Sunday, December 13, 2009

On chaos and the teaching of mathematics, in no particular order

The normal busyness continues apace but I fancy punctuating this chaos with a little update. I'm currently doing some proofreading of a book (not my own) which is both fascinating and densely packed with information (I'll reveal details when possible). At the same time I'm attempting to get two papers finished before Christmas and if at all possible next week.

Ah, yes, and I'm back in Santiago, if only briefly. My carbon footprint continues to increase month on month and December is no exception as I had to come back to Santiago for a week in between my Dublin trip and Christmas. After an 11 hour mammoth journey back to Spain on Thursday (starting from Oxford at 4am and culminating in a 4pm collapse back home) I have lots of things to finish before I head off again on Thursday including giving a short talk to the postdocs and grad students in the department. I'll be introducing in 15 minutes the depths of string theory, gauge theories, the problems with strong coupling dynamics, AdS/CFT and its applications to heavy ion physics, and more importantly why they should care about all this. This will be aimed at a diverse audience ranging from the groups which work on non-linear systems to those in nanotechnology and beyond. Anyway, it'll be a challenge but it should be a fun one.

Christmas farewells are filling the evenings, with a big party last night (in which I managed to make sushi for a group of 30+ whilst avoiding food poisoning, the latter being my principle triumph) and dinners until I leave but somehow I have to get these papers finished and as much of the book proofread as possible in the meantime (snide comments about my own bad spelling are not strictly necessary/neccessarry/necisary/nessacary).

On the night before coming back to Spain I had dinner with a friend of my parents, an ex maths teacher who has spent a great deal of time attempting to spread his ideas for teaching maths not only more effectively, but in a way which avoids the building up of the normal hierarchy of students in a class which leads to a range of bad feeling between those who can and those who can't. The method is simple and I'd like to talk more about this some time, but the basic idea is to get the students to read out a very short section from an appropriately chosen text book following which another student will explain what the section means. I think this is an extremely intelligent way to get pupils not only to be able to solve maths problems but to truly understand the workings of mathematics as they are introduced to it. Far too much emphasis is put on getting kids to learn through repetition of solving problems and not enough is put on building up the background of true understanding which is needed for getting onto ever more complex concepts without getting lost in the forest of terminology and notation. Clearly problem solving itself is necessary for polishing the edges but problem solving is infinitely easier if one has a thorough understand of the internal workings of mathematics rather than simply knowing how to turn the handle.  Unfortunately it seems that getting teachers to try this method is extremely difficult, especially in the current climate where schools are terrified of trying anything new for fear of dropping down the league tables - one of several curses of the current UK education system. Anyway, I'd love to devote some more time to discussing this so we'll see if the Christmas 'break' allows. Until then, it's back to reading and typing...


Dale Ritter said...

In the most recent particle physics research a method for mathematical modeling of string topology and force dynamics has been written. Recent advancements in quantum science have produced the picoyoctometric, 3D, interactive video atomic model imaging function, in terms of chronons and spacons for exact, quantized, relativistic animation. This format returns clear numerical data for a full spectrum of variables. The atom's RQT (relative quantum topological) data point imaging function is built by combination of the relativistic Einstein-Lorenz transform functions for time, mass, and energy with the workon quantized electromagnetic wave equations for frequency and wavelength.

The atom labeled psi (Z) pulsates at the frequency {Nhu=e/h} by cycles of {e=m(c^2)} transformation of nuclear surface mass to forcons with joule values, followed by nuclear force absorption. This radiation process is limited only by spacetime boundaries of {Gravity-Time}, where gravity is the force binding space to psi, forming the GT integral atomic wavefunction. The expression is defined as the series expansion differential of nuclear output rates with quantum symmetry numbers assigned along the progression to give topology to the solutions.

Next, the correlation function for the manifold of internal heat capacity energy particle 3D functions is extracted by rearranging the total internal momentum function to the photon gain rule and integrating it for GT limits. This produces a series of 26 topological waveparticle functions of the five classes; {+Positron, Workon, Thermon, -Electromagneton, Magnemedon}, each the 3D data image of a type of energy intermedon of the 5/2 kT J internal energy cloud, accounting for all of them.

Those 26 energy data values intersect the sizes of the fundamental physical constants: h, h-bar, delta, nuclear magneton, beta magneton, k (series). They quantize atomic dynamics by acting as fulcrum particles. The result is the exact picoyoctometric, 3D, interactive video atomic model data point imaging function, responsive to keyboard input of virtual photon gain events by relativistic, quantized shifts of electron, force, and energy field states and positions.

Images of the h-bar magnetic energy waveparticle of ~175 picoyoctometers are available online at with the complete RQT atomic modeling manual titled The Crystalon Door, copyright TXu1-266-788. TCD conforms to the unopposed motion of disclosure in U.S. District (NM) Court of 04/02/2001 titled The Solution to the Equation of Schrodinger.

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