Strategies in Single-Digit Addition: Patterns and Perspectives

This dissertation addresses Danish students’ use and development of mental strategies in single-digit addition in the first years of school and relates it to teaching practices, later mathematical achievement and teachers’ perspectives on teaching and learning of number and arithmetic.

The work builds on data from a study of 147 students’ development of strategy use from year one to four, and a study of six year one classes (83 students, six teachers) assessed twice (October/November, April/May) in year one. The latter study also included data from teacher interviews, classroom observations, and students’ achievement in arithmetic, fraction knowledge and word problem solving in year four.

From year one to year four, students’ use of counting strategies decreased, and their use of fact-based strategies increased, but with substantial individual variation. On average boys, were two years ahead of girls in strategy use development. Strategy use patterns varied little between classes and did not develop differently across classes in year one. It follows that differences in teaching practice did not result in any traceable differences in the pace of development of strategy use during year one. Measures of strategy use in year one explained variation in mathematical achievement in year four that could not be explained by other year-one variables, achievement test measures included.

The results indicate that habits of strategy use are deeply rooted within the individual child and seem to establish either before or at the outset of formal schooling, after which it develops slowly over time. The results highlight the relevance of students’ early understanding of number and arithmetic (i.e. strategy use) both as indicators of later achievement and as a focus for intervention and targeted teaching to support student development in all cases.