The Acquisition of Addition and Subtraction Concepts in Grades One through Three

TLDR

A 3‑year longitudinal study followed 88 children from Grades 1–3 to examine their solutions to simple addition and subtraction word problems. Before formal instruction, children used modeling and counting strategies that persisted over years, progressing through four levels—from object modeling to sophisticated counting—challenging existing models of arithmetic development.

Abstract

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problem-solving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.