The experimental curriculum, called Visualizing Mathematics is based on the idea that, for pedagogical reasons, the function is the appropriate fundamental object of secondary school mathematics and that this focus permits the organization of the algebra curriculum around major ideas rather than technical manipulations (Schwartz & Yerushalmy, 1992). The central assumption of this approach is that, although the intuitions that students bring to the classroom are important, the education system still is responsible for creating an environment that supports the development of these intuitions into scientific and mathematical concepts (Nesher, 1989). We have been exploring these basic principles as part of an algebra curriculum adopted by a few schools (Grades 7 to 9) in Israel.

The curricular sequence of this algebra course is organized in three major phases. In each phase, functions are represented in four different forms: numbers, graphs, symbols, and words. The three phases are (1) building the concept of function, (2) comparing functions, and (3) exploring the invariance (families) of functions. In the first phase, we assume that students are fluent in arithmetic and are familiar with natural language. In this phase, we support the transition from discrete data and natural language description to the mathematization of processes using symbols and graphs. Throughout the second and third phases, the emphasis shifts toward symbolic manipulations of expressions and relations. One uses words and graphs to describe the effect of the symbolic manipulations, plus symbolic language to express and explore the nature of the function in greater delicacy than can be done otherwise.

Mathematics is peculiary appropriare to the creation of exploratory envitonments that offer a rich set of tools for making conjectures. Environments like Calculus Unlimited, The Geometric Supposer-3 can display quickly the results of the conjectures. Using such environments as intellectual mirrors, users can probe their own understanding of a domain as well as devise new relationships among the objects of the domaunIt becomes inviting and engaging in such environments to think inductively and to explore one's inductive notions. Similarly, the software enviroment and its tool s invite users to to generalize their thinkong and to axamine the range of validity of those generalizations.   Schwartz, J. L. (1993), "A Personal View of the Supposer: Reflections on Particularities and Generailties in Educational Reform", in Schwartz, J. L., Yerushalmy, M. & Wilson B. (Eds), The Geometric Supposer: What is it a case of?, Erlbaum, NJ, pp. 9.

Guiding principles   The computer as a tool for developing mathematical understanding: Mathematical understanding is achieved when cognitive relations are formed as a result of moving back and forth between processes and objects, using multi-representation.   The computer allows the student to learn mathematics in a multi-representation environment. The computer allows the student to look at a lot of information in many different ways. The computer contributes to the process of turning mathematical concepts into concrete objects without damaging the mathematical abstraction.

The nature of learning in the computer are: Organizing the mathematical content around important mathematical concepts, mainly the concept of function. Emphasizing the mathematical tools rather than certain algorithms. Using concepts that can be multi-represented. Mathematical content that explains the importance of the mathematical language.   The curriculum integrates original activities with predefined goals:

A meaningful learning of mathematics takes place when the student forms for himself the mathematical concepts while performing creative activities. Meaningful learning processes are based on inquiry activities. An image of a concept should be formed by integrating inductive and deductive ways of inquiry. Every student is capable of performing inquiries and of discovering mathematical relations, according to his level. Important procedures and algorithms are learned as a way of explaining, arguing and proving the findings.