Pedagogical Philosophy
“The
mediocre teacher tells. The good teacher explains. The superior teacher
demonstrates...
The great teacher inspires." – William Arthur Ward
The most effective teachers are those who make a lasting impact on their students’ lives. In order to do so, my role as a mathematics teacher is not only to provide students with a challenging curriculum that results in a firm grasp of mathematics content, but also to prepare students with the tools and skills they need for success later in life. Students will leave my classroom as experienced mathematical thinkers, problem-solvers, collaborators, and life-long learners who have confidence in their mathematical abilities and possess the skills necessary for successful, productive, and active contribution to 21st century society. The following five key components ground my beliefs about mathematics education and drive my instructional practice for the purpose of achieving these goals.
First, it is my firm belief that achieving mathematical excellence requires students to develop a deep conceptual understanding of mathematics that stretches beyond rote memorization and mindless calculation. Teachers must promote students’ understanding of the reasons why certain mathematical procedures are implemented. I believe that engaging higher order thinking skills through problem-solving activities is essential to achieving this goal. In my classroom, I engage students in mathematical inquiry through collaborative discovery activities and investigations. Students work together to develop a deep understanding of the intricate relationships between graphical, numerical, and analytic representations of mathematical solutions. As a result, they learn to form and test conjectures, to develop the art of problem-solving, to search for solutions by asking logical questions, and to communicate their ideas to peers. Developing these skills will help students to eventually reach a point of true understanding, that ‘aha' moment in which mathematics concepts really begin to make sense on the abstract level.
Second, confidence is often a precondition for reaching high levels of achievement in mathematics. For many students, however, it can also be a barrier to success. Anxiety about mathematics can take away the enjoyment and appreciation of the subject, causing students to overlook its value and beauty. Thus, it is my role as a mathematics teacher to establish a supportive, respectful, and collaborative mathematics community in which students are encouraged to ask questions, voice their concerns, and discuss their thinking processes, so they can actively engage in and enjoy learning. I believe that creating an environment that fosters collaboration and ownership of mathematics is essential to building students’ confidence in their mathematics abilities. Communication skills, openness to new ways of thinking, and willingness to exchange ideas are all extremely important qualities for students to thrive not only in high school, but in college and beyond. Peer-to-peer interactionsand discussions enhance learning because they provide opportunities for students to scaffold and teach each other; it is through the act of teaching that one develops the deepest form of mathematical understanding. For these reasons, I am a strong advocate for group work and collaborative learning in mathematics education.
Third, our schools are enriched by diversity; students come from a variety of racial, ethnic, cultural, linguistic, academic, and socioeconomic backgrounds, and possess multiple learning styles and abilities. In a mathematics classroom, this is often demonstrated through the rich variety of approaches that students bring to solving problems. Therefore, it is important for teachers to use many different instructional techniques, learning activities, and assessment strategies in order to provide all students with the opportunity to achieve at maximum level. I address the needs of diverse learners in my classroom by creating a balance between teacher and student-directed learning activities, presenting and explaining mathematical concepts in multiple ways, developing creative approaches to assessment that allow students to showcase their skills in alternative ways, and involving students in their own learning as much as possible.
Fourth, in order to become life-long learners who are prepared to adapt to a changing world, it is essential for students to learn how to self-regulate and take responsibility for their own learning. This view is reflected by John Dewey who states that “to prepare [a child] for the future life means to give him command of himself.” Thus, mathematics teachers must communicate to students the value and rewards of taking responsibility for their own learning, and teach students the self-regulatory skills necessary to do so. In my classroom, this involves teaching students how to organize known information, to ask the right questions to seek knowledge, and to recognize and advocate for themselves when they need help. Since I continually emphasize the importance of effort in my classroom, students learn that if they put effort into learning, they can achieve greatness.
Finally, due to the abstract nature of many mathematics concepts, it is the responsibility of teachers to make mathematics meaningful to students' own lives. In my classroom, this means providing students with real world applications of math problems and with opportunities to research how mathematical modeling is applied to issues of interest and relevance to their lives. Demonstrating how mathematics is applicable to students’ lives increases its value in their minds, and therefore, assists in engaging students and motivating them to take interest in their learning.
Simply stated, I believe that the universal goal for teachers is to provide students with the most intellectually stimulating, useful, and meaningful educational experience possible. In order to achieve this goal, teachers must act as guides, providing students not only with the content knowledge to promote academic excellence, but also with skills for life-long learning and success in 21st century society. In mathematics education, this involves fostering a deep conceptual understanding of concepts, helping students to become effective problem-solvers and critical thinkers, promoting a collaborative environment so that students develop fluency in the language of math, catering to the individual needs of diverse learners, emphasizing the importance of responsibility and effort in learning, and making mathematics relevant to students’ lives.