Delineates who you are as a mathematics educator-- what is your philosophy of education,of mathematics education, and your "world view" as to your role as an educator
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What is my philosophy of education?

        Throughout my education, I have developed three statements that describe my philosophy of education. First, education is about the desire to learn, not the obligation. The process of learning should be pleasurable, interesting, and helpful. Learning should not only be limited to schools. It should teach students should understand how to pursue, value, and love knowledge (or wisdom) and enjoy learning. Students would like to construct their own knowledge through understanding via gathering data, exploring the truth, analyzing the information, and making decision for their own learning.

        Second, education is a life-long learning process, which is indispensable. What students learn in schools is not enough to prepare for practical living. Students should be able to organize, understand, and apply what they learn in order to deal with the complex and diverse questions of their daily life. They should have the abilities to know how to use what they have learned and to continue to learn and create "new" knowledge to solve problems they meet when they leave schools.

        Finally, education is life. Education supports life; life (experience) connects to education. Students need to be educated to become a modern citizen for the needs a society. They also use their life experience in their learning. Hence, they need to think critically and solve problems independently.

        Further, as an educator, I use the following three questions to answer "what is my philosophy of mathematics education?"First, "why do we need to teach/learn mathematics?". Students usually ask this question when I taught mathematics in Taiwan. My answer to the question resembles that of Travers et al. (1977) : "mathematics is useful, mathematics is beautiful, and mathematics disciplines the mind". In addition, I suggest that mathematics is a pump, not a filter. It is a powerful implementation to help individuals think critically, solve problems mathematically, and satisfy the needs for their daily life (e.g. jobs) rather than hinder their learning.

        The next question that answers for me is "How do students learn mathematics?". Students need to learn independently and actively. They should think and understand what they learn. Learning for students is not a simple task, composed of only memorizing and practice. Students are active learners constructing their own understanding of concepts rather than "tabula rasas" to "copy"  knowledge directly from teachers. I believe that students learn best when they work cooperatively and develop understanding through using prior experience, discourse, and reasoning. In a word, this idea is a social constructivism, a student-centered, negotiated, and active mathematical environment. They can enjoy the delight of learning and gain the confidence from the process of exploring and building knowledge. This learning process is necessary for  constructing knowledge and solving problems through this kind of learning.

        The third question is "How do teachers teach mathematics?".  I always taught mathematics by lecturing and examination only in Taiwan. However, I do not think it the best teaching style for students'  learning. Form my five years of teaching experience, I that feel the role of a teacher is complex and diverse, rather a simple lecturer preparing well in classrooms. In addition to have the solid background knowledge of mathematics, effective teachers should have good instructional skills to teach, promote, and assist students' effective learning. Teachers are the guiders and facilitators, not transfers, of knowledge. They should motivate students to actively examine and extend their thinking, shape a conversational environment in which students share and construct their own knowledge, design instructions that enable students to learn by doing, align the curriculum according to standards and students'  assessment, and apply technology to improve teaching and leaning. In a word, teachers make the classrooms that maximize students'  learning.

        Finally, effective mathematics teachers should be able to apply advanced learning theories, teaching skills, and technology in mathematics instruction in order to really promote students'  mathematics academic performance and understanding, improve out-of-data instruction of teaching, and align curriculum to standards, etc. In addition, he/she should pursue his/her professional development constantly. It is an ideal situation for all mathematics teachers. I always look for the goal in order promote the level and improve the situation of mathematics education in Taiwan. Fortunately, I came here to study. I think the goal is not too far away.

Reference:

Travers, K. .J., Pikaart, L., Suydam, M. N., & Runion, G. E. (1977). Mathematics teaching. New York: Hprper & Row.

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A short synthesis of my six projects

        When I came here to study, I wanted to promote my professional knowledge. I would do projects which encompassed application of technology in education, theories of learning, development of mathematical standards, and integration of learning theories, instructional skills, and technology in mathematical curriculum design.

        First, my project entitled  " New Teaching Strategy", represents my ideal of mathematics instruction. In my project, I try to integrate small group instruction, technology, and constructivist teaching. It also intrigued me to learn more details like learning theories (e.g. cooperative learning) and the implementation of technology. Second, called "The Era of Standards", not only did I learn why mathematics educators want to enact the standards (e.g. NCTM 1989, 1991) in order to reform current mathematics education, but also I thought more about how to apply it in practical educational situations because  no so clear and excellent the mathematical standards were in Taiwan. Third, the cooperative learning instruction stimulated me to think more about how to help students learn mathematics effectively. It let me make it clear to apply the social constructivism for students' learning in classrooms. Forth, in the project of "Teaching with technology", I practically used technology, like computers and graphic calculators, in mathematical lesson plans. It let me think the purpose and function of technology in mathematics education and how to generate the best learning results through using technology in mathematical instruction. Fifth, because of the power of technology in education, I hope all teachers can use it effectively in their teaching.  I found there were some factors resulting in that teachers could not apply it well in their instruction from my project entitled  "Computer using in education". There is a distance between practice and theory. The project intrigued me began to investigate more what kind of help or support teachers need in order to improve their computer using skills for their instruction. Finally, because technological progress, the model of education will grow different. The use of distance education is inevitable in future. My discussion of  "Distance education" allow me to outline  future education and the influence on teachers, students, and curriculum.

        My  initial and primary reason for coming here to study was to teach differently and effectively when I came back. Form these projects, I developed my professional knowledge and gain more confidence in teaching. I learned and integrated them as main parts of my core knowledge of mathematical instruction. These projects gave contributed to my teaching, learning, and application of technology in mathematics education.

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Niche of the future

       The quality of teachers plays a key role in education. What I want in the future is to be an excellent mathematics educator in a university in Taiwan for promoting pre-service teachers'  mathematical teaching quality to improve the standards of mathematics education, especially teaching and learning. I hope I can guide these student teachers to learn more about mathematical learning theories, teaching instruction, mathematics curriculum design, and the use of technology in mathematics education from current research results, and documents in order to improve the situation of mathematics education in middle schools.
        In addition, I want to work with my colleagues in the university to develop a teacher-training center for current mathematics teachers. This center will provide various educational resources and inservice programs, like the effective teaching programs, the application of technology, or contemporary research in mathematics education, for those teachers who want to improve or promote their teaching quality in mathematics classrooms. Not only does it offer inservice programs, but also provides mathematics education research as the support for teachers, programs, and educational policy.



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