"Teachers live through their students to eternity"
(Heard at National Science Foundation Conference, Washington, D.C., June, 2008.)
“Anyone who has never made a mistake has never tried anything new.”__(The guy sitting next to me said
My Teaching Philosophy
I believe teaching is a mutual process that inspires and empowers both the teacher and students in a transformative experience. Transformative learning is a reciprocally educative endeavor, both informative and uplifting for teachers and students alike. Students are not empty vessels to be filled with facts but active agents that select and construct knowledge that is meaningful to their own lives. Moreover, learning is a complex process that is individual, content, and context-specific. Understanding the diversity of students’ experiences and diverse cultural and lingual backgrounds is crucial in enhancing their engagement in this dynamic interaction, inspiring both sides to cultivate their curiosity and grow intellectually.
Based on this belief, constructivism is my approach to mathematics instruction. In contrast with the instructional approach, constructivism stresses that knowledge is constructed by students from their own experiences. Teachers in a constructivist classroom can use classroom questions as a strategy to help students reorganize existing information and connect with new patterns to lead to new meanings and interpretations. Two thousand years ago, Socrates observed that wisdom begins in wonder; by asking: “Why? How? Why not? What next?” teachers can tailor their instructional strategies to student responses and encourage students to analyze, interpret, and predict information. Making it a habit to ask a variety of guiding questions during instructional time, teachers can foster the habit of algebraic thinking in the students.
Instructional strategy in a constructivist classroom includes the use of manipulatives (such as a diagram, pattern blocks, tiles, and cubes) which can be important tools in helping students to think and reason in more meaningful ways. Mathematics can be perceived as “abstract;” the use of manipulatives brings experiential education to bear on students' mathematical understanding. The Principles and Standards for School Mathematics (NCTM) recommend students to “select, apply, and translate among mathematical representations to solve problems.” In order for the students to use manipulative effectively on a problem-solving task, teachers should foster students’ manipulative literacy by: (i) providing opportunities for students to explicate their ideas about manipulatives and identify which type of manipulatives is most appropriate for particular problems; (ii) explaining the links between the structure of a problem and its representation; (iii) emphasizing the importance of precision in location and movement on, for example, algebra tiles.
Mathematics teachers should also pay attention to designing tasks based on their cognitive demands. The cognitive demands of tasks typically evolve and change during classroom instruction. Since the level and kind of thinking in which students engage that determines what they will learn, it is important to set clear goals based on which tasks can be selected or created for student learning. Depend on what kinds of knowledge, procedural skill or conceptual competence, the students need to learn that the teachers match tasks with student levels without being misled by superficial features. When designing tasks, teachers should keep in mind all the factors about the students (their prior knowledge and experiences, their age) and about the setting of time and expectation. Practicing regularly will help make this an effective routine for both teachers and students.
Each math lesson, therefore, is a journey in which both students and their teachers explore a new realm of concepts and symbols and construct them in a way that makes their world more understandable and manageable.