1. To investigate the mathematical foundations of the secondary school mathematics curriculum from the point of view of constructive possibilities for students
2. To investigate the mathematical foundations of the secondary school mathematics curriculum to reveal mathematical connections
3. To investigate the organization of the secondary school mathematics curriculum
4. To investigate the epistemological foundations of the secondary school mathematics curriculum

The four goals of the course are worked on concurrently in the context of the daily activities of the course. The mathematical activity of the students is emphasized. The reason for emphasizing the students’ mathematical activity is a belief that each mathematics teacher should re-construct school mathematics as being problematic in nature and establish connections among seemingly unrelated topics. The general view of the course is that there must be a shift in emphasis in mathematics teaching from the activity of the teacher to the activity of the students under the guidance and support of the teacher.

The course begins with a fundamental mathematical concept - the natural numbers. When starting with the natural numbers - that is, those numbers that are used in counting - the first and fundamental goal is for the students to modify their counting toward ever more sophisticated counting processes. Sophisticated ways of counting hold rich possibilities for secondary school students. Reorienting students to count in systematic ways is critical in developing multiplicative reasoning as well as the concept of natural number variation. 

The fundamental principle of counting is one of the first contexts in which natural number variation emerges. The key is the idea of possibility. Say we are thinking of drawing two cards from a full deck of 52 cards and are thinking of the possible outcomes of this experiment. In doing this, we need to distinguish between the two selections. This can be accomplished by the idea of a first selection and a second selection (order of selection). The student has to imagine making a selection from the deck followed by another selection. On the first selection, it is critical for the student think of selecting any one of the 52 cards, but no particular one, which is the essence of a natural number variable. As a capstone to the work on the the fundamental principle of counting, the binomial theorem is investigated in the context of combinatorial reasoning. 

The conceptual construction of the integers, the rational numbers, the real numbers, and the complex numbers are also investigated. The students experience a natural progression through these various number systems. Algebraic structure is emphasized whenever it naturally arises in the study. The correlation of algebra and geometry is emphasized and transformations of the plane are developed both geometrically and algebraically. Both plane and solid geometry is considered with emphasis on the line in the plane and in space, and the plane in space. Finally, the students engage in mathematical activity in the context of technological tools in computer laboratories for the major part of the course.