Michael Tabach, Abraham Arcavi and rina Hershkowitz (all from the Weizmann Institute of Science, Israel) have written an article called Transitions among different symbolic generalizations by algebra beginners in a computer intensive environment. The article was published online in Educational Studies in Mathematics on Saturday. Here is the article’s abstract:
The transition from arithmetic to algebra in general, and the use of symbolic generalizations in particular, are a major challenge for beginning algebra students. In this article, we describe and analyze students’ learning in a “computer intensive environment” designed ad hoc and implemented in two seventh grade classrooms throughout two consecutive school years. In particular, this article focuses on the description and analysis of how students initial generalizations (which relied on computerized tools that enabled different students’ to work with different strategies) shifted to recursive and explicit symbolic generalizations.