An expert in an occupation or task, that requires skill, notes regularities and common patterns because they are opportunities for automation. As far as teaching goes certain concepts always seem to be problematic or draw incorrect answers, these regularities make the teachers job easy because they mark areas that need attention and opportunities for growth.

Recently I have been working with a number of physics students on Faraday’s Law. Students need an intuitive understanding of the Sin function because it describes how the magnetic flux changes as a generator rotates. A common misconception that the majority of students hold is that when the angle between the field lines and the coil is 45 degrees the flux will be 50% of the maximum amount, however the actual proportion is 71%. This bias is due to the  way we use shortcuts when reasoning, consequently my physics students memorize the important values of Sin[x].