Dr. Jennifer Szydlik - Page 2
(Excerpted from Dr. Jennifer Szydlik's Regents Teaching Excellence Award application. Reprinted with permission.)
Statement of Teaching Philosophy and Practice
by Jennifer Szydlik
Mathematics is the human expression of the patterns and the logic in the world; it is something that we all do. When we study the patterns and symmetry in artwork, we do mathematics. When we work on a puzzle that requires logical thinking, we do mathematics. When we solve a problem that allows us to quantify, generalize, organize and find patterns, we do mathematics. It is as natural for us to create and love mathematics as it is for us to create and love art, music, or literature.
This view of mathematics shapes my philosophy of teaching and learning: (1) All students love mathematics - but most do not know this because they do not recognize mathematical activity. (2) Most students do not know that mathematics is supposed to make sense and therefore rely on the external authority of the instructor for the determination of validity rather than on the internal consistency of the subject. This is distinct from the assertion that students do not understand the mathematics they study. Many students are not even aware there is something to understand. (3) Students will not hear until they are "made ready" to hear. The corollary is a vital assertion: Lecturing students in mathematics is often an ineffective method of teaching. This is not to say lecturing never works. It will work with motivated students who have prepared themselves to hear the lecture or with students who have seen appropriate examples or worked appropriate problems beforehand. However my students, most of them future elementary and middle school teachers, are often mathematically unsophisticated and unprepared.
Over the past two decades my teaching practice has evolved to reflect my beliefs about mathematics and student learning. My specific aims as a teacher are to reveal to my students the nature of mathematics; to make them skilled and enthusiastic problem-solvers; to support them in understanding mathematical content; and to help them become effective communicators of mathematical ideas. I have come to view the mathematics classroom as a culture of doing mathematics and to see learning as a process of acculturation. Mathematicians value precise definitions, simple examples that illuminate complexity, powerful models for objects and relationships, deductive reasoning and logic, and careful language and notation. It is my job to convey the values of the mathematical community both covertly and explicitly to my students. For it is these values and practices that give mathematicians power to create mathematics. In the classroom, I must be a living model of the culture wanted.
In order to support a culture of doing mathematics, I ask that my students work in small groups on carefully constructed problems and activities and then to discuss ideas as a whole class. This concentration on the process of mathematics rather than on the finished product allows students to see the sense in mathematics, and the format allows for significant mathematical communication. Because these students have often memorized mathematics in the past, I am careful to refrain from
giving answers or overtly participating in the problem solving process. I watch and listen as they work. Only after they have tried to derive a formula, prove a theorem, or solve a problem will we have a whole-class discussion about the content that arises from the work. This way even when the students are not able to derive, prove, or solve, they are, after the attempt, ready to hear.
On a good day the class discussion is a symphony of mathematics. My work is to bring to the fore in some reasonably connected and melodic way, the ideas, representations and connections that individuals or small groups have made. I am armed with all that I have learned from twenty minutes of concentrated eavesdropping on group-work and twenty years of practice. I often sit with the class in the semi-circle, providing a silent (or not so silent) invitation for them to teach. On a good day they talk to us all and not to me alone. On a good day they help one another at the board. On a good day they ring out their misconceptions along with their brilliant ideas and we address it all as a class. On a really good day they applaud each other. Most days are good days.
On a not so good day, we wait. I coax specific students and ideas into the open. I try to add a mathematical rhythm that makes music more likely. We return to small groups to think again and eavesdrop again. Later, I’ll write a new class activity, one that might work better next time.
Our set of mathematics textbooks for prospective elementary and middle grades teachers has evolved from this process. (I wrote each book with one other colleague. These are listed in my vita.) We wrote them based on a philosophy of learning that asserts that humans construct meaning within a cultural context. In the books we attempt to provide normative mathematical definitions, notation and language, and to raise problems, questions and issues in a pedagogically reasonable order to support a classroom culture of doing mathematics.
The textbooks are an observable extension of my teaching. I have participated in many wonderful faculty development programs and I have conducted several studies that inform my work in the classroom – but this writing project has brought together my ideas in a way that solidifies and supports not only my own teaching practice, but that of others who would seek to show students that they too are mathematicians.
Finally, a word about my mathematics education scholarship: it is conducted for the purpose of improving the education of our students. I do this by investigating how students view mathematics and mathematics learning, and by studying how students can be nurtured to adopt more powerful mathematical behaviors. The fact that my teaching and scholarship are so intertwined helps me to reflect in careful and organized ways on my own practice; it allows me to benefit from the research of others; and it requires that I form and maintain a coherent philosophy of learning.
Teaching is nothing without learning – I will now try to provide evidence that my students have learned something important in my classes: namely, that they have learned to learn mathematics and that they have learned to study and attend to the mathematical thinking of their future students.
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