Tony Gardiner on Financial Mathematics

Our first excerpt from Tony Gardiner’s Teaching Mathematics at Secondary Level is here. Our second excerpt is a short remark on “financial mathematics” in a mathematics curriculum (p 75). The relevance to Australia’s draft curriculum is obvious.

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Finally, while it is perfectly fair to require that pupils be required to

“develop their use of formal mathematical knowledge to interpret and solve problems”,

this challenge applies to problems of many different kinds. So there is no possible excuse for adding the words “including financial mathematics” in [the English Mathematics Curriculum]. There is no such subject area as “financial mathematics” … so its explicit inclusion can only reflect an enforced response to improper political lobbying. Some material relating to financial matters will inevitably be included (e.g. as an application of percentage increases and decreases, and of iterated powers as a model for the returns on long term investment or the accumulation of debt). But the precise words are no more worthy of special mention in a national curriculum than many other examples.

9 Replies to “Tony Gardiner on Financial Mathematics”

  1. To say that there is no such area as “financial mathematics” is strange. There are books on this subject area and journals (eg SIAM Journal on Financial Mathematics). Certainly it has been one of the growth areas of applied mathematics in recent years. For a short time, I worked for a bank in this area: indeed the bank had a mathematics department. There was a stage where to best place for a mathematician to look for jobs was in the Financial Review. (There is a good Australian movie on financial mathematics “The bank”.)

    In the more distant past, applied mathematics was dominated by applications in physics, but things have changed. Mentioning “including financial mathematics” explicitly could be seen as emphasising the changing nature of applied mathematics. I note that few mathematics teachers have had experience in this field: perhaps it should be taught in university courses in mathematics.

    One of my concerns about this topic in the curriculum is that it is assumed that this will resonate with all students. In my experience, some students have little idea about money. You can’t even assume that all students have a bank account or a paying job – and I am talking about Year 11 students. They can learn to press the buttons in the financial solver on their CAS calculator, but do they really understand the problem?

    1. You’re being deliberately obtuse. Again.

      There is no such (school) subject area as financial mathematics. The existence of financial mathematics as an advanced discipline(s) is entirely irrelevant to school practice, and it bears no relation to the 40-odd, heavy-handed occurrences of “financial contexts” and the like in the draft curriculum.

    2. Hi Terry. Just to pick up on a comment you made: At least at UOW, we *do* have financial mathematics and many students take the subject. Especially students who enrol in our Bachelor of Mathematics and Finance, but also often students who are just studying our Bachelor of Mathematics.

      I can guarantee that it is not much like anything in a high school subject, which I guess is part of the point. For me, the most important part of this point is: why is it here at all? Why not something else, like cryptography? Or biology? How about climate change?

      Or how about nothing at all? Oh sorry, that would make too much sense….

      1. Well done UOW. I agree that it is useful for students to see applications of mathematics outside the mathematics classroom and that there are loads to consider. One should also consider how likely it is that the applications will resonate with students (the world of the students is not the same as the world of teachers) and that teachers are able to adapt to new applications being introduced.

        Financial mathematics is, as Marty correctly points out, an advanced discipline; so too are arithmetic and algebra. Like arithmetic and algebra, financial mathematics can be taught at various levels; see the classic work G. Chrystal “Algebra: An Elementary Text Book”, Chelsea. (many editions from 1886 onwards). Chapter 23 in Volume 1 deals with financial mathematics.

        And while we are talking about the English system of education, there could be lots of work for mathematics teachers if Britain reverts to the Imperial system. I recall have to divide 32 pounds, 14 shillings and tuppence halfpenny among 13 students. I never got such problems right on the first try.

  2. FWIW, I suspect the inclusion of the line was intended more as a link to the Further Mathematics curriculum where “Business-related Mathematics” (or whatever it will be called post 2022) has made the transition from “optional module” (which very few schools seemed to choose) to “core”.

    I could, of course, be very wrong as I have no idea what (if?) the authors of the draft curriculum are/were thinking.

    1. @RF: During last term, I’ve been involved in teaching this financial mathematics material in General Mathematics to Year 11 students. It’s a nice coherent unit. Essentially there is one idea that permeates the material, namely V_{n+1} = RV_n + D, but it allows numerous variations. I am not sure that students see it as simply as I do.

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