should enrol their kids in them, regardless of their interest in French.

      One difficulty is that if your child gets into a program that really is designed for gifted students and finds that it is not as quick or as committed as the other students in the class, then it can be counterproductive with respect to self-esteem.

      There is the same risk with private schools if the child finds itself in an environment that is noncongenial.

      I have met a good many gifted mathematics students over the years, and where I have met the parents, things work best when the parents are supportive but not intrusive and willing to let things evolve as they will.

      1. Thanks, Ed. I accidentally started a Maths Club at my daughters’ (public) primary school a few months ago, and many of your comments resonate.

        I also strongly agree with your comments on the potential/actual value of the public system. I went to my local secondary public school, which just happened to be a “music hub”, and which turned out to be the most rewarding aspect of the school. In very little time I went from no musical background to being the world’s worst bassoonist. I loved it (even if the audience didn’t). Such “extracurricular” “add-ons” can be invaluable. I don’t know how regularly (or how well) such activities are now conducted in Melbourne’s public system.

  2. Nice comment. I agree.

    It makes me think of my recent time volunteering at a local public primary school to teach mathematics enrichment. Good things can be achieved, but it seems to be only through extraordinarily generous teachers or community involvement, the system does not encourage or support it.

    I suppose I would add a final point: if the government wish to promote excellence in our students via curriculum, they should support these activities, they should support teachers especially doing these activities, and they should dispense with much of the current “opportunity class” and “selective school” system.

    1. Well, given the government(s) quite evidently do not wish to promote excellence in our students, it doesn’t really matter, does it?

      1. It does matter. Because we should still try to offer kids a decent education, which means facing up to the reality of enabling volunteers in schools to do what they can, and enabling schools to help.

        It matters because even if schools do the above (and they do) they should never act as though this is somehow a good situation. It is not. It is just people doing what little good they are able to when faced with the alternative.

  3. My school is a government 7-10 secondary college which is in an area that is far from wealthy!

    The school is keen to encourage students who are better than average in mathematics. I have been hired to contribute to this effort. Students from Years 8 and 9 are selected to spend one lesson each week with me instead of one of their normal lessons in mathematics; there are 5-10 students in each group. My position is a 0.4 position.

    A lesson from this week is attached. The sources of the problems are given in the notes that the students have. I was pleased that students did better than I expected with these problems. In a couple of cases, students developed an algorithm that enabled them to tackle all the problems.

    Also, I teach a subject called “Challenge Mathematics” which is an elective subject for Year 9 students; there are 15 students in this class.


    1. Thanks, Terry. I think this is a reflection on you and your school, not on the governments.

      How does the Challenge Year 9 maths class differ from the “selected” Year 9 class, either in cohort or content/style? I liked the Smullyan puzzles (of course), although I don’t remember 2(d) being one of his.

      1. As the notes (which are given to the students) say, many of the problems are based on Smullyan (Q1) or Popular Mechanics (Q2). 1g and 2d are my additions. 2d arose from my experience that indicates that many (most?) students do not know that Australia has spies. And I guessed that almost nobody would know the meaning of “knave”; hence 1g.

        Challenge Mathematics is an elective Year 9 subject that deals with four topics across the year; one/term; indices, quadratic functions, trigonometry, and logarithms. I like the fact that a whole term is devoted to each of these topics. In these classes I have considerable freedom in how I present the topics; but the essential idea is to challenge the students. Students will encounter some of these topics in other classes. For example, this week my students had a task on logarithms that asked them to write 250 words on the life and work of John Napier using only the article in Wikipedia as a source; I set this exercise because I have found that students are not very good at reading and summarising.

          1. That too crossed my mind.

            When I lived in the US, Gough Whitlam visited the US and appeared on meet the press. We listened to it on the wireless. Here is what I remember from some questions about spies (G=Gough J=a journalist).

            J: Are there foreign spies in Australia?
            G: Of course.
            J: Which country has the most spies in Australia?
            G: Britain.
            (shock, horror)
            J: Does Australia have spies in Britain?
            G: Of course.
            J: How many spies does Australia have in Britain?
            G: Ah – that’s a secret.

  4. The new Victorian Government School Agreement includes clauses about staff receiving time in-lieu for work done outside of normal hours of attendance – such as running music events, clubs, camps, etc. The advice from the union has been that volunteering should no longer occur; either a staff member works at such an event because the school requires it, and in which case they should receive time in-lieu, or the staff member does not work at the events. (Staff can still attend these events as a “member of the public”, but they should perform any duties as a staff member).

    While it is good that this overtime is now being compensated, the Victorian Government did not provide schools with the funding to cover it (ie. for schools to pay for relief teachers). The likely effect is that schools will no longer offer the same range of extra-curricular programs/activities they have in the past.

    New agreement: The time-in-lieu clauses begin on page 37.

    1. Thanks, SRK. It’s a diabolical Agreement. The “Victorian Government did not provide schools with the funding to cover it (ie. for schools to pay for relief teachers).” Blind Freddy could see that “the likely effect is that schools will no longer offer the same range of extra-curricular programs/activities they have in the past.” It is a disaster for Victorian education. Just when you thought it had reached peak stupidity. 1/3 of union members voted against it, but 2/3 voted for it (strangely, I cannot find a single teacher anywhere who says they voted for it …)
      The Victorian Govt has screwed over public education in Victoria and should hang it’s head in total shame. It should never have ratified the Agreement. And as for the VEU … I have the words but they’re inappropriate for this blog.

    2. Thanks, SRK, and JF. A pox on every house you can find. Schools without “volunteering” cannot function in any meaningful manner, and anybody who pretends otherwise should be First Against The Wall.

    3. Hi again, SRK. I think you mean

      “(Staff can still attend these events as a “member of the public”, but they should [NOT] perform any duties as a staff member).”

      I’m not sure where you got this ‘advice’ from, but it is bad advice, loaded with danger. If you attend “these events”, you are NOT considered a “member of the public” in the eyes of the law. You continue to have a duty of care as a teacher, even if the event is outside school hours. In fact, you can be walking home from work outside of school hours and still have a duty of care if you see students doing something stupid and dangerous. If you don’t take reasonable action and an incident occurs, you can be held legally liable for having failed in your duty of care. If you don’t intend to volunteer at a school event, do not turn up thinking that you can be treated as just another member of the public. You’re not.

      On a related note, it is a constant amazement to me that some staff think that their Yard Duty ends at the time it says on their timetable and will leave even when their replacement has not turned up, thinking that the Yard Duty has now become the other person’s responsibility. Not so. If an ‘incident’ happens after you leave, the other person might get a slap on the wrist for not having turned up on time but YOU will suffer the full legal consequences of the incident. It amazes me that with the amount of stupid, box-ticking PD imposed on teachers by schools, very rarely do schools bring out a lawyer to talk to teachers and help them understand the full extent of their duty of care.

      1. @JF: I have found this to be a useful reference: Vivien Millane, “Teachers, Students and the Law” (Fourth Edition). A PD could be arranged around this small book.

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