Binary forms of back propogation (B), which dominate in teaching, only provide a yes or no answer to whether the technique was perfomed correctly. Floating point back propogation (F) on the other hand tells the degree to which something was correct or incorrect. Either way this can be applied in two forms, which psychologists call positive (+) and negative (-) reinforcement. I.e. either the student receives praise when it performs correctly, or criticism when it performs wrong.

So really good teaching is F:+-, where you give floating point back propogation (F) and provide both positive (+) and negative (-) reinforcement. Most good teaching is mostly B:+, which is boolean back propogation with positive reinforcement. This takes the form of emotional reward when the student succeeds, but without precise adjustment. Bad teaching is usually B:-, which is boolean back propogation with nengative reinforcement. This is represented by emotional punishment when the student fails.

The best teaching is where students are able to provide the feedback to themselves. This allows the student to use negative reinforcement more effectively, since negative emotional reward is often more damaging when it comes from an external source, short circuiting training. Students can quickly be taught how to given themselves B feedback, but it takes much longer for a student to be able to give itself F feedback. So students will often be able to quickly train themsef own with B feedback, but need teacher training to get F. But students who criticism themselves harshly will always show more benfit from external feedback.

After completing initial training in a skill, a student should be able to provide internal floating point (I:F) feedback. The student should apply I:F:+ liberally, but I:F:- sparingly. Ideally the intensity of the feedback should be calibrated based on how close/far off optimal the performance was. At some degree of variance, feedback should shift from + to -. So the best a student has ever done should get full +, the worst should get full -, where - is an order of magnitude less intensity than +. Half way between them we go to zero, before shifting to the other.