In my opinion, students are the focus of teaching. The material needs to be presented in a manner that the student can best understand. Sometimes this means multiple presentations of the same material to educate all the students present.
Part of my task is to ensure they understand that I believe they can do the work. I communicate this through one-on-one conversations and instruction/tutoring, through personal experiences I have had in my own math career, and other anecdotal examples. I put their mind at ease that I am not here to hurt them with numbers, but rather help them understand.
While teaching, I ask for responses and answers. I ask for clarification of how they arrived at their answer, whether correct or not to verify their understanding of the process they are using. I present multiple pathways to finding solutions. I do not believe there is one way to solve any problem if the procedure they use is correct. The important thing about teaching math is giving the students the skills to explore different ways to find the solutions. Making math a puzzle to solve, rather than a monster to slay, using tools they are given or discover.
While working examples and procedures, I invite questions and ask a few of my own. I teach for understanding not simply trying to cover material. I seek a relaxed classroom, where students are unafraid to ask questions of me or each other and where students are just as willing to answer questions as I am.
学习是一个协作的努力。学习/研究groups help the learning process tremendously and I encourage group work in class and out.
Basically, do what is necessary to encourage learning, lessen confusion, and explain, explain and explain yet again, in as many ways as possible in whatever format possible till they all understand.
This is basically the same process I use in tutoring. With tutoring I can focus on one person or a small group of people, which focuses the teaching/tutoring to correcting misunderstandings, re-enforcing current understandings and building up confidence.
I have been teaching for 30 years now and I have always focused on student understanding and confidence in mathematics. I started on this path to teaching when I was in the 5th grade and decided I wanted to teach math when I was in High School Geometry. I went to college with that intent. Circumstances changed that path and I got a BA in Geology from Trinity University in San Antonio. When I was in my 30's, I decided to get back to my path of becoming a math teacher. I went to UTSA and picked up over 50 hours of math, got my teaching certificate and started teaching. In the early 2000's, I was given the opportunity through a grant to get my Master's in Mathematics at UIW in San Antonio. Two years after I received that degree, I started teaching at the college level for Alamo Colleges, starting at San Antonio College and ending up at Palo Alto College, where I currently teach.
Over the years, I have successfully tutored high school students who need help in their courses. Some of them needed reassurance in their skills, confidence in their abilities and understanding. Others needed some groundwork in their basic math and algebra so they could get caught up and succeed in their current classes.
I am a math/science/science fiction/puzzle geek. I play with numbers. I read/watch science fiction. I work different types of puzzle games and logic puzzle games. I like to have fun and play, and I do try to make my classroom/tutoring a fun and safe place to learn.