Hernando Burgos Soto

• Teaching Experience
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• Teaching Philosophy

Statement of Teaching Philosophy

Learning is the process whereby an individual passes from one level of knowledge to a higher level of knowledge. This process involves: subjects, which are what the individuals learn and actions which are what individuals do or perform with the subjects. Therefore I conceive learning as a continuous movement, not only because it is a sequence of different status or levels, but also because the individuals have to act over the subjects—they need to use, modify, compare and state relations among them.

Teaching is the set of actions by which I help students to learn. It is the process in which I construct the bridge between different levels of knowledge and help students to cross it. It is the final decision for the student whether to cross it or not but I feel that is my obligation to give them the hand and guide them to cross it.

There is no such a thing as a zero level of knowledge or a complete level of knowledge. The students always come to class with some level of knowledge and I feel obligated to have them leave the class with a higher one, which is in fact an intermediate level, since afterwards it becomes the initial level for the next class, and so on for the next step in their life. I expect my students leave the class room with higher level of knowledge, and recognize that this is not the final one. I hope they recognize that and try to attain even higher levels after leaving the class room.

When I am teaching, I present students with the objects they need to learn and allow them to interact and to state relations among these objects. If I am preparing to teach measures of central tendency, for example, I think of the objects that my students need to know, i.e., mean, median, mode, etc. I know that these objects by themselves mean nothing if the students do not interact with them. So I think of the operations that students need to do with these objects, i.e., what actions they need to carry out, what problems they need to solve using these measures and why they are useful. I present problems and encourage them to solve them using the mathematical tools given in class. They need to state the relations, compare the different measures of central tendency and compare them with the other kind of measures.

Their passing from one level of knowledge to the other is achieved through the action of the individual over the learned object. So I do not believe that thing could be achieved if either I or the students are in a passive position. All the process is action, so the students and I need to act. The more we act the more we learn. The students interact with the subject that they learn, when they observe, read, listen, draw figures, ask question about the subject, give opinions, write, solve problem using it, etc.

Nothing acts without an impulse or without a motive. So I usually present at the beginning of the class the need and the purpose of the subject. Then I use what they already know. If I am teaching to add algebraic polynomial, I know that they are familiar in adding apples, so I am going to start from this situation, which is a part of what I call the first level of knowledge. Students need to be awake to act, hence I never appear memorized. I speak spontaneously with enthusiasm, with eye contact, showing pleasure for what I am doing, and using visual aids, whenever is possible. I guide learning by helping students individually, lecturing and encouraging class participation. Always acting and trying to keep my student motivated to act.

In the same way I don’t believe in a complete level of knowledge; I don’t believe in a final goal. In my opinion, the successful completion of a goal is an intermediate step in an endless chain of purposes. Therefore, my preferred word in this matter is “continue”. Thinking in this way, my teaching objectives are to:

• Have empathy for my students
• Continue to research about the difficulties some of them find understanding mathematical subjects
• Continue to find new ways to connect with my students
• Get them interested in questions associated with Mathematics and understand how these questions’ answers can be applied to solve problems in their field of study or in the real life.

To achieve that, I try to keep my skills up-to-date. I am a continuous learner and a continuous researcher. I know that the more tools I find in my life the more opportunities I have to get my students acting over the subject they learn.