Ugur Eren Canakci

I use an iPad to show and write on the teaching material. After the lecture ends, by the request of the student, I can send a PDF/Image copy of the material discussed/written in the lecture.

I discuss the topic at hand with the student, starting with the definitions and the mechanisms of the considered material.
Then I start presenting how the material is used to solve problems, which simply requires the presentation of the mechanisms and how they interact with each other.
Then I ask the student to explain the material as if I am their student, pointing out various types of questions that may be asked by anyone being taught this material.
After being ensured that the student has a good grasp on the material, we start solving examplary problems for the material, and I help with the pitfalls the student might encounter.

The main purpose of my teaching is improving the analytical thinkings skills of the student. By this, the student becomes a better problem-solver in ANY field, including mathematics.
One must realize that what is classified as "mathematics" is a collection of tools to help solve problems. The main focus is never these tools, but the situation at hand. Hence, the "scary" or "unpleasant" part of learning mathematics is nothing but a "scarecrow" per se, non-disturbing at the very worst.
The main pitfalls(not unique to mathematics) a person falls into are called "biases" and "fallacies" which have evolutionary advantages but blocks the person from having a proper comprehension of the real world. For example, "wishful thinking", as a fallacy, makes people not consider important variables that can alter the end result of a situation or an activity and then people make their plans with respect to the assumed situation, which is not the real situation itself. Survivorship bias makes a person think of the "survivor" of one situation as an extraordinary thing even though what is at play is just probabilistic. Similar biases and fallacies stray people away from taking a clear look to situations.