**Principal Investigator:** David Carraher **Funders:** National Science Foundation and =
Tufts University**Website: http://ase.tufts.edu/education/earlyalg=
ebra/default.asp **

Early Algebra is an approach to early mathematics teaching and learning.= It includes many topics in arithmetic, such as the four operations, but it= does so in novel ways. Consider the operation of addition. By second grade= most students know how to add 3 to another number. But they probably have = not been asked to consider expressions such as "n n +3", where n might refe= r to any number. As surprising as it may seem, we are finding that young le= arners from typical public schools can understand such expressions and use = them to describe relations among numbers and quantities. In doing so they g= o beyond computational fluency: they begin to develop the ability to make m= athematical generalizations using algebraic notation.

Early algebra does not aim to increase the amount of mathematics student= s must learn. Rather, it is about teaching time-honored topics of early mat= hematics in deeper, more challenging ways. We have good reason to suspect t= hat children who become familiar with algebraic concepts and tools from an = early age and in meaningful contexts will do better in mathematics, regardl= ess of the criteria used.

Early Algebra is also an area of research. The research from our project= and others should help to clarify what works and what does not work. But m= ore importantly, it should help to clarify the issues young learners inevit= ably face when they attempt to apply their present modes of representation = and reasoning to new circumstances--and to reconcile their prior knowledge = and experience with new ideas and concepts being introduced in Mathematics = classes. And it should help to identify fruitful types of learning activiti= es for educators and curriculum developers.