Signed Numbers and Algebraic Thinking

We suggest that signed numbers1 and their operations belong in early grades. If carefully introduced, signed numbers can make fundamental algebraic concepts such as equality and function accessible to young students. In turn, negative numbers and operations with signed numbers can be learned more meaningfully when taught within an algebrafied curriculum. We first identify some of the problems related to the learning of signed numbers. Then we show how algebraic contexts can facilitate the learning of this problematic topic. Finally, we look at how signed numbers provide a supportive context for learning algebra. 303 1Signed numbers are positive and negative numbers. They refer to integers, not merely the natural numbers or positive integers. They refer to rational numbers, not merely the non-negative rational numbers. They refer to real numbers, not merely non-negative real numbers. Students may learn to accept negative num-bers in the co-domain (output of computations) before accepting them in the domain (input of computations). When they are comfortable with both, we say they have learned not only that signed numbers exist, but they can serve as the input for addition, subtraction, multiplication, and division as well as other functions. Kaput Chapter 12.qxd 11/28/2006 11:11 AM Page 303 The present discussion of signed numbers and algebra builds on mounting evidence suggesting that young children can learn algebra (Blanton &amp