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by John Kellermeier |
My teaching philosophy is based upon the concept of connected teaching developed by Belenky, Clinchy, Goldberger, and Tarule in Women's Ways of Knowing, (1986). This concept emphasizes teaching that begins with the student where teachers are to be midwives helping students to give birth to their own knowledge. It is essential for teachers to develop an atmosphere where students feel comfortable and respected while at the same time challenged and engaged in their own learning.
In mathematics, connected teaching is done by having students learn through the doing and redoing of mathematics in what I call the “riskable classroom.” (See Kellermeier, 1996) This involves creating a classroom environment where students feel free to risk asking questions, making mistakes, taking guesses and using their intuition to learn the material. In my math classes, I often have students write journals, work collaboratively, and revise, rework and correct their mathematical work, which all lead to a steady growth of knowledge. I employ active learning techniques such as the requirement that students develop a statistical project in which they collect and evaluate data about a topic of interest to themselves.
My classroom technique is dominated by the problems approach. As part of the syllabus students are given a daily schedule of topics to be covered, along with reading assignments and exercises. These assignments are either from a textbook or from materials found online in the course website. Students are expected to read the assignment before coming to class and to have at least attempted some assigned problems. Then in class, students are asked to volunteer to write their solutions to problems on the board. As an incentive, students are given a small amount of extra credit for doing so. I make it clear to students that their solutions do not have to be correct to be written on the board. In fact, I encourage them to present the problems for which they have not gotten a complete solution.
The problems written on the board then serve as the basis for discussion of the material. Each student is asked to explain what she or he wrote on the board. As instructor, I oversee the ensuing discussion and any revisions required in the presented solutions. In particular, I draw attention to the thinking processes that the students use in solving problems and the way in which these solutions are written. After these discussions, the students then have an example of how to think mathematically about the material covered and how to arrive at a well–reasoned and well–written solution. I typically end class by having students work in groups on additional problems. On most days this technique requires little or no lecture from me. Instead, students generate their own learning. I act as a manager of learners and as a resource for information. I have found that students learn well and seem to retain material better when they have been active throughout the class doing, reworking and discussing mathematics.
My teaching methods also make use of classroom assessment techniques to determine the students' learning and to gauge the effectiveness of my instruction. For example, at the end of every class, I have students fill out a sheet of paper that has a space for their name, the date and two questions.
Besides providing me with a way to take attendance, this helps to keep channels of communication open. It also gives students another low–risk way to ask questions. It keeps me apprised of the material that they know and that with which they are still having trouble. The language they use in telling me what they learned also helps me to see how well they understand. I answer the questions asked at the next class. This serves as a review of the previous material and a segue into new material.
For more information on my teaching philosophy see "Feminist pedagogy in teaching general education mathematics: Creating the riskable classroom."
©2005 John Kellermeier