I used to teach particle physics to our third-year students. We found it a frustrating experience.
To understand how scattering amplitudes reveal particle symmetries requires a modicum of familiarity with the formalism of quantum mechanics. To understand what Dirac did with his equation requires a willingness to manipulate 4 × 4 complex matrices. If I cannot assume this, and have to recap it, then in my 12 lectures I get nowhere near covering the highlights of a basic particle physics curriculum.
If I do assume this, then the students get nowhere near understanding much about particles, except for the top dozen or so who became the target market. The problem is that it requires multiple revisits over an extended period of time to master the basics of complex ideas. The fact that students have covered quantum theory or matrices is not sufficient for the required mastery.
In the development of educational curriculums this was recognised most influentially by Jerome Bruner in 1960, particularly in the book The Process of Education. One of the principal ideas in that book was that of the spiral curriculum: “A curriculum as it develops should revisit these basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.” This was highly influential initially in curriculum reform in the US, and now most of our school curriculum is based around the idea of a spiral.
In higher education in physics we give a passing nod towards a spiral curriculum with module titles such as Elec&Mag 1 and Elec&Mag 2, but, as in my particle physics, with a view to building on supposedly existing knowledge rather than explicitly redeveloping it. In any case, this spiral is probably too loosely wound. In an interesting 2009 paper, Doug Rohrer looked at the increase in student performance within a single mathematics module by mixing the questions on each topic over many weekly problem sets. Some of this happens automatically, but not necessarily systematically.
Underlying the spiral curriculum are two critical ideas. The first is the forgetting curve. According to this well-documented effect, the ability to recall learned material decays exponentially on a timescale that increases with each presentation. It is at least conceivable that a lot of the positive results claimed for student-centred pedagogies are actually the result of repeated processing of material over varying timescales through reading, discussing, writing and revising that the approach enforces.
The second cognitive component of a spiral curriculum is the testing effect. According to this, repeated testing of material even without re-teaching improves retention and (hopefully) understanding. In fact, my own totally untested hypothesis is that a lot of what appears to be a lack of conceptual understanding in students is a manifestation of an insecurity in basic knowledge. (I probably can’t deconstruct a functional linguistic expression if I don’t immediately cognise what the key phonological units connote.)
If all this is true, then in higher education we have a difficulty. We need more assessment and feedback – not, as is currently the fashion, less – but we don’t have the resources. Here technology can come to the rescue. Spaced repetition computer software is used in language learning, and other contexts, to present students repeatedly with questions on material to be learned, with the repetition interval spaced according to the correctness of the learner’s responses. It will be interesting to see if this can be adapted to learning important ideas in physics. On a small-scale trial last year Alison Voice, Arran Stirton and I achieved some interesting (by which I mean inconclusive) results in a first-year thermodynamics module at Leeds. We are planning to extend the trial this coming year.
This brings me back to my particle physics: mea culpa. If I had been wise enough to treat my course as part of the spiral curriculum I would have spent more time on the generic basics and accepted that we would cover less of the particle physics. Then I would perhaps have explained to a somewhat wider audience how beautiful it is that 2 × 2 is the square root of 4 × 4 and 3 × 3 = 8 + 1.
Derek holds the Bragg Medal from the Institute of Physics and was awarded an MBE for contributions to Science education in 2012. He is also a National Teaching Fellow.