The role of repetitive examples: practice makes perfect?

A few months ago, I read a journal article that I have subsequently lost track of. It was on cognitive demand/overload and related to calculations. If I recall correctly, it showed that the simplest type of calculation is essentially using an equation in its presented form (e.g. speed of light = wavelength x frequency) with all quantities in their most appropriate units and giving an answer in the most straightforward units. The most complex was then using multiple equations requiring manipulation with quantities in units requiring conversion and an answer requested in different units again. If there were more subtle points to the paper (or if anyone can recall it before I get to my office and see if I printed it for the file), please let me know.

It got me thinking, as do many such papers that present something that is perfectly logical once it has been pointed out to you. Mainly I was thinking back to high school maths where new concepts would be met with multiple examples of increasing complexity before any type of context has been applied. I thought I’d give this a go this year with my 1st year spectroscopy. We do a lot of equations and there can be a good amount of additional complexity added in through unit conversions and the like. For each equation (mainly the equations of light) I came up with exercise sheets that started with using the equation in the presented format with quantities in appropriate units. The final exercises involved rearranging the equation, and generally converting the units of the starting quantities and often the answer. These were uploaded to the class blog along with the answer sheet (numerical only) and highlighted to the students that were struggling a little more with the maths. Problem sheets and exam style questions were then used in workshops and for class test preparation that put the maths into the spectroscopy context.

I can see how this approach could be really useful for more complex equations – I’d suggest that most of my students tackle the exercises for IR vibrational frequencies, particularly getting practice at calculating reduced mass (kg people!).  I’m not sure, however, how this approach translates in to less mathematical areas of chemistry. It would work really well for organic mechanisms, and balancing equations, but not so sure about other bits.