Mathematics is not a collection of problems to solve. It is a way of analyzing and thinking through a problem. In math you think about how to measure. Math describes properties using numbers and symbols. When you talk "math" you talk about how things are related to each other. Learning math requires communication. People learning math have conversations about what they observe and what they think it means. They make predictions and wonder about things. Sometimes they write down what they are thinking.
We are all here to help you learn calculus, but we know we can't teach it to you - you must learn it yourself. We'll be here to coach you, clear the way for you, try to figure out where your questions lie, ask you guiding questions, nag you, make suggestions, and cheer you on, but you must do the thinking and you must construct your own learning. In this classroom, you will have a lot of responsibilities. The most important is to discuss, contemplate, experiment, and investigate your ideas about math and to record what you do, think and observe. The electronic lessons are designed to help you with this, and the mentors are here to help you with your own discovery of calculus.
Learning mathematics is not an individual sport. It is a team event, and you must participate. As much of your working as possible will be done in a group with other people. If it's a bunch of people at your school, that's great! If it's a cybergroup, learn to overcome the initial obstacles and go with it. You will be amazed at how a simple discussion about a problem will clear up the worst misunderstandings.
Talking is a very powerful tool for learning math. You will need to get used to talking and writing about math with other students and your mentor. You'll find out what this means when you and your mentor actually have conversations instead of just solving problems together. You may get annoyed because your mentor wants to talk instead of answering questions or helping you get the right answer. Mentors will expect discussion and explanation in the work that you turn in.
Another thing that you may find different is that we like it when you make mistakes. That means you are taking risks, trying things out, and pushing out of your "comfort zone." Mistakes are always the companions of learning. You will have lots of chances to learn from them and to correct them.
We think communication is a very important aspect of math, and life in general. A good deal of this course focuses on communication. You will learn to talk about math. You will learn to express your problems. It won't be easy, trust us. Part of your grade will depend on how well you communicate. This includes keeping in touch with your mentor, and giving DETAILED answers to problems. You may even find that you have to redo homework problems even though you have reached the right answer. We believe that the right answer doesn't do a whole lot of good if you can't explain why it's right. This will be different from every class you have ever had before. We'll be here to help. All you have to do is ask.
Our beliefs about learning also affect the way we teach. We believe that you are here to learn calculus, and everything we do is to make it possible for you to do that. We do not focus on the grade or on the points; we focus on how much you are learning and how well you can communicate that learning to others. Most of the time we will not tell you how to do something. We will rarely just explain anything. We will certainly not lecture. We will encourage you and ask you questions. We will try to get you to think. We will expect you to talk about math in plain English. We will expect you to write about math in complete sentences.
We will expect you to make mistakes and to try to figure out what they were and try again. We will often allow you to re-do your work until you are satisfied with it. We will be there for you when you need us, but we may not respond the way you are used to or the way you would like, at first.
This is our approach to teaching. You will find it frustrating at times. We know that. You will get stuck at times. We know that. You will get mad at times. We know that. You will discover in yourself the ability to apply calculus when analyzing a problem, and that will be very satisfying. We know that, too.