Thursday, May 12, 2011
Tuesday, January 11, 2011
The Theory That Motivates My Practice
Theory and My Practice
Like most math teachers, my educational philosophy motivating my life's work is classical liberalism, which means I believe that people who graduate from 4-year colleges should have studied a smattering of mathematics, science, history, literature, languages, and writing; these subjects form the basis of the traditional definition of what it means to be an educated human being. A more cynical soul might suggest that classical liberalism is the only philosophy that justifies my continued existence as a purveyor of a system of knowledge that descends directly from the ancient Greeks.
Community colleges are hybrids; they contain characteristics of universities and of technical colleges. My students are as likely to be seeking a 2-year Associates Degree, a 1-year Professional Certificate, or transfer to a university. My students may be recent high school graduates, recent GED program graduates, or people who have been out of the educational mainstream for 20 years. None of my students know or care about classical education and have only the vaguest awareness that mathematics is an ancient art; their concerns are finding employment while balancing student, single parent and work responsibilities. Increasingly, my students are unemployed and attending college to learn a new career. They are all stressed by life and terrified of mathematics.
My job as a developmental mathematics instructor is to follow Lindeman's maxim that the purpose of adult education is to change “individuals in continuous adjustment to changing social function.” (Merriam & Brockett, 1997, p. 37). While I would love to cure classrooms full of people of their mathematics phobias and ignorance, 15 years of attempting to teach mathematics have taught me that my victories occur only one person at a time; I therefore subscribe to Beatty's individualist educational philosophy: As the number of educated individuals increases, society will improve (Beatty & Ilsley, 1992). Brookfield would consider me hopelessly naive...or, perhaps, just stupid.
From experience, I am a cognitivist. I know and see constantly that the only students who survive my classes are the ones who enter with their schemata prepared to be rearranged and augmented, that is, they are ready for insights (Merriam, Caffarella, & Baumgartner, 2007). I see all the time, unfortunately, how students fail who have remained in Piaget's concrete stage and have not progressed to the abstract. The abilities to imagine, visualize and perceive patterns are essential to success even in developmental mathematics.
Social cognitive theory states that people learn in social contexts by observing others (Merriam et al., 2007); in other words, modeling is an effective and efficient teaching tool. For that reason, I spend a good deal of time at the whiteboard not just working problems but sharing my thinking process as I write. I also encourage students who have mastered categories of mathematics problems to share their expertise with their fellow students; peer tutoring can be very powerful and non-threatening (usually).
Teaching tools I frequently use are group work and project based learning; these allow me to use constructivist/Vygotskian theory and learning styles. As students work together to solve problems – homework or community service – less skilled group members learn from the more experienced, and students have the opportunity to use their favored learning style: visual, auditory, kinesthetic, tactile. Learning projects should double or even triple my retention rate; but they do not. So many personal factors prevent students from attending school or group meetings that group work and projects are useless for a sizable minority.
Brookfield says that theories help people make sense of the world (2005). Merriam and Brockett (1997) say exactly the same thing. For me, in my teaching, all philosophies and theories are provisional. I use what works best for me in my classes. I am always on the hunt for new methods that might prove more effective. One day, I hope to discover a magic best practice that will transform mathematics education.
References
Beatty, P. T., & Ilsley, P. J. (1992). Part One: Should the Starting Point of Adult and Continuing Education Be to Change the Individual or Society?. New Directions for Adult and Continuing Education, 54, 15–34.
Brookfield, S. (2005). The power of critical theory for adult learning and teaching. Maidenhead: Open University Press.
Merriam, S., & Brockett, R. (1997). The profession and practice of adult education. San Francisco: Jossey-Bass.
Merriam, S., Caffarella, R., & Baumgartner, L. (2007). Learning in adulthood : a comprehensive guide (3rd ed.). San Francisco: Jossey-Bass.
Like most math teachers, my educational philosophy motivating my life's work is classical liberalism, which means I believe that people who graduate from 4-year colleges should have studied a smattering of mathematics, science, history, literature, languages, and writing; these subjects form the basis of the traditional definition of what it means to be an educated human being. A more cynical soul might suggest that classical liberalism is the only philosophy that justifies my continued existence as a purveyor of a system of knowledge that descends directly from the ancient Greeks.
Community colleges are hybrids; they contain characteristics of universities and of technical colleges. My students are as likely to be seeking a 2-year Associates Degree, a 1-year Professional Certificate, or transfer to a university. My students may be recent high school graduates, recent GED program graduates, or people who have been out of the educational mainstream for 20 years. None of my students know or care about classical education and have only the vaguest awareness that mathematics is an ancient art; their concerns are finding employment while balancing student, single parent and work responsibilities. Increasingly, my students are unemployed and attending college to learn a new career. They are all stressed by life and terrified of mathematics.
My job as a developmental mathematics instructor is to follow Lindeman's maxim that the purpose of adult education is to change “individuals in continuous adjustment to changing social function.” (Merriam & Brockett, 1997, p. 37). While I would love to cure classrooms full of people of their mathematics phobias and ignorance, 15 years of attempting to teach mathematics have taught me that my victories occur only one person at a time; I therefore subscribe to Beatty's individualist educational philosophy: As the number of educated individuals increases, society will improve (Beatty & Ilsley, 1992). Brookfield would consider me hopelessly naive...or, perhaps, just stupid.
From experience, I am a cognitivist. I know and see constantly that the only students who survive my classes are the ones who enter with their schemata prepared to be rearranged and augmented, that is, they are ready for insights (Merriam, Caffarella, & Baumgartner, 2007). I see all the time, unfortunately, how students fail who have remained in Piaget's concrete stage and have not progressed to the abstract. The abilities to imagine, visualize and perceive patterns are essential to success even in developmental mathematics.
Social cognitive theory states that people learn in social contexts by observing others (Merriam et al., 2007); in other words, modeling is an effective and efficient teaching tool. For that reason, I spend a good deal of time at the whiteboard not just working problems but sharing my thinking process as I write. I also encourage students who have mastered categories of mathematics problems to share their expertise with their fellow students; peer tutoring can be very powerful and non-threatening (usually).
Teaching tools I frequently use are group work and project based learning; these allow me to use constructivist/Vygotskian theory and learning styles. As students work together to solve problems – homework or community service – less skilled group members learn from the more experienced, and students have the opportunity to use their favored learning style: visual, auditory, kinesthetic, tactile. Learning projects should double or even triple my retention rate; but they do not. So many personal factors prevent students from attending school or group meetings that group work and projects are useless for a sizable minority.
Brookfield says that theories help people make sense of the world (2005). Merriam and Brockett (1997) say exactly the same thing. For me, in my teaching, all philosophies and theories are provisional. I use what works best for me in my classes. I am always on the hunt for new methods that might prove more effective. One day, I hope to discover a magic best practice that will transform mathematics education.
References
Beatty, P. T., & Ilsley, P. J. (1992). Part One: Should the Starting Point of Adult and Continuing Education Be to Change the Individual or Society?. New Directions for Adult and Continuing Education, 54, 15–34.
Brookfield, S. (2005). The power of critical theory for adult learning and teaching. Maidenhead: Open University Press.
Merriam, S., & Brockett, R. (1997). The profession and practice of adult education. San Francisco: Jossey-Bass.
Merriam, S., Caffarella, R., & Baumgartner, L. (2007). Learning in adulthood : a comprehensive guide (3rd ed.). San Francisco: Jossey-Bass.
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