MB4T (MATHEMATICS BY AND FOR TEACHERS): MULTIPLYING INTEGERS

As mentioned in the September column, the development of integers historically was not in response to real-world contexts, but rather as a way of dealing with expressions such as 10 + 2 x... = 4. Thus, constructing classroom real world examples becomes more of a challenge. Eventually students may generalize that the product of two like-signed integers is always positive, and that the product of two unlike-signed integers is always negative. Relying on rules alone, without engaging students in activities that allow them opportunities to develop understanding, is dangerous -- and can result in misinterpretations, such as thinking that - 3 - 5 is 8 (because there are two negatives). After modelling enough examples, students will soon begin to construct and internalize the general procedures for integer products on their own. The difference is that if they forget, they have something to fall back on -- reasoning.