Learning

• What is learning?
  

People are not blank slates. People have preconceptions (usually misconceptions) about how things work because we inherently want to make sense of the world around us. Learning takes place when the preconceptions are changed. The change can take place in many different places and can be caused by many different reasons. The classroom is one of the most formal settings in which we can change preconceptions.

• How can learning be best effectuated by a teacher/trainer?
  

I believe that learning can be best effectuated by a teacher/trainer in two ways: 1) Linking new knowledge/information to previous knowledge and 2) to motivate them by showing them the usefulness of what they are learning. For example, in my pre-calculus class I build upon their previous knowledge of adding fractions when we are simplifying rational trig equations. (I will try to demonstrate with an example, but its hard to without the use of the equation editor.) They are given something like 1/1 – cos x + 1/ 1 – cos x to simplify. They tend to freak out seeing this the following conversation usually takes place:

Me (teacher): "How would you simplify 1/3 + 1/4?"

Students: "Oh that's simple, get a common denominator."

Me: "How do you get the common denominator?"

Students: "Multiply the denominators together."

Me: "Okay, so let's do the same with the trig equation."

From there most students pick it up.

The second way to effectively bring about learning is showing them the usefulness of the material. When I teach a unit on probability, I talk about gambling. Now of course I steer the conversation toward the house always winning, but students find that information useful.