This simple mantra is reinforced in my brain by my native tongue, in which to teach and to learn are expressed as different inclinations of one same verb. So teaching starts with caring about whether your students are learning, caring about what your students are learning. Therefore the effectiveness of the teacher is increased when he has to teach the things he believes are meaningful. Teachers beliefs are best expressed in the design of a course.
I had the opportunity to design and teach a course, Introduction to Number Theory, for Boston University Summer Term. In the following I will discuss what I did, and let this concrete example tell you what kind of a teacher I am.
Three factors influenced the design of the course – the prospective students, the tradition, and my personal tastes. I will describe these considerations in the rest of this article.

This is an ideal no one would argue with. However, there are various real world factors that hinder the attainment of this ideal. The inherent customization required is resource-expensive. The prospective students are not always a known variable. So how did I dealt with these problems? As a young instructor, I was eager to experiment and have full control of my course, prove myself by doing the things in a better way, my way. So I was not scared of the required extra work. Looking back, I can say that I have underestimated the quantity of the work needed. But also I can say that I had enough enthusiasm to carry me through to successful completion. Having experienced teaching courses of both follow_the_textbook type and customize_and_handcraft_all type, I consider myself now to be a wise teacher, with the ability to make the right choice in any situation and the power to execute that choice at high quality. And my enthusiasm is still going strong.
I knew what types of student to expect for that summer course, since this was going to be my third course for BU Summer Term, and also since I was able to read the academic information for the students who registered for the course in advance. The students you get for summer term courses fall into three main categories – BU students who really need the course as a graduation requirement, most of them seniors, some of them having already tried unsuccessfully the same course during the regular semester; ambitious students who want to get extra credits during the summer, to graduate faster or to satisfy a double major requirements, some of these coming from colleges other than BU; graduates, who are contemplating returning to school or like to enhance their credentials, and enroll in the course while holding full-time jobs. An audience that presents a challenge with its diverse backgrounds and disparate goals. To overcome this, I made sure that I have a coherent and minimal set of assumptions of what mathematical knowledge the students will bring to class, and made an effort to communicate these assumptions and to check on them as soon as possible. Fortunately, an Introduction to Number Theory course is very amenable to such circumstances - there are few requirements beyond high school algebra, complemented with some level of mathematical maturity. At the other end, I made sure that the work required for passing the course is not beyond reach for any motivated student, and at the same time there was enough challenge so that no one will feels cheated or being led through a watered-down version of the real stuff.

When designing a new course, the instructor should be aware of the surroundings. The course is taught for a certain department in a certain school, and these institutions have their traditions. One should be extra careful, highly experienced, and consult with others, before departing from these. Departure from the traditions might take the form in either changing the course content (no matter how enamored is one with numerical methods, skipping the Leibniz-Newton theorem from a calculus course should be double checked), or changing the course mode (turning a Engineering Calculus class into a Appreciation of Calculus through its History writing intensive course is bold, but the instructor for the subsequent Multivariate Calculus course for which your course is a prerequisite will not appreciate that history).
When designing a course, the instructor should pay attention to which courses are prerequisites for the course, and for which courses the course in its turn is a prerequisite. A good practice is to talk with both sets of instructors for these two types of connected-to-your-course courses, and gather their opinions about what should be included in the course. For example, Discrete Mathematics is a prerequisite for the Data Structures and Algorithms course in the Computer Science Department. So one might think to emphasize graphs and trees. It turns out that the people at CS will do these themselves, but they will be happier if you taught your students (soon to be their students) proof by induction, so they could then use this technique when they have to provide estimates for the complexity of various algorithms.
One should also be aware that most Math Departments offer their majors a three-stage course progression, where in the first level mostly proficiency with computational techniques is emphasized, so a course at that stage should be quiz and exam intensive; the second level is geared toward creating an intelligent user of Mathematics, so at that stage a course can have more challenging homework assignments and open book exams; the third level is about deeper understanding and appreciation of mathematics, with the full use of the 4C skills for a Mathematics course – Computing, Conjecturing, Concluding, Communicating. As the Number Theory course that I have to teach certainly was a third level course, I had to provide course components for exercising the 4C skills. The emphasis and the flavor of these components was where my tastes for Mathematics could be best read.

There should be a balance between contents and skills. One cannot acquire skills by manipulating empty space. On the other side, content is often overemphasized. Unused information tend to fade quickly from memory, and then even the awareness of the existence of such information starts eroding. The overemphasizing of contents coupled with lectures as only delivery method can be behind much of the ineffectiveness of and displeasure with a mathematics course. While I didn't want to give up on lecturing, as an important facet of teaching is performing like actor on a scene, and I like this, I severely limited the time I spent lecturing. Persisting with lecturing for a 6:00pm class is the surest way to turn the room into a sleeping hall. In addition to making the lectures more interactive, I assigned 1/3 of the meeting times for workshops, which were student centered activities with emphasis on skills and discovering.
Since I consider communicating as an important skill, the students were required to work on a project, which was to be a investigation into a problem from a list of topics I had selected. The project work gave the students the chance to train their information gathering and processing skills, their writing and oral presentation skills, and their ability to meet deadlines, as the projects had various deliverables (a plan, a draft, a final version, presentation) distributed throughout the course duration.