Some Considerations Concerning the Teaching of Negative Numbers

Abstract

The teaching of negative numbers is dealt with herein from the point of view of expanding the number classes from those containing only positive numbers to those that also include the negatives (and zero). The expansion involves generalizing the concept of “number” and making modifications in the definitions of the arithmetical operations. Each of these actions generates cognitive obstacles, both historically and pedagogically. In contrast to the historical situation, the concept of negative number is not problematic for the contemporary student because he/she encounters them with certain frequency in his/her daily life. The addition of negative numbers, especially in the case in which it becomes equivalent to subtraction in the natural numbers with the subtrahend greater than the minuend, is subject to a didactical obstacle, which can be overcome by using the number line as a visual/conceptual support. Also, the multiplication of two negative numbers, resulting in a positive number, constitutes a genuine epistemological obstacle due to the fact that the usual metaphors used to explain the negative numbers do not clarify this operation. The article thus proposes to consider double negatives as inverses of inverses and delineates a sequence of activities based on this metaphor to overcome the mentioned epistemological obstacle.