Teaching Philosophy
Simply stated, I believe that students should have the opportunity (both within and without class) to do as much active, participatory learning as possible. In my classes, I strive to present "learning problems" - that is, problems that will teach students a mathematical concept as they work through and discuss the problem. Discussion and communication are also large parts of my classes. I believe that mathematical communication is an essential part of learning mathematics. Communication is even more essential for teachers. My classes for preservice teachers and my professional development workshops for inservice teachers are 40-50% discussion. I try to establish a safe space in my classroom for sharing thoughts.A sample lesson outline (from Math 105: Math in Modern Society)
This is a lesson introducing the different ways you can compound interest.
Consider the following problem:
You deposit $1000 in a bank account that pays 3% interest annually. This means that at the end of each year, the bank deposits 3% of the amount of money currently in the account back into the account. How much money do you have in your account after 5 years? After 10 years? After 40 years?
Students have the opportunity to work on the problem for about 10 minutes. They are encouraged to use any strategy accessible to them to answer at least the first two questions. Then, 5-10 minutes are set aside to allow students to share their solutions and for the class to discuss . Usually, I will circulate during work time and cherry-pick certain approaches that are particularly interesting, then ask students privately if they would not mind sharing with the class. The solutions are presented in an order than leads up to the main mathematical point that I want to make with this problem, which is the introduction of the algorithm for computing compound interest.
In a 5-10 minute lecture/debrief, I formalize the mathematical structure that most students would have noticed as they worked through the problem: 1.03 is multiplied to itself a number of times and then multiplied to the principal $1000. In this debrief, we as a class develop the formula for compound interest. Depending on the class, we may spend a little time practicing the use of the formula with some similar problems.
Now, I ask the class to consider another problem:
Consider the following problem:
You deposit $1000 in a bank account that pays 3% annual interest, compounded monthly. This means that at the end of each month, the bank deposits money into the account. How much money do you have in your account after 5 years? After 10 years? After 40 years?
Students again have the opportunity to work through this problem for 10 minutes. Students who feel comfortable applying the formula just introduced are encouraged to analyze what the different parts of the formula mean and how to use it meaningfully to solve this problem. This is followed by a 5 minutes of sharing and a quick 5 minute debrief. The main points made in the debrief are that the formula can be adapted to solve this problem and what the result of compounding at the same annual rate more frequently is.
This lesson sets up the goal of the next lesson, which is to introduce continuously compounded interest.