It is amazing how new information can change how we think and ultimately what we do. There used to be this idea in the fitness industry that it was better to exercise at a low intensity if you wanted to burn body fat, low intensity being a heart rate of 120-130bpm. Depending on your fitness level this is probably a walk. New research of late suggests that greater amounts of fat are burnt post exercise for longer if you do higher intensity bouts of exercise.
So who is right? Will it all change again?
The way I look at these things is to do weigh up where most research is and then serve up a combination of methods that are likely to first: do no harm and secondly give the client the most chance of achieving the goal they are after. The bottom (not trying to be funny!) line as usual for optimal fat loss is to simply use up more energy than you consume on a daily basis and the only way to track this is by regular measuring and a good understanding of the energy densities of the foods that you eat and the energy output of the activities that you do.
You old school teacher was right, mathematics does make the world go around!