I totally agree with Pace, in my opinion it is a good idea for a student pilot to have experienced a spin and flown the recovery, equally teaching the student the sets of conditions that might lead to a spin are just as important.
I instructed to both the old syllabus (which included spinning) and to the current syllabus. Both have merits and a combination of the two is in my opinion perhaps the safest way of being a better pilot.
At the time of spinning being removed from the syllabus I can remember the debate about if a properly taught spin was dangerous or if it made the pilot feel ill....
With respect to the PA38 spin, that is not difficult. It does recover easily if correct technique is used. However what caught people out was the fact that the rate of spin rotation increased when anti spin technique was applied, prior to the spin stopping. Some people are thought to have panicked at this, hence giving up and spinning into the ground.
Pace is again correct, people need to be able to instinctively recognise the difference between a spin and a spiral dive and the recovery techniques.That is not from having been told about the differences but from practical first hand knowledge.