Math With Galina: Education Philosophy

Education Philosophy Statement

Introduction

My views of education in general and in mathematics education in particular are based on experiences obtained in two extremely different countries. In general, immigration is an experience that tests a person’s survival skills, challenges him or her to make sense of a new reality and to adapt an established philosophy towards that new world. Changing philosophical perspectives requires an enormous amount of time, so I must confess that my philosophy of education continues to evolve as I change in my new country. In addition, education and educational practices renovate over time to accommodate needs of every society. Thus, I view my education philosophy as a work in progress.

Russian experience

I was born in Moscow, Russia in a family that for generations valued high quality education. I was expected to perform excellently in school without questions or doubts, so I obliged. In grade seven or eight, I decided to become a mathematics teacher despite everybody’s opinion that a successful graduate from the “Special English School” had to pursue a career that incorporated knowledge of English. I was enrolled at this school as a result of an entry exam given in a second grade. My family could not understand my decision to become a teacher of mathematics, so I had to argue my case and present reasons in favor of both mathematics and teaching. This argument lasted for several years and marked the starting point of my education philosophy.

Why did I choose mathematics, and, more specifically, why did I want to teach it? In Russia, a person had to actively demonstrate support for Communist Party proclamations, especially in the fields of literature, history, economics, and arts. There were only few areas in which a person could argue or challenge opinions: mathematics and hard-core sciences like physics. Even the fields of biology and genetics were under Communist Party control. So, it was not surprising that I picked mathematics as a field associated with greater freedom. In addition, I appreciated the solid beautiful construction of mathematics; it could never be changed by the latest decision taken at a Communist Party meeting.

My mathematics teacher from grades four through nine had a major influence on both my learning of mathematics and my attitudes towards it. In Russia, students remained with the same subject teacher through many grades. This teaching organization fostered trust and bonds among students and teachers. Our mathematics teacher encouraged us to solve interesting problems, to present and defend our solutions, and to evaluate each other’s opinions in a constructive critical manner. As a result, I perceived mathematics as an area in which one was permitted the freedom to critique or challenge other people’s opinions and was supported in reasoning and proving his or her point of view.

In contrast to pure mathematics, teaching was under the political party control. However, the teaching of mathematics was less controlled than the teaching of history or literature. Teachers of mathematics could encourage students seeking alternative strategies to solve problems or to use different ways to prove theorems. As a result, I chose mathematics teaching in order to share the same opportunity given to me when I was a student to learn how to think critically, to future students.

Moreover, in Russia, the field of mathematics was a rare place where students could learn critical and creative thinking skills. Later, when I became a mathematics teacher, I started to realize that challenging Russian students in mathematics was a “secret weapon” to raise their critical abilities and to fulfill a dream to change the world. To live in a democratic society, a new generation had to be educated. I had a dream that I could make a difference in the world around me.

During five years at the Moscow State Pedagogical University, I took many advanced mathematics courses (e.g. multivariate calculus, analytical geometry, advanced algebra, etc.), courses in elementary mathematics and problem solving, courses in pedagogy and methodology of teaching mathematics, and field practices. I was taught mathematics in the traditional Russian manner: lectures, seminars, a multitude of routine exercises and solving numerous application problems. Problem solving, and inquiry methods were used intensely in mathematics courses. Inquiry in the mathematical university classroom included solving difficult problems, posing and testing hypotheses, reflecting on results, checking the results, and searching alternative solutions. Learning mathematics at the university was challenging and exciting for me.

My university pedagogical courses included cognitive psychology and methods of teaching middle and high school mathematics. The study of elementary mathematics combined with teaching methods gave me a fundamental perspective of how to teach key mathematical ideas to students of different ages and how to accommodate students with different learning styles.

The course, History of Pedagogy, also gave me a unique perspective of teaching children in Russia and other countries. My studies included the influences of Locke, Vygotsky, Kaminski, and Piaget in the field of education. I learned that one of Locke’s major contributions to educational theory was introduction of concept of "the tabula rasa." All individuals enter the world as equals with their minds at a blank state. Locke suggested several "commonplaces" or ordinary assumptions, some of which were then popular in Russia. According to one of his assumptions, education is dependent on the securing of right habits of thought and action. He asserted that children are not mature enough to understand why they need to perform habitually. Thus, adults are responsible for setting up correct examples of behavior and force children to follow these examples.

Authority resides in the hands of adults and children are treated as recipients of adults’ knowledge and values. In Russia, I shared Locke's radical traditional position in education and I believed in teacher-centered classroom and in securing students’ right habits through mathematical problem solving. Since then my educational views shifted from traditional teacher-centered to students-centered education, yet, I still believe in securing habits of mind through critical thinking and mathematical problem solving.

Mathematics curricula in Russia were based partially on Piaget’s theory with the addition of Vygotsky’s perspective. I used Piaget's approach to identify students' development level and Vygotsky's idea of a zone of proximal development. This allowed me to separate what learners definitely knew and could accomplish independently from what they could do with guidance from more mature peers or me. According to Vygotsky, instructor questions, tasks, and encouragement can promote students’ intellectual development. Vygotsky proposed leading intellectual development by providing challenging opportunities for a child to move forward in his or her development. I was moved by Vygotsky’s view about looking at a child’s potential. I still believe in promoting intellectual potential and growth of each student by demanding high learning standards, by expressing high expectations of students, and by providing challenging activities.

Even though my university training left me with a traditional teaching philosophy according to which the teacher controls the learning process, I was open-minded about learners’ potentials. I enjoyed promoting students’ active learning, their mathematical thinking, and “pushing” them to the next intellectual level.

My university education and my teaching practices in Russia convinced me that creative problem-solving and critical thinking lay at the heart of learning and teaching mathematics and, therefore, had to be at the center of my educational philosophy. Try to imagine my cultural shock when I started teaching college mathematics in the United States and on my first day students revealed to me that there was only one right way to solve a mathematical problem. I was told that I had to tell them the steps they could memorize, practice, and follow! I was told that debates, discussions, and alternative approaches were appropriate for humanities but not for mathematics. Before teaching in America, I had thought that discussions were forbidden in history not in mathematics. I was shocked to find myself in what seemed to be a mirror image of teaching in Russia: what was right became left or maybe it became wrong.

At first, I felt devastated and thought of changing professions. Having a strong background in mathematics opened some opportunities, while friends expressed concerns about the poor quality of mathematics teaching in American schools and advised me to switch to computer programming, a profession that was “less stressful and more profitable.” I argued for staying in education. I tried to convince my Russian friends that pitfalls existed in any field, that it was easier to criticize education in America or Russia, than to do something constructive about difficulties. I still had a dream that I could make a difference in lives of American students as I had tried earlier for Russian students.

I decided that the battle was not over, and I still needed to fight, even though I had not expected to do so. Up until then, I had experienced fighting and starting over again and again. Almost a year before my family was permited to immigrate from Russia, I started my dissertation research on assessing problem-solving abilities of students. I was made to quit because we applied for immigration. We wanted to be free to express our religious beliefs. We had to move quickly because we did not think that the window of opportunity to leave Russia would last. We were refugees who dreamed of freedom to work, study, and live our lives without Communist Party control.

American experience

Before my first encounter with teaching mathematics to American college students and finding out that they thought that there was only one right way to do a mathematics problem, my first American job was as a kindergarten teacher in the Kinder Care Learning Center. Since I did not have any experience working with children in grades K-3 in Russia, I decided to take evening classes at the North Shore Community College. Working with five-year olds and taking courses Introduction to Child Study, Programs for Young Child, and Expressive Arts for Children marked the beginning of my American education and a shift in my education philosophy. I learned how to balance keeping children happy with demanding active learning to read and count, how to infuse serious learning into games, and how to have fun and relax while learning and working. Although I had some experience with combining games and learning reading and mathematics with my own children in Russia, the idea of fun and relaxation in a school setting was completely foreign to me.

Later when I was enrolled in my doctoral program at Boston University, reading Dewey’s chapter “Play and Work in the Curriculum” in Democracy and Education (1916) helped me to realize how my early American experiences had changed my perception of education. Here, I was to learn of the vital role played by each learner’s experiences that are brought to the classroom as a starting point of teaching, rather than goals based on pre-planned curriculum. In Russia, we had a national mathematics curriculum with well-defined goals, scope, and sequences. As a result, in Russia, I had to prepare my classes and teach based on what was defined and required by the Ministry of Education. Although I used feedback from students regularly and assessed continuously whether they understood a topic, I rarely planned my classes based on students’ experiences outside the school in Russia.

Dewey and Bruner were the main figures who influenced my American teaching and changed my philosophical position from traditional to progressive education.

In Democracy and Education (1916), Dewey discusses three kinds of instruction. The first, which treats each lesson independently, is the least desirable as Dewey argues. The second is better because teachers try to guide students to utilize the earlier lessons for understanding the present one, but school subject matter is still isolated here. It is, however, the third type of teaching which encourages students to apply their knowledge and make connections with everyday life that I find is the best kind of teaching. In Russia, I used the third type of teaching without knowing that Dewey had suggested it. I still share Dewey’s view that teaching is only successful if students are able to understand obtained knowledge. I always make sure that my Wheelock students understand relevance of the mathematics they study.

Dewey (1916) also stressed the vital role of teaching thinking. Teaching thinking has been a focus of my education philosophy since I started working in Russian schools. I still believe that teaching thinking is the ultimate goal of modern schooling. I try to provide mathematical activities that promote students’ thinking in every class. When class is over I reflect on what students have learned and what type of thinking has been used.

In The Process of Education (1960), Bruner discusses intuitive and analytical thinking and stresses the complementary nature of both types of thinking. I agree with Bruner that both types of thinking should be taught in schools since both are necessary to approach and solve real life problem situations. In mathematics, it is easier to teach analytical thinking skills (e.g. solving equations) than intuitive thinking. However, when I ask Wheelock students to guess a problem answer or predict a next number in a pattern, I teach students to think intuitively.

In my opinion, thinking and problem solving are the most fundamental capacities that all students need. I inspire and encourage my students to think creatively, to go beyond what is taught, and to learn mathematics by doing. For example, to promote geometrical thinking of future teachers in MAT 140-141, I do visual proofs to build confidence of the truthfulness of a theorem; then, I introduce students to rigorous formal proofs. To prove visually that the sum of the angles of a triangle is 180 degrees, students draw triangles, cut them, tear angles, put angles together, and see that the angles form the straight line (angle) which is 180 degrees.

In addition to teaching thinking, my American philosophy of education includes the vital role played by learners’ experiences. In Democracy and Education (1916), Dewey stresses that learning demands both experience and thought. Thinking or reflecting on experiences allows learners to act with an aim in view and to accept future responsibilities that flow from present actions. Through thinking individuals achieve the formulated experience which is the turning point in the learning process. I have concluded that curricula should be constructed around student's experiences. Therefore, my role is not to direct but, rather, to facilitate and advise.

Dewey also suggests that a student is the center of education. From Dewey, I need to know every student in order to teach mathematics to all of them. I incorporate students’ background into learning, share authority over learning with students, and am in charge without dominating students. When I combine “experience and thought,” students are motivated to learn mathematics and actively participate in class. I passionately believe that learning experiences should combine thinking and doing to move students to better understanding. If they do both, all students can learn mathematics and achieve high levels.

At Wheelock College, we want to actively improve the lives of children and families. To reach this goal, we build our programs based on the assumption that all our students can learn and learn at high levels. I teach with this assumption in mind. I teach all students to be educated mathematically and reach the optimum of their potential. I teach all students how to approach problem situations, how to think, how to reflect on their thinking, and how to deal mathematically with this rapidly changing world.

I think that we must provide equal educational opportunities to all students and establish a positive intellectual climate for learning. I am aware that different students need different time to achieve high levels. I tailor curriculum materials to fit capacities and needs of all students. Adjusting curriculum materials to individual differences is a difficult task but I take the challenge seriously. I use different pedagogical techniques to accommodate students’ differences such as: class and small group discussions, inquiry learning, adaptive teaching, and cooperative learning. I guide every student to her or his maximum level.

Based on my education philosophy, I developed the following teaching goals:

· Teach mathematical content to all students and show the relevance of mathematics

· Teach mathematical thinking and reasoning to all students

· Base teaching on students’ learning experiences

· Address students’ different learning styles

To be able to reach these goals, I need to be a student myself and continue to learn and grow professionally. I expand my knowledge about teaching by reflecting on students’ feedback, by discussing mathematics and pedagogy with my colleagues at Wheelock, by attending and presenting at professional conferences, and by my scholarly work.

References

Bruner, J. S. (1960). The process of education. Cambridge, Harvard University Press.

Dewey, J. (1916). Democracy and education: an introduction to the philosophy of education. New York,

Macmillan.