EPISTEMOLOGICAL DISCONTINUITIES AND COGNITIVE HIERARCHIES IN TECHNOLOGY-BASED ALGEBRA LEARNING Michal Yerushalmy University of Haifa There is speculation about the degree to which new technologies will lead to replacement of current curricula with new content. How does the use of new curriculum that is based upon new epistemological assumptions change our capability to anticipate students' difficulties and strengths? Taken from a series of studies carried out as design experiments in algebra classrooms over the last decade, I will present examples where students’ performance in a technology-supported curriculum is different from the performance one might have predicted for students learning this content in a non-technology supported environment. These examples suggest that technology can transform student learning. The technology and the sequence help to bridge known transitions that assumed difficult to students to be 'natural' (for example: Modeling, recursive thinking, solving unfamiliar equations or visualizing equation in 2 unknowns in 3D). However, the transitions between fundamental concepts or operations remained the difficult and non-trivial parts. In doing such analysis, I suggest that identifying critical discontinuities is an important research tool for studying students' construction of knowledge and for analyzing classroom guided inquiry supported by technology. School algebra reform In popular culture, school algebra, has a negative reputation. It is believed that school algebra classroom involves students in the application of unjustified methods to classes of problems, and that this is problematic because it does not get students involved in creative thought that is representative of mathematical work. Studies of educators and mathematicians concerning the ways in which the discipline is portrayed to students have not demonstrated interest in algebra, probably because it presents students with limited opportunities to engage in something like the solving of problems in ways that reflect hallmark of mathematical thought. Indeed, school algebra has been described as a part of the curriculum "overly focused on “meaningless manipulation.” memorized rules focusing on specific strategies for specific types of problems. As part of the larger reform movement across the world, during the last fifteen years, mathematics educators have tried to work to reshape school algebra and respond to the above mentioned criticisms. There have been calls for more contextually-based problems that would allow algebra to emerge from quantitative situations in the lives of students. There have been calls to integrate attention to justification and proof throughout the school curriculum, including school algebra. And, influenced by the increasing availability of computer and calculator technology that supports multiple representations of functions, there have been moves to use this technology to change the nature of the school algebra curriculum (e.g, Heid et al., 1995). Algebra reform for algebra beginners has taken several forms, some of them called functions approach to algebra. Although there are important differences between them, these new forms organize the algebra curriculum around the concept of function, emphasize and support concrete representations, and base learning on situations that appear realistic and are centered on mathematization in the form of modeling and of abstractions at different levels (Kieran & Yerushalmy 2004). With