My teaching and research philosophy is based on the foundations of Activity Theory and Developmental Approach (L. Vygotsky, A. Leont’ev, V. Davydov).

I firmly believe that effective teaching is a student-centered activity. In actual university classrooms or auditoriums, emphasis should be on learning rather than teaching: we are not supposed to teach only, we are supposed to help students to learn. Teacher’s role is to engage students by posing challenging problems and creating an atmosphere of mathematical and pedagogical exploration and sense making. In order to achieve this goal, teachers should use different strategies to encourage students’ learning (e.g. problem-based instruction, open-ended approach, cooperative learning groups, multiple representations). They should also use modeling and technology as thinking tools. In my classes, I try to follow “small pedagogical wisdoms” which I have learned from my school teachers and college math professors. Here are some of them:

• Conceptual learning leads procedural development.
• Better to solve one problem by three methods than three problems by one method;
• The purpose of mathematical problem solving is not to get the right answer but to promote students’ thinking;
• Giving right answers to students is to do their thinking for them;
• It doesn’t matter if you know how to solve 100 problems, it does matter how you approach the rest of them;
• Do not be afraid of making mistakes but be afraid of repeating them;
• Fun is a derivative of challenge;
• What we assess is what we value.

I do believe that students construct their own understanding in active learning environment. As teachers, we cannot simply transmit ideas to passive learners. Knowledge cannot be poured into students as if they were empty jars. Each student comes to my classes with his or her unique experience, understanding, beliefs, attitudes, and own “collection” of ideas about learning and teaching mathematics. Frankly speaking, majority of them come with previously developed negative experience and attitude toward mathematics. Nevertheless, I try to use students’ unique experience and ideas as a springboard to construct their conceptual understanding of math as they “wrestle” with challenging problems, projects, and activities which I use in my classes, discuss and present ideas and solutions, use different representations to explain their methods, and reflect on their learning. In other words, I try to create challenging but, at the same time, mathematically friendly learning environment where they can realize that each of them can learn math and learn how to teach it successfully.

I am looking forward to sharing some of my beliefs and ideas about an effective teaching and learning with my colleagues through team teaching and research, collaborative (workshops, seminars, etc.) and individual meetings. The key point of my research objectives on Cognition and Visualization is an investigation of the cognitive-visual paradigm in contemporary mathematics education which will help us to explore: how to combine cognitive and visual potential of math concepts; how to teach mathematics to right- and left-hemispheric students; how to solve math problems and do proofs visually; how to develop students' visual thinking through new technologies; how to generalize mathematical knowledge graphically and improve students' systems thinking.