PHILOSOPHY OF MATHEMATICS EDUCATION
I love mathematics! However, how many school-aged students can truthfully say this? To most people, mathematics consists of hard-to-read textbooks, numerous worksheets, and boring lectures. In reality, mathematics is much more: mathematics is a way of knowing. Mathematics is asking questions and then using ways to try to find the answers, often discovering more questions in the process. Mathematics is a way of learning about the world we live in. Beyond that, mathematics teaches one how to think, question, investigate, solve problems, and how to apply these skills to all areas of life. As a mathematics teacher and “ambassador” of the educational community, I want to transform the classroom from a virtual lecture hall to an interactive investigating society where mathematics will be an active inquiry process filled with the wonderment and excitement of discovery.
First, mathematics education is much more involved than learning about mathematics. Mathematics is not an isolated activity. Students can acquire a mathematics mindset without becoming a professional mathematician. Even if the students, once out of school, remember nothing about the mathematical content, more encompassing principles can be ingrained into their life. Mathematics, if taught in the right way, can teach students how to learn, to think independently, and to solve problems.
Mathematics, to me, is synonymous with learning. Learning is gaining knowledge, comprehension, and skills through experience and study. But could not this definition be for mathematics also? Mathematics teaches one how to ask questions and how to find answers to those questions. Learning is not merely the means to an end product; it is also the process. Likewise, mathematics is as much a journey as it is a destination.
Furthermore, mathematics teaches people to think independently. Mathematics is not always black and white, right or wrong. Mathematics is conducted according to the particular procedures that are applicable to the question or problem and methods that conform to the personal preference of the individual rather than a rigid procedure for all investigations. Students are good at modeling; they often memorize steps and specific procedures teachers use without understanding the concepts or purposes behind them. Consequently, mathematics teachers need to teach the thinking process behind the steps as a predecessor to having them think on their own. Mathematics can give students the freedom to develop their own mental processes when given the opportunity to explore.
Mathematics also has lifelong application in developing critical thinking skills to solve problems. In the world there exists no solution manual. Problems in life do not just include recalling information for a multiple-choice test. They require analysis, synthesis, and evaluation. Mathematics can help students practice these higher thought processes.
My purpose as a mathematics teacher is to direct and facilitate meaningful learning. A mathematics teacher should not be a dictator but rather a guide. Teachers need to challenge students to accept and share responsibility for their own learning. Three ways to accomplish this goal are to use an inquiry-based mathematics program in the classroom, to provide an environment where innovative learning can occur, and to relate all learning to the unifying concepts and processes of mathematics.
Mathematics teachers must base their mathematics program on inquiry. Inquiry involves generating questions, collecting evidence through investigation, and proposing explanations. These processes, which are integral to constructing scientific knowledge, are opportunities for critical thinking. Inquiry enables students to learn the mathematical concepts, learn to apply the knowledge to mathematics and life, and give the students the joy of accomplishment in discovery.
Likewise, mathematics teachers guide meaningful learning by creating a learning environment that provides students with the time, space, and resources needed for innovative learning to occur. It is imperative to structure my class periods to allow time for students to conduct exploratory investigations. My classroom must also be a setting which is flexible and supportive for student inquiry. To allow student inquiry, I must be willing to incorporate my students’ ideas and questions about mathematics concepts and societal issues in meaningful mathematics lessons. For worthwhile learning to occur through inquiry, tools, materials, and technology should be made available to assist the students’ exploration. Ultimately, I want to guide my students to design their own learning environment whether in my classroom, in other classrooms, or in life.
Meaningful learning also occurs when every concept can be related to a unifying concept or process of mathematics. These integrative principles help students see the “big picture.” New knowledge is not just isolated bits of information; all new knowledge should be integrated purposefully into the schemata of the unifying concepts.
In order to expect my students to continue developing their inquiry, I must model continued learning in my professional development. Learning is a life-long process. By applying the principles I teach in the classroom such as inquiry, reflection, interpretation of research, and guided practice, I can build understanding and skill in mathematics teaching. I must also utilize the opportunities to expand my knowledge by reading mathematical literature, by attending seminars hosted by professional organizations, and by collaborating with other mathematics teachers for feedback on my teaching. Mathematics teaching can easily become stagnant if it is static. For my teaching to continue to be effective and pertinent, I have to engage is continuous self-reflection.
Overall, mathematics is an integral part of students’ education. Mathematics encompasses much more than an hour-period in a school day. It is a way of quenching our curiosity of the way our world operates. Mathematics, like learning, is a lifelong process. My underlying mission as a mathematics teacher is to be a representative of “true” mathematics to my students, reviving the childlike wonder, awe, and love of inquiry, discovery, learning, and knowing. Let the journey begin!
I love mathematics! However, how many school-aged students can truthfully say this? To most people, mathematics consists of hard-to-read textbooks, numerous worksheets, and boring lectures. In reality, mathematics is much more: mathematics is a way of knowing. Mathematics is asking questions and then using ways to try to find the answers, often discovering more questions in the process. Mathematics is a way of learning about the world we live in. Beyond that, mathematics teaches one how to think, question, investigate, solve problems, and how to apply these skills to all areas of life. As a mathematics teacher and “ambassador” of the educational community, I want to transform the classroom from a virtual lecture hall to an interactive investigating society where mathematics will be an active inquiry process filled with the wonderment and excitement of discovery.
First, mathematics education is much more involved than learning about mathematics. Mathematics is not an isolated activity. Students can acquire a mathematics mindset without becoming a professional mathematician. Even if the students, once out of school, remember nothing about the mathematical content, more encompassing principles can be ingrained into their life. Mathematics, if taught in the right way, can teach students how to learn, to think independently, and to solve problems.
Mathematics, to me, is synonymous with learning. Learning is gaining knowledge, comprehension, and skills through experience and study. But could not this definition be for mathematics also? Mathematics teaches one how to ask questions and how to find answers to those questions. Learning is not merely the means to an end product; it is also the process. Likewise, mathematics is as much a journey as it is a destination.
Furthermore, mathematics teaches people to think independently. Mathematics is not always black and white, right or wrong. Mathematics is conducted according to the particular procedures that are applicable to the question or problem and methods that conform to the personal preference of the individual rather than a rigid procedure for all investigations. Students are good at modeling; they often memorize steps and specific procedures teachers use without understanding the concepts or purposes behind them. Consequently, mathematics teachers need to teach the thinking process behind the steps as a predecessor to having them think on their own. Mathematics can give students the freedom to develop their own mental processes when given the opportunity to explore.
Mathematics also has lifelong application in developing critical thinking skills to solve problems. In the world there exists no solution manual. Problems in life do not just include recalling information for a multiple-choice test. They require analysis, synthesis, and evaluation. Mathematics can help students practice these higher thought processes.
My purpose as a mathematics teacher is to direct and facilitate meaningful learning. A mathematics teacher should not be a dictator but rather a guide. Teachers need to challenge students to accept and share responsibility for their own learning. Three ways to accomplish this goal are to use an inquiry-based mathematics program in the classroom, to provide an environment where innovative learning can occur, and to relate all learning to the unifying concepts and processes of mathematics.
Mathematics teachers must base their mathematics program on inquiry. Inquiry involves generating questions, collecting evidence through investigation, and proposing explanations. These processes, which are integral to constructing scientific knowledge, are opportunities for critical thinking. Inquiry enables students to learn the mathematical concepts, learn to apply the knowledge to mathematics and life, and give the students the joy of accomplishment in discovery.
Likewise, mathematics teachers guide meaningful learning by creating a learning environment that provides students with the time, space, and resources needed for innovative learning to occur. It is imperative to structure my class periods to allow time for students to conduct exploratory investigations. My classroom must also be a setting which is flexible and supportive for student inquiry. To allow student inquiry, I must be willing to incorporate my students’ ideas and questions about mathematics concepts and societal issues in meaningful mathematics lessons. For worthwhile learning to occur through inquiry, tools, materials, and technology should be made available to assist the students’ exploration. Ultimately, I want to guide my students to design their own learning environment whether in my classroom, in other classrooms, or in life.
Meaningful learning also occurs when every concept can be related to a unifying concept or process of mathematics. These integrative principles help students see the “big picture.” New knowledge is not just isolated bits of information; all new knowledge should be integrated purposefully into the schemata of the unifying concepts.
In order to expect my students to continue developing their inquiry, I must model continued learning in my professional development. Learning is a life-long process. By applying the principles I teach in the classroom such as inquiry, reflection, interpretation of research, and guided practice, I can build understanding and skill in mathematics teaching. I must also utilize the opportunities to expand my knowledge by reading mathematical literature, by attending seminars hosted by professional organizations, and by collaborating with other mathematics teachers for feedback on my teaching. Mathematics teaching can easily become stagnant if it is static. For my teaching to continue to be effective and pertinent, I have to engage is continuous self-reflection.
Overall, mathematics is an integral part of students’ education. Mathematics encompasses much more than an hour-period in a school day. It is a way of quenching our curiosity of the way our world operates. Mathematics, like learning, is a lifelong process. My underlying mission as a mathematics teacher is to be a representative of “true” mathematics to my students, reviving the childlike wonder, awe, and love of inquiry, discovery, learning, and knowing. Let the journey begin!