*Why do I
enjoy teaching mathematics? * Creating a lesson involves problem solving. I
enjoy the creative process of identifying learning objectives, creating activities
that require students to think, anticipating students’ responses to those
activities, and visualizing a learning trajectory. Teaching a lesson is
exciting for me. I enjoy the challenge of having to respond to unanticipated
situations during a lesson and having to make decisions within a set of
constraints such as time constraints, the need for closure, and the need to
preserve students’ autonomy in solving the problem. Metaphorically, planning
and teaching a math lesson is like strategizing and playing a sport; a sport in
which my students and I are on one side and the problem to be solved on the
other. Winning occurs when my students engage in the problem, solve the problem
independently, learn the underlying mathematical ideas, and enjoy the process. Winning
is rewarding, but winning does not always occur. With practice and reflection,
the chance of winning increases over time.

*What is my
view on learning and teaching?* I consider learning to be the process by
which students construct new knowledge from their existing knowledge as they
interpret and make sense of a situation. Teaching is the process of creating
and managing situations conducive for desirable learning to occur.

*What is my
role as a teacher?* While students are responsible for their own
learning, I am responsible for creating the opportunities for them to learn.
With target learning goals in mind, I select and design meaningful problems
that can provoke students’ intellectual need for those goals. For example, the
task of finding the speed at a specific time, say *t*_{1}, on a distance-time graph that is created by a motion
detector will potentially necessitate students’ attending to the meaning of
speed. If *t*_{1} is within the
at-rest interval of a walk-stop-walk motion, then students who use the formula
speed = distance / time to obtain a value, say *d*_{1}/*t*_{1},
will be disconcerted. I am also responsible for creating an environment
conducive for students to explore ideas, to express their ideas, to challenge
each other’s ideas, and to learn from mistakes. Like a coach I will facilitate
the learning process by intervening discriminately, by challenging them to
communicate, formulate and justify their ideas in ways that are amenable to the
mathematics community, by orchestrating whole class discussions, and by
assuming a figure of authority in situations in which I need to communicate
standard mathematical conventions or to clarify misinterpretations. To help
students retain what they have learned in class, I will assign homework
problems that require them to repeat productive reasoning rather than merely to
practice procedures. Students may resist this mode of learning initially but
their resistance is likely to diminish as they see how their struggle with
mathematics has helped them deepen their mathematical understanding and develop
confidence in their problem-solving abilities.

*What do I
want my students to learn?* I once asked why we make students learn
algebra, calculus and higher mathematics when most students do not use these topics
in adult life. I then realized it is mathematical ways of thinking that our
students should be developing instead of a collection of rules, procedures,
theorems, and proofs. Examples of mathematical ways of thinking include making
and testing conjectures, justifying one’s claim, finding the underlying cause
for a mathematical phenomenon, using heuristics to solve a problem, making
connections, and seeking efficiency. Some of these ways of thinking can be
useful in solving non-mathematical problems such as identifying the cause of a
production breakdown or defending one’s business proposal. In teaching a topic,
I try to identify two complementary sets of learning goals:(a)
key concepts and (b) the associated ways of thinking. In addition, I try to
interact with students in a manner that fosters desirable habits of mind such
as taking ownership in one’s learning, practicing patience with oneself and
with others, accepting and learning from mistakes, welcoming feedback, and
being reflective.

*What qualities
do I value? *Based on my teaching experience, I think students
respect teachers who are principled yet flexible, confident yet humble, and
challenging yet encouraging. A teacher should strive to teach according to a
set of teaching principles while accommodating students’ needs and the
university’s requirements. A teacher should be competent and efficacious, but
should respect students regardless of their mathematical competence. Students
should be challenged to meet high expectations, but at the same time the
teacher must identify with their struggle and provide support and
encouragement. One of the most important attributes is that a teacher should be
passionate about teaching and should care deeply about the students’ learning.
In summary, teaching is exciting and rewarding for me; it is something that I
can continually improve by being reflective and staying current in the field.

Updated on September 1, 2006

Reality is the same for all, yet it is perceived differently by
each.