Rethinking the role of counting in mathematics learning

Abstract

This paper challenges the emphasis on counting in New Zealand’s Numeracy Development Project (NDP), arguing that subitizing provides an alternative pathway to quantification. Longitudinal data is presented showing that children’s subitizing skills at the age of five years were a strong predictor of their later success in mathematics at the age of nine years. Sophian’s work of comparison of continuous quantities is explored. Data from students whose teachers participated in NDP professional development programmes are compared with the expectations documented in the Mathematics Standards. The analysis shows that the percentages of students who reach the expected level for their year group is well short of the Standards. It is
suggested that the large number of micro-stages at the lower end of the Number Framework together with the positioning of part-whole strategies as the fifth stage on the framework may give the impression that teachers should not focus on the relationship between a whole and its parts until students are able to count on (stage 4). The paper concludes by suggesting that a dual focus on subitizing and counting right from the beginning might help students to develop a deeper understanding
of cardinality and of the relationship between a whole and its parts, resulting in them reaching expected levels earlier.