TEACHING PHILOSOPHY

Below is my teaching philosophy.  To view sample lessons that correspond with each aspect of my teaching philosophy, click on the heading.

            Teaching mathematics to students at the secondary level is a challenging and exciting job.  Throughout my Junior Field Experience and Student Teaching Experience, my style of teaching has evolved.  Although I began these experiences with some preconceived notions of what type of teacher I wanted to be, and which teaching strategies I wanted to employ, being able to work with students in the classroom has truly impacted the way I teach today.  There are four key aspects of teaching mathematics that I feel define the classroom I desire to create:  cooperative learning, reasoning through written explanation, technology, and discovery learning.

COOPERATIVE LEARNING

            Learning to work with other students is a valuable skill in the mathematics classroom, as well as in the real world.  In my classroom, students are required to work with various classmates to complete tasks.  This creates a student-centered environment, in which each student is comfortable enough to share their thoughts and ideas without feeling threatened.  Each student has a role in working in a group setting, and each student is held accountable to learn and teach one another.  Cooperative learning allows students who are struggling with difficult material to benefit from being taught by students who have a better understanding of those specific concepts.  Students who often grasp material easily benefit from being exposed to other ways of thinking and solving problems.  I am an advocate of the idea that “the best way to learn is to teach”.  As a result, if students can teach each other, they can learn the material efficiently.

TECHNOLOGY

            In order to keep up with the fast pace of today’s world, technology plays a key role in my classroom.  Students’ lives today are centered around technology in so many ways, and being adept in this area can greatly improve their ability to learn in school.  Fortunately, there are a variety of ways in which technology can be incorporated with mathematics, especially at the secondary level.  Whether I use graphing calculators to supplement a lesson, guide students to use the Geometer’s Sketchpad when they are learning about properties of shapes, or show PowerPoint and Microsoft Excel presentations when teaching about different topics, I strive to employ many technological elements in my classroom on a daily basis.  The visual flexibility of different technology programs accommodates various types of learners, and can make somewhat unclear topics easier to understand.  In addition, employing technology in the classroom allows me, as a teacher, to transition between topics and problems easily.  When students are familiar with such programs and have grown up in a generation in which they enjoy using this equipment, it creates an excitement and enthusiasm about mathematics. 

REASONING THROUGH WRITTEN EXPLANATION

            After learning about the results of the TIMMS study, one area which I feel should be addressed in my classroom is students’ ability to reason.  In comparison with other countries, students in the United States lacked a strong conceptual understanding of mathematics.  I believe that this is due to mathematics teachers’ failure to provide students with adequate time to develop conceptual understanding, and express their understanding through written reasoning.  During  my student teaching experience, I spent a great amount of time allowing students to do activities which would enforce important mathematical concepts and asking questions which would require them to think critically, instead of using class time to review a multitude of examples and ask questions requiring    one-word answers.  Students were then assessed (through oral discussion, formal assessments, and journal entries) on both their ability to solve problems and their ability to write how and why they solved such problems in the way that they did.  Students today are suffering because they are not encouraged or taught how to express their mathematical ideas in words.  If they are given the opportunity to write exactly what they are doing, and provide reasoning for why they are doing it, I believe that students will show tremendous improvement in their conceptual understanding of mathematics.

DISCOVERY  LEARNING

            My inquiry project this semester was based on the effects of discovery learning.  In each of my classes, I guided the students in completing many activities in which they “discovered” mathematical concepts individually and in cooperative learning groups.  I did this primarily through the use of manipulatives and technology.  I would allow the students time to try to complete tasks on their own, and then guide them to make discoveries through oral questioning and direction, when necessary.  Students were often encouraged to make conjectures about the material they were manipulating, and ultimately, I would provide the students with the formal definitions, postulates, theorems, etc., to provide further reinforcement of such ideas.  Discovery learning activities allowed me to be consistent with my goal of developing the students’ ability to reason and gain more conceptual understanding of material.  Although it is not practical or possible to use discovery learning activities every day in the mathematics classroom, I used this teaching strategy as much as possible.  It allowed me to keep students’ interest and motivate them to learn new material.  It also helped them to become responsible for their own ability to learn, and ensured that they think critically in order to make and verify conjectures.   I was pleased after analyzing the effects of discovery learning; students generally showed much improvement on assessments, when asked questions about specific concepts.  They also seemed to retain this material from chapter to chapter, which is an essential quality in every successful math student.

            Through cooperative learning, technology, reasoning through written explanation, and discovery learning, I feel that I positively impact my students.  I strive to vary my teaching strategies, while focusing on these key aspects when in the classroom.  Being enthusiastic and truly caring about the way in which students learn has allowed me to develop and practice this teaching philosophy.   I know that this teaching philosophy will change as I continue to teach.  I will always make every effort to develop into an effective and influential teacher of mathematics.

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