My dear wife is having a terrible time understanding how and when she should be shifting. Actually, I take that back... she's shifting alright and she knows to downshift before going uphill, but she doesn't understand the underlying scientific reasonings why she should be selecting different gears. She just doesn't understand torque and how to use it effectively.
I trace the blame back to her mother teaching her to drive a stick shift. She didn't teach her why gears work, just "go higher to go faster (and make the engine quieter) and start in 1". While I can't disagree with her execution, the logic is entirely incorrect (or at least unfounded). Some are content to go through life without understanding underlying concepts... fair enough until it hurts or hinders you.
While teaching her shifting basics when we bought her bike, I had her run up and down the rear cog so that she could "feel" the difference. I was told in no uncertain terms that the laws of physics were not applying to her particular bicycle and that it was "more difficult" either direction she shifted. [p.s. Guys: laughing to avoid getting angry is not the correct response in this situation]
She has a (chemical) science background, but seems to have problems with basic physics concepts (torque, rotational force, amount of work, power output, etc.). She can't wrap her head around the fact that spinning faster (higher cadence) is actually "easier" (from a force standpoint) when it means she's working "harder" (more out of breath vs. muscle fatigue).
The wikipedia article on Bicycle_gearing was of little help as it dove into details of which cogs to pick before fully explaining the "why".
Anyone have any simple explanations or analogies that can help us?