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My primary goal in teaching is to make each of my students an ``active learner.'' Besides teaching my students mathematics, I teach them techniques on how to study, how to take notes, how to read the text, and how to help each other working in groups. Raising the number of ``active learners'' in the class raises the interest of the whole class because there is a lot more participation.
Since my primary goal is to make sure that most of my students participate actively, the first week of class is probably the most important, and in particular the first day. I spend a good amount of time on that first day talking with them, learning their names, and giving them information on me and on the course. Their first homework assignment is always to send me an e-mail with some information about themselves, and I answer those e-mails one by one, addressing any concerns they might have. During the rest of that first week, I try to convey the message that they can get a lot more work done in the same amount of time if they spend their time wisely. I give them a list of tips on how to study, how to take notes, and how to read the text making the most out of it.
To keep my students active during the rest of the semester, I have them work in groups several times, and I encourage them to work together outside of class. I use group work a lot when I am reviewing the material before a test. I either assign problems for each group to work on and then report to the rest of the class, or I ask each group to come up with a list of possible test questions on an assigned topic.
The paragraphs above describe the core of my teaching philosophy, and I would use them when teaching any subject. When teaching mathematics, though, there are also two problems that I like to address on the first day of class.
To solve these two problems, I first of all point them out to the students. I tell them right away on the first day of class that it is possible that they might have to change the way they think about mathematics to succeed in my class. If it is a lower level course where most of the students in the class are not science majors, and they are there just to satisfy a requirement, I tell them that they can use the class to their advantage. I tell them that they were required to take the course because trying to think about those mathematical problems will help them in their lives. Memorizing formulas does not help much, but thinking in a certain way to solve problems does. I also tell them not to worry, because I am there to help them, and I will make sure that they succeed as long as they are willing to follow my instruction and put forth their best effort.
To address the second problem, I tell them right away that every homework assignment will have a few questions that I have not shown them how to do in class. They are expected to use all that they learned in class and common sense to solve them, and they can ask me if they cannot figure it out, so that I can point them in the right direction. I also tell them that there will be at least one such ``brain-teaser'' question on every test. Most students are very surprised when I show them the solution to those harder questions during the first couple of weeks of class. ``That was so easy,'' they say. After a month or so, most of them start enjoying these challenging problems and come to appreciate the value in learning to reason mathematically.
Last updated on November 11, 2005.