Teaching Statement
Ever since I started going to school, I have always known that I wanted to teach mathematics. Mathematics is a subject that I love dearly and am excited to share with other people - especially since I feel that so many students are being shortchanged in their education.
In my experience, mathematics is one of the most commonly feared and hated subjects taught in school. I believe this is largely due to the fact that students are not being taught in a way that helps them appreciate the fundamental nature of the subject. Since mathematics is something that often does not come naturally to students, it has been made easier by moving to a more procedural presentation rather than a conceptual one. Students memorize countless formulas and step-by-step processes for their exams, and promptly forget them when they are no longer needed. For example, factoring polynomials is a topic that requires some practice before it becomes instinctive. There are many ways to “teach” how to factor in an easy formulaic way, but this may mask what is actually at work (that is, the distributive property is being used in reverse). Teaching in this cookie-cutter fashion may make the subject easier, but it robs students of learning any valuable lessons that they can take away from the class.
I want to be a teacher so that I can give students a positive experience of mathematics. I believe mathematics has a unique ability for teaching people how to solve problems and think critically. Therefore, my emphasis is not on memorizing procedures and how to solve specific problems, but rather on teaching concepts that will help students develop the ability to solve new problems. The fact is that most students will never need to remember how to factor polynomials in their careers or daily lives - and so presenting mathematics in a way that solely revolves around memorization takes away from the true benefit of the subject. My hope is that students will no longer wonder why it is that they should learn mathematics - their education will help them see that its benefit lies in its ability to teach people, in a most fundamental way, how to think.
Three qualities that I have tried to cultivate in my classes are connections, patience, and flexibility. First, I think that students learn best when they are shown how different topics are connected. Too often, students are presented related ideas as entirely separate concepts. To avoid this situation, whenever possible I motivate new topics to help students understand where we have been and where we are going. Second, patience is essential to pedagogy. Students need to ask and be asked many questions, and even more importantly, they must be given time to answer them. Too often students are asked questions, but not given sufficient time to think about the solution before it is simply handed to them. Once this precedent is set, students learn they do not need to think in order to gain the answers they desire. Equally important to giving students sufficient time is carefully and patiently helping them when their answers are incorrect. I occasionally allow students to make mistakes so that they can figure out for themselves where they went astray, and thus will better understand their error. Furthermore, this sort of learning is good preparation for the real world, where it is rare to be correct on the first try. Lastly, flexibility is a vital skill. Everyone has a different learning method, and what “clicks” for one person may not for another. A teacher must be versatile, using many different modes of presentation, and must be able to find the explanations that work for different students.
As a teacher, I believe that my students should not be the only ones learning in my classroom. I must constantly be learning more about my subject and more about how to become a better instructor. To teach, and to learn how to teach, is one of my greatest opportunities and privileges.
In my experience, mathematics is one of the most commonly feared and hated subjects taught in school. I believe this is largely due to the fact that students are not being taught in a way that helps them appreciate the fundamental nature of the subject. Since mathematics is something that often does not come naturally to students, it has been made easier by moving to a more procedural presentation rather than a conceptual one. Students memorize countless formulas and step-by-step processes for their exams, and promptly forget them when they are no longer needed. For example, factoring polynomials is a topic that requires some practice before it becomes instinctive. There are many ways to “teach” how to factor in an easy formulaic way, but this may mask what is actually at work (that is, the distributive property is being used in reverse). Teaching in this cookie-cutter fashion may make the subject easier, but it robs students of learning any valuable lessons that they can take away from the class.
I want to be a teacher so that I can give students a positive experience of mathematics. I believe mathematics has a unique ability for teaching people how to solve problems and think critically. Therefore, my emphasis is not on memorizing procedures and how to solve specific problems, but rather on teaching concepts that will help students develop the ability to solve new problems. The fact is that most students will never need to remember how to factor polynomials in their careers or daily lives - and so presenting mathematics in a way that solely revolves around memorization takes away from the true benefit of the subject. My hope is that students will no longer wonder why it is that they should learn mathematics - their education will help them see that its benefit lies in its ability to teach people, in a most fundamental way, how to think.
Three qualities that I have tried to cultivate in my classes are connections, patience, and flexibility. First, I think that students learn best when they are shown how different topics are connected. Too often, students are presented related ideas as entirely separate concepts. To avoid this situation, whenever possible I motivate new topics to help students understand where we have been and where we are going. Second, patience is essential to pedagogy. Students need to ask and be asked many questions, and even more importantly, they must be given time to answer them. Too often students are asked questions, but not given sufficient time to think about the solution before it is simply handed to them. Once this precedent is set, students learn they do not need to think in order to gain the answers they desire. Equally important to giving students sufficient time is carefully and patiently helping them when their answers are incorrect. I occasionally allow students to make mistakes so that they can figure out for themselves where they went astray, and thus will better understand their error. Furthermore, this sort of learning is good preparation for the real world, where it is rare to be correct on the first try. Lastly, flexibility is a vital skill. Everyone has a different learning method, and what “clicks” for one person may not for another. A teacher must be versatile, using many different modes of presentation, and must be able to find the explanations that work for different students.
As a teacher, I believe that my students should not be the only ones learning in my classroom. I must constantly be learning more about my subject and more about how to become a better instructor. To teach, and to learn how to teach, is one of my greatest opportunities and privileges.