Locating negative decimals on the number line: Insights into the thinking of pre-service primary teachers

This paper explores misconceptions of the number line which are revealed when pre-service primary teachers locate negative decimals on a number line. Written test responses from 94 pre-service primary teachers provide an initial data source which is supplemented by group responses to worksheets completed during a lesson and individual interviews. Two main misconceptions leading to incorrect placement of negative decimals on a number line are identified. One relates to having separate number ‘rays’ for positive and negative numbers, which are aligned according to context. The other (with several variations) results from creating the negative part of the number line by amalgamating translated positive intervals. These misconceptions explain a large percentage of wrong answers. The most important implication for education at school, as well as in teacher education, is that the teaching of negative numbers and of the number line must not be confined to integers, as is frequently the case, but must also include negative fractions and decimals.

Research highlights▶ Some pre-service elementary teachers cannot place negative decimals on number lines. ▶ Two main misconceptions were identified, explaining a large percentage of errors. ▶ Some students use separate rays for positive and negative numbers, aligned by context. ▶ Some students make the negative number line by merging translated positive intervals. ▶ Location of negative fractions and decimals on number lines needs explicit teaching.