RESOURCES AND PSEUDOREASONING
I began by looking at the literature and resources available to classroom instructors that would help explain why (-1)(-1) =+1. Many of the resources contained some type of analogy involving elevators moving up and down, mail delivery, or a football team gaining and losing yards during a game. Although other resources tended to rely on pattern recognition and language assignment, they did not incorporate the sense of consistency and structure of student' number systems; rather, they seemed, through false logic and rule making, to distract from finding a logical explanation.
In a paper entitld " Fourteen Different Strategies for Multiplication of Integers or Why (-1)(-1) = +1" (1972), Peterson presents a compilation of strategies from various authors and educators that address this question. Peterson's goal seems to be to present enough strategies so that a teacher can choose one that will be most appropriate for a particular teaching situation. I will be not consider all the strategies in Peterson's paper; only one strategy is necessary to convey my message and explore the questions mentioned above.