Positive experiences with negative numbers: Building on students in and out of school experiences

The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. As one teacher observed, “All of a sudden there are these concepts in maths where half the numbers are negatives and they’ve got no idea what it’s all about…” Despite the confusion that working with negative numbers can cause for middle school students, there is evidence that the concept of numbers less than zero is not difficult. In fact the National Council of Teachers of Mathematics (NCTM) (2000) recommended that “in grades 3–5 all students should explore numbers less than 0 by extending the number line and through familiar applications”. Simple games that involve losing as well as gaining points or experiences with debt can facilitate quite young children believing that it is possible to have less than nothing and that such amounts are less than zero. In the Australian curriculum (Australian Curriculum Assessment and Reporting Authority (ACARA), 2011) although the continuation of number patterns is mentioned from Year 1 and could lead to the discovery of negative numbers they are not specifically mentioned until Year 6. In the middle years, particularly Years 7 and 8, students need to build on their intuitive understandings in order to use negative and positive integers to represent and compare quantities and extend number properties developed with positive integers to negative integers as well.