I remember the early days of my teaching, when I had to provide a simple example computer program to calculate 9/4=2.25. I would teach it like this:
*** CASE 1: Use two variables a, and b that can hold two fractional values (called float). Store a=9, b=4, and calculate a/b=2.250.
*** CASE 2: To calculate 9/4, choose INTEGER types which could not temporarily hold fractional values. I asked the students the following question: What happens when you divide 9 by 4 and multiply back by 4. The question was almost insulting to a highly intelligence 50 students, since 4*(9/4) should be 9. With great boredom, they watch me to write a computer program to divide 9 by 4, and multiply back by 4. The result was 8 !!! This happens, since integer type variables CHOP fractional values intermediately, so, 9/4=2 and 2*4=8 ...
The interesting thing is, whenever I used CASE 2 type of "surprise factor" in teaching, the retention of what is LEARNed went from 40%-50% to almost 100%. Why ? Let's borrow some research from neuroscience to explain this:
*** It takes approximately half a second (0.5 s) for stimuli content to reach consciousness (Libet , 1950)
*** Left hemisphere (LH) of the brain performs analytical processing: Although this is slower, it is a lot more detailed. Right hemisphere (RH) respond to unexpected stimuli, and is a lot faster (MacNeilage 2009)
*** Inter-hemispheric congruence means, both hemispheres are in concert. Each hemisphere has its own memory (Moss, 2014)
What these studies suggest is that, my brain is made up of twin-TOLGA's : TOLGA-E (emotional TOLGA, located on the RH) responds mainly to emotional and unexpected stimuli in about 0.15 seconds and has his own emotional memories. TOLGA-A (Analytical Tolga, on the LH) has a 0.5 second delay and can do a lot of analytical processing, with its own memories. The CASE 2 was able to engage both TOLGA-E and TOLGA-A, and made the recording of this example a lot stronger, thereby significantly improving retention.
This means that, in a class of 50 students, you really have 100 twins. One responds to unexpected stimuli faster, and the other (twin brother or sister) responds a lot slower with a lot more understanding on the details. When both of them record a memory, the retention is significantly better. So, does this mean that LEARNING (or TEACHING) are EMOTIONAL or LOGICAL processes ?